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| 134 116 | White money game Blue |
Chuck Bower: 21/16.
Before rolling, Blue was thinking "I have a nice 5-prime and the race lead. I sure hope I can keep both assets." 3-2 was a decent roll, and allows Blue to follow through with the game plan.
Steve Clark: 8/5, 8/6.
21/16 looks pretty straight forward. It does seem like it should bedeparture time. But the opponent would have lots of good rolls to hitwith while she is trying to escape. It is worth noticing that she is theone with the stronger board. I have tried to escape lots of times in thistype of situation only to find myself on the bar and my opponent escapedwith one or two men. Maybe we should try to find something better.
8/5, 8/6 represents a type of play that often comes out best in therollouts, but I have never been quite sure why. Who wants a 4 point primewhen they could have a 5 pointer? Both of the hitting plays suffer fromthe lack of flexibility on the next roll. Sure White might destroy hisboard, but he has lots of rolls that keep everything together. Bycomparison 8/5, 8/6 keeps everything rather well placed for the next fewrolls. This concentration of extra checkers close together is a verydesirable formation. It is true that 6's and 1's might play badly nextroll but I seem to roll fewer of them than most people. I'm still notsure why but maybe I will take a chance on 8/5, 8/6.
Malcolm Davis: 21/16.
Well ahead in the race - might as well run - the 6's are duplicated.
Hal Heinrich: 8/5, 8/6.
Truly a difficult problem -- all four candidates are reasonable, and thebest play is probably significantly better than any alternative. 21/16 isthe thematic play -- escape your opponents prime before your opponent escapes yours. However this play fails tactically -- you expose yourself toan attack at the precise moment your opponent is stretched to the breakingpoint! After this play, your best chance of winning comes from hitting youropponent back. This is especially troublesome with White owning the cube --there'll be a lot of tough cubes coming at Blue after this play. What aboutmaintaining the prime and the anchor? This gives White a lot of bad enteringrolls -- in particular 6/1* sets up 5-3, 5-2, 4-3, 4-2, and 3-2 as rootnumbers. On the downside, Blue exposes blots to White's stronger board andstrips his prime of spares. Note that it's harder to exploit White's blotsin the outfield from the roof! Still, I believe that 4/1*, 4/2 or 6/1* mightbe the right approach. 8/5, 8/6 says, in effect, "Listen, you go first.". Itgives up an enormous asset, the fifth point of prime, to avoid the pitfallsof the other plays. White has seven points and very little flexibility -- soBlue exposes nothing and prepares for next time.
Ron Karr: 21/16.
My strength is my 5-prime, which serves to restrain White's back checkers.The prime is at its best, but could potentially break, and I have anumber that allows me to run, so I'm running. The chances of gettinghit, failing to hit back, getting closed out & White's escaping enoughcheckers to win seems fairly small. It seems more likely that I couldget in trouble by staying on the anchor. I can't see voluntarilybreaking the prime. And I don't see what I gain by hitting in myboard. If White fans, he maintains his position, which makes it harderfor me to escape, and then I have a blot or two to worry about.
George Klitsas: 4/1*, 4/2.
Play a (21/16) Blue keeps his front position intact, but cedes the initiative at a moment when his opponent has the stronger board. Playing the position out, I was surprised by the great number of games in which White was able to win by going forwards - most games of this kind actually play themselves granted that White plays boldly his initial roll - at least!- (as an example, I believe that if he rolls a 4-3, he should play 8/4* 10/7, leaving everything open, risking a catastrophe if Blue hits from the bar and White is unable to hit him back, but having much the better of it otherwise). White does not need to reach a closeout in that case. It's enough for him to escape with one or two checkers from Blue's board and redouble. These redoubles tend to be optimal for White (on the verge of take/pass) which is a liability of play a. In 72 games, Blue won 32 plain games and 11 gammons, White 28 plain games and one gammon, for a net equity of +0.67 points per game for Blue on a two-cube.
Play b (8/5 8/6) Blue breaks his five-point prime but in return creates additional spares on his shrunk by now prime and - most important- keeps his anchor on White's four point. Now the main danger for Blue (and what actually usually happens after play b) is losing the control battle, namely �outfield control� and �timing�. If White steps into the outfield on his next roll (with 6-1 for example) he is a huge favorite to win that battle and the game. Strangely enough, White has optimal doubles after play b, as well, although the relevant positions are quite different in nature compared to the ones in variation a. Here a typical redouble-pass or redouble-marginal take occurs in a position, where White is stuck on the four point and White has complete control of the outfield. White could also simply win the race, since he is not far behind in that area. In 72 games, Blue won 22 plain games, 14 gammons and 2 backgammons, White 33 plain games and one gammon for an equity of +0.58 points per game for Blue on a two-cube.
Play c (4/1* 4/2) A play which is based on seeing clearly the big picture, admittedly difficult to find at the table. Blue's two blots are but meaningless trees. The main body of the forest is Blue's five-point prime, which is not likely to shrink after play c. The trees might be rooted out (hit) by White, but they should have no difficulty re-entering (re-plant) and march towards the main body of the forest. This recirculation, which helps also Blue's timing in the sense that he won't be obliged to break his anchor on White's four point, might actually end up in Blue forming eventually a six-point prime in front of White's anchor. In all variations, White is hard-pressed to roll lots of sixes to win. In the meantime, he must be lucky not to bust his inner board. Even if White flunks, sixes and fours (which are blocked by White's points in the outfield) play well for Blue in the front battlefield, covering his blots and forming a strong inner board, which results in a number of gammons for Blue. Green[forest] (I mean Blue, but the two colors are close, ancient Greeks had but one word for both of them), in a sample of 72 games won 27 plain games, 16 gammons and 2 backgammons, White only 27 plain games. Net equity +1.06 points per game for Green on a two-cube.
Play d (6/1*) Inflexible. Just imagine that Blue is hit and reenters with a roll like 4-1, 2-1, 4-4 etc. This is a big liability of play d and not limited to this first exchange of rolls. I believe that after play d, Blue is only a slight favorite and variation d is by far the worst of the four candidates.
My vote is for play c (4/1* 4/2). A wonderful problem.
Rob Maier: 21/16.
I think I've seen this problem before, but I don't remember the answer:). This seems like a time to let White play, but I'm not breaking theprime with 8/5, 8/6. That fifth point is worth too much. In fact, Ithink it so valuable that I'm going to trust it to keep me in the gameeven if I roll badly from the roof. Making one of the inside hittingplays could easily back fire, especially if I get stuck next roll and haveto break the prime.
Dave Montgomery: 21/16.
Something has to give. 6/1* leaves Blue with no good spares, and if hitBlue could enter awkwardly. 4/1* 4/2 looks ineffective. Blue doesn't wantto get hit. Better to just let White play, breaking some point.
Blue is ahead in the race, and his offense is at maximum strength, sorunning is thematic. If Blue had a number that ran past White's 10-point,I'd be certain Blue should run. Here White will have more shots and goodchances to pick up both of Blue's stragglers.
8/5 8/6 gives up the five prime, but is safe and gives Blue useful spares.White will have to play, and she has several awkward numbers including someblotters. Still, White can handle most rolls and her position only rarelyfalls apart next turn. With 8/5 8/6, Blue will probably be faced with asimilar decision next turn. Thus Blue should probably just run now while hestill has a five prime.
Snowie: 4/1*, 4/2*.
A touch of high life. Breaking my five-prime is unthinkable, and leavingthe anchor gives White attacking chances. If White enters and hits, itmight be better for me to have recirculated the hit checker.
Kit Woolsey: 21/16.
I'm not going to break my beautiful five-prime, since that is my biggestasset. The loose-hitting plays behind White's anchor only ask for trouble,as well as only prolonging the inevitable. By running now I force Whiteto prove himself before he is ready. He will have a lot of work to do.
Chris Yep: 21/16.
8/5 8/6 keeps the anchor, but gives up the 5-prime. With 3 men trapped behind Blue's prime, the difference between a 5-prime and a 4-prime is huge. The hitting plays keep the anchor and the 5-prime, but at great cost. 6/1* removes the useful spare on the 6 point and leaves an awkward position -- Blue's position will be stripped except for two spares on the 4 point, which can't go anywhere except behind White's anchor. 4/1* 4/2 keeps the spare on the 6 point, but dumps two blots behind White's anchor. If White can pick up one or both blots and roll a few 6s he even has gammon chances with a strong board already built. The advantage of the hitting plays is Blue keeps his anchor and White often has to bust up his blocking structure upon entering. On the other hand, if White flunks, Blue needs to roll a 3 or 5 quickly in order to avoid having to break up his prime.
21/16, while not fully escaping either back checker, attempts to make a run for it now. White will usually be forced to attack. Blue has several things going for him. White's 6s are duplicated; while White will attack with any 6 except 6-2 (with 6-1 I think he should hit twice, but 22/16 10/9* might be right), he also desperately needs 6s on the other side of the board. Second, with the ace point already made, any attack will leave White with a strong board, but (usually) not a strong prime. If Blue can survive the attack by anchoring anywhere (or by escaping both checkers), he will usually be in command of the game. With only 12 men up front, 3 men trapped behind a 5-prime, and White not even being able to use most 6s to escape on the first roll, White will have a difficult time closing Blue out.
Summary.The popular choice was to run and force White to roll well.However, Snowie's interesting choice (not what you would expect from a bot)is certainly worthy of consideration.
Play Votes Score21/16 7 1004/1*, 4/2 2 708/5, 8/6 2 706/1* 0 40
Problem 2
| 172 157 | White money game Blue |
Chuck Bower: 14/10, 7/5*.
Not much else. Blue's 5-point is the trophy both sides are lusting after.7/5* zeroes in on the big prize and 14/10 brings a builder (or shooter) into position. White may never be this vulnerable again, and if Blue playspassively, a 3 by White almost evens the game. Note that every play leavesdirect shots, so why get some gain out of your (forced) risk. You may only get to the Olympics one time, so GO FOR THE GOLD!
Steve Clark: 20/14
We have the stronger board so hitting an advanced checker seems quitedesirable. Unfortunately we have to give up the 7 point to do it, andthat does not seem very appealing. If we had the cube available whenWhite flunks, I might be more interested. In this situation, I hate toleave all the blots. I think I will look for something more conservative.
There are lots of play available but nothing really seems to appeal. Forinstance 24/18 gives White lots of good numbers like 1's, 2's, 3's and6's. 14/8 looks a little better. It only gives him 3's and 6's. Also ifhe misses, I am well placed to do him damage. Well this play is startingto look a little more attractive. Also it only leaves one blot around(Blots on the 24 point don't count until the opponent has something of aboard.) . Another rather unusual play has some appeal. I am referring to20/14. We give the opponent's 5 point which is a major sacrifice but weare well ahead in the race and have to go sometime soon. It should bebetter to leave before our vicious opponent has a board. Also with thisplay we have created a major duplication of 3's. I am not big onduplication in most positions but it is nice to have it in a move that hasother attractions. I take a stab at 20/14.
Malcolm Davis: 24/18.
Somehow or other, this seems like the natural play. Might as well invite a blot hitting contest with a superior board. Don't want opponent to start escaping by hitting my blots, and don't want to break my prime by hitting with so many return shots.
Hal Heinrich: 13/7.
Blue has achieved a solid edge and spun the cube. Blue's home board isstrong, but difficult to improve without bringing builders into range. IfWhite can make the twenty point, Blue's advantages will be balanced by White's cube ownership making the position roughly even. 14/10, 7/5* is abrute force approach to denying White the twenty point. Even though five'sare duplicated, White has seventeen return hits which hurt Blue's plan. 14/8is another duplication play -- this time three's which White needs to make the twenty point. Still, plays which allow White's back men to advance whilehitting are thematically wrong. 20/14 is an easily overlooked play with somenice features -- it safeties the blot on the fourteen point while developingBlue's position. White's position is undeveloped, so abandoning the twentypoint is not unreasonable -- note the three duplication at work. But thetwenty point is important and giving it up here is a little too risky. Whichbrings us to 13/7 -- not much of a play, but it avoids several risks and aims at going after White next time.
Ron Karr: 20/14.
An odd-seeming play, breaking the anchor, but it feelsright. With the better board I'd like to attack, but can't withoutmessing things up too much. A play like 14/8 just asks to lose racingequity, while not improving the offense significantly. 20/14 exertsmaximum control over the entire board, and I'll be able to playflexibly whether White makes my 5 point or not. White has to be verywary of leaving shots. Only the 5 numbers that make the 20 pointreally hurt, and they're far from decisive.
George Klitsas: 14/10, 7/5*.
Actually the various plays here fall into two sets, one with seven elements (the non-hitting plays) and one with a single element (14/10 7/5*). From the first set, I picked up play b (24/22 14/10) in the first place because it's the first serious play on the list (play a [24/18]) is stupid) and in the second place because the first part of the play (14/10) is common with the hitting play, but play e (14/8) or play f (14/10 13/11) could be slightly (if at all) better than play b. Fortunately, the question is only to pick up the best play here and not to rank all plays. So, if the hitting play is going to be found clearly superior to play b, then play b practically is as good as anything. Let's see.
Play b (24/22 14/10) The main danger for Blue is not that he might be hit, but that White might anchor on Blue's five point.Then it will be anybody's game (Blue will have the better of it in the race and, consequently, White will have the better timing). So, Blue's blot is practically immune to rolls like 5-3 or 3-2. Of course, White can (and is well advised to) hit with the remaining five's and with 6-2, losing his anchor on the two point or the base for an anchor on the five point, but gaining race pips in return. One should make the remark that, because of his undeveloped position, White will have to leave blots in the outfield in the process, some of them or in a fraction of the time will be sent back - still- all in all, it's a quiet variation. White will probably anchor again and start over. Blue and White, surprisingly enough, win about the same number of games, a small sub-set of which are gammons for Blue. I played 36 games and the result was +0.28 points per game for Blue on a two-cube.
Play g (14/10 7/5*) A totally different approach. Blue realizes that with a little luck he can restrain White to a two-point game with suspect timing in some cases and goes for it. Blue has everything to gain by going for the throat and little to lose. Even if he completely fails and White enters always from the bar with the best of rolls, White can't take from him his strong inner board, which, sooner or later, will play again a role in the game. We must not forget that in a quarter of the time White will flunk and then Blue is a favorite to make his five point and has also an excellent chance to make a five-point prime (at least!). After that, White, if he enters inconveniently from the bar at any time, will be obliged to leave an additional blot - and more gammon chances for Blue. A set of 36 games was sufficient to make up my mind. Hitting was huge, resulting in 15 plain games, 7 gammons and 1 backgammon for Blue, only 13 plain games for White, for an overall equity of +1.06 points per game on a two-cube for Blue. Last but not least, one should mention the (overkill, actually) argument in favor of the hitting play, that it restricts also White's potential re-cubes, which are numerous after play b.
Rob Maier: 14/10, 7/5*.
How much is it worth to keep White from anchoring on our five point? I'mnot sure, but I know that our gammon rate will fall a great deal if Whitemakes it. What's more, there is no quiet play that seems palatable. Timeto make use of our board. Even if we are hit on the five point, we havean excellent chance of recovering the bar point on the next roll.
Dave Montgomery: 14/10, 7/5*.
Blue can't play safe. Blue wants the five point. Blue has a far biggerboard and an advanced anchor. Blue should try to take what he wants. 14/107/5*.
Snowie: 14/10, 7/5*.
I have the bigger board and the advanced anchor, so what can go wrong?No way I'll give White a chance to get back into the game by making myfive point. Big gains if I win the battle, and no disaster if I am hit back.
Kit Woolsey: 24/22, 14/10.
Much as I would like to fight for the five point, I don't think I can affordto risk losing my bar point if White hits back. My play builds up thepressure and forces White to give up his chance to make the anchor on myfive point if he hits, as well as duplicating his fives and threes aroundthe board.
Chris Yep: 14/10, 7/5*.
Blue has a decent lead in the race, but both sides have three men back. Blue has an advanced anchor and enjoys a 3 to 1 advantage in board strength. This argues for a bold play. Usually breaking the bar point to hit loose on the 5 point is wrong, but here I believe it is the correct play. Blue should take advantage of his stronger board and the security of sitting on an advanced anchor by attacking. Making the 5 point would be huge -- Blue would then have the 4 best inner board points; White would likely be forced to play passively for a long time. In addition, making the 5 point will give full value to the already made 3 and 4 points. White's best chance is to make the 20 point anchor and hold on for dear life. 14/10 7/5* hits White off this point and gives Blue firepower to either cover (with 2s, 5s, and 8s) next turn if not hit or to keep attacking if White hits back next turn. With Blue's 3 to 1 advantage in board strength, he is a solid favorite to win any hitting contest.
Summary: Our bloodthirsty felt that two birds in the bush were better than one inthe hand. I can understand since Blue has the stronger board, but whereare the builders?
Play Votes Score14/10, 7/5* 6 10020/14 2 7024/22, 14/10 1 6024/18 1 6013/7 1 6024/20, 13/11 0 4014/8 0 4014/10, 13/11 0 40
Problem 3
| 82 126 | White money game Blue |
Chuck Bower: 18/12.
White's strong board and fragile timing argue against hitting loose here.White is hoping for a 5, and 18/12 leaves fewer good 5x combinations.
Steve Clark: 18/12.
There is no doubt that I would play 18/12 at the table. The othercandidates have certain disaster rolls lurking too near the board to bevery appealing. If White doesn't roll a 5, he will have to wreck hisposition. If he does roll the 5, we are likely to have substantialopportunities to hit him. Actually I don't see the merit to 18/14,12/10. This is intended to be flexible but it wont' be very flexible whenour opponent rolls a 5-3 or a 5-5.
18/14, 4/2* is an attempt to take advantage of the fact that White thenwill have to roll 2 number to escape rather than just a 5. Here I thinkthe idea is misplaced. For us to be hit would be a disaster. And evenif White flunks, we are only a slight favorite to cover. If hit by us andflunk by him would nearly end the game, it might be right. Here the mostlikely quick end would be hit by him and flunk buy us. This could be theright move to make but not by me.
Malcolm Davis: 18/12.
Make 12 point, and let opponent roll. with no five, he has to break something. I hate to attack with an inferior board and a lack of ammunition with which to follow through. Only 8 fives are good, and they are not devastating.
Hal Heinrich: 18/12.
White has a five-point board -- so some caution is in order. 18/12 leaves noshots, restrains White's back man, and gives White some bad rolls. Case closed!
Ron Karr: 18/12.
Though I want to prevent White from escaping, it doesn'tseem right to hit loose and leave 3 blots against a 5-point board. Ifhe escapes with a 5, I'll have some return shots, and if I don't hitI'll just have to live with that. If he doesn't escape then somethinghas to give, so he may have to leave a shot or weaken his board; so itmay be safer for me to attack later if I can hold out for a roll ortwo.
George Klitsas: 18/12.
Play a (18/12) The quiet approach. If White escapes with a five in the outfield, Blue should have a decent chance to bring him back, slotting his bar point in the process for a relatively easy closeout. If, instead, White does not roll an escaping five, he might leave a blot on his ten point (with most sixes) or worsen his inner board (I think that in general White should prefer to retain his strong board than avoid leaving a blot on his ten point, for example with a roll of 4-2 my feeling is that White should play 10/6 10/8). In 36 games the result was +0.78 points per game for Blue on a two-cube.
Play b (18/14 12/10) Looks to me inferior to play a, for I don't see enough compensation for giving White three potentially game-winning rolls (5-5 and 5-3).
Play c (18/14 4/2*) If White hits and Blue flunks, White has an efficient redouble (actually, I think it's a pass). If White enters on the ace point, Blue has to cover the blot on his two point, and, even if he succeeds in that, he must live for a while with the danger of an indirect shot from White's rear checker. If White flunks, Blue has to cover the two point again. In 36 games Blue won only 0.12 points per game on a two-cube and I am pretty confident that play c is not even close to play a, which is the winner here.
Rob Maier: 18/12.
White is on the verge of having to either expose another blot or break hisboard, the worst time to put him on the roof. Even if he does roll a 5and not get hit, he still will have to run that checker home and clear theten point. All of this points to not hitting this turn. If White doesn'troll a 5, there is not much difference between the non-hitting plays.When he does, 18/12 actually provides more shots on average than doeskeeping the checkers split. The swings on 5-3 and 5-5 are the difference.
Dave Montgomery: 18/14, 4/2*.
If Blue leaves White alone, he may get a chance to capture a second checker.On the other hand, if White rolls a 5, Blue will be under pressure torecapture the first checker. Letting the first checker get away hurts morethan capturing the second checker helps. I would hit so that White has toenter and roll a 5 to escape.
Snowie: 18/12.
This is not the time to have an accident. Let's see White finda play if he doesn't roll a five.
Kit Woolsey: 18/12.
Normally it would be right to hit loose with the two, sinceI don't want to give White a chance to escape in one roll. Here, however,White is at the end of his rope, and if I sit tight and he doesn't rolla five something will probably have to give. My play leaves nothing, andas a bonus blocks double-fives.
Chris Yep: 18/12.
First consider the hitting play 18/14 4/2*. Attacking with a 4 point board versus a 5 point board is usually wrong. In this case, Blue backs up his 4 point board with a 5-prime; however, it is a broken 5-prime. If White can enter on either the ace or deuce point, he still will only need one specific number (most 6s or most 5s respectively) to escape. In addition, if White comes in with a 2, Blue will be on the bar facing a 5 point board with 2 more vulnerable blots. Blue could end up with as many as 5 men back! Attacking feels wrong to me.
18/12 and 18/14 12/10 play for outfield coverage. When trying to cover the outfield, one usually tries to stay 10 to 13 pips away. 8 away is generally too close. Since the checker 8 away only adds a small amount of additional outfield coverage, I'm inclined to go with 18/12 due to the huge swings on White's 5-3 and 5-5.
Let's try a more accurate analysis by looking at each of White's escaping numbers on the next roll. It should be close enough to just count the number of direct shots that Blue gets at White's fleeing blot. Note that White will run out with all 5s, including 5-1.
5-1: double shot after either play
5-2: single shot after 18/12; double shot after 18/14 12/10; advantage to 18/14 12/10
5-3: single shot after 18/12; no direct shots after 18/14 12/10 (only the 5-4 joker hits); in addition, Blue still has another vulnerable blot - it looks like White is close to even money to gammon Blue. If Blue stays on the bar for awhile, White can bring his straggler home as well as clear the 10 point without ever giving up a direct shot. Blue may only get a few more indirect shots at White as White tries to get home safely. Huge advantage to 18/12.
5-4: single shot after either play
5-5: double shot plus White is forced to break down to a 4 point board after 18/12; zero shots and no future shots at White's straggler after 18/14 12/10; moderately large advantage to 18/12
5-6: 6 shots (any 7) after 18/12; 15 shots (1s and 7s) after 18/14 12/10. Advantage to 18/14 12/10.
From this rough analysis, Blue is better off having played 18/12 if White rolls 5-3 or 5-5 (3 numbers) and 18/14 12/10 if White rolls 5-2 or 5-6 (4 numbers). However, since the swings on 5-3 and 5-5 are much larger than those on 5-2 and 5-6, my choice is 18/12.
Summary: Our astute panel recognized the value of playing the waiting game. I am quiteconvinced this is correct. A tricky problem, as the loose hit is very tempting.
Play Votes Score18/12 10 10018/14, 4/2* 1 5018/14, 12/10 0 40
Problem 4
| 149 150 | White money game Blue |
Chuck Bower: 24/22, 13/8.
13/8 is the easy part. Blue wants to build either the barpoint or the3-point so bring down the builder. 11/9 brings a second builder intoplace, but Blue's position would then be rather cramped. White hasquite a few combinations which make either his 5-point or 7-point, andthen Blue will desperately want to disconnect the deep point. The 2 this turn allows for a "pre-emptive" split. The dice may not be so generous next roll.
Steve Clark: 13/8, 11/9.
What about 8/1*? we have the stronger board so hitting becomes appealing.Other hits don't have a cover in range. Could this be right even thoughit is not listed as a candidate? Last month the best move for one of theproblems was not listed, nor was it mentioned by anyone else.. Couldlightning strike again? Well actually not; we really don't want to giveup the 8 point for some stupid hit on the ace. The other hits also loseattraction because no covering checker is close.
I don't want to split up to the 22 point. Now that White has put a spareon the 21 point, he will be more inclined, and more able, to make the 22point on my head. So we are left with various plays which bring buildersdown. 13/8, 13/11 can't be right. It would be crazy to leave a directshot. So we are left with 2 candidates.
I always used to play 11/4, no blots, lots of builders. In my newfoundwisdom, however, I am more attracted to 13/8, 11/9. At first I was notsure why I would want to leave some jokers. But now I see that this isconsiderably more flexible, threatening to make the 2 or 3 or 7 or 9points, all of which are important. Maybe my new wisdom is a chimera butI will play 13/8, 11/9.
Malcolm Davis: 24/22, 11/6.
Tough play. I believe I would play 24/22 and 11/6. The split seems essential, and stripping the 13 point looks wrong. Maybe safeing-up the blot on the 11 point is not all that bad either. I would hate to get hit with 6-4 or 5-4.
Hal Heinrich: 24/22, 11/6.
Blue is slightly ahead in the race which means that, all things being equal,splitting the back men is a good thing. Attracting White's builders lookslike a necessary evil here. Hitting on the ace risks too much for the gain.Building plays involving the outfield suffer from the defect that Blue is upin the race and White is already split -- both factors are a disadvantage inprime vs. prime contests. So now that we've split with 24/22, 11/6 looksright. It removes a blot as a target at a time when it's unlikely to beused as a builder. At the same time, it brings in extra wood for attackingWhite's back men.
Ron Karr: 13/8, 13/11.
My first thought is to split the back checkers, sincethere are no clear offensive plays, and I'd like to try to escapeWhite's potential prime. But there are some problems with splitting. It's usually right to split when the opponent hasn't yet brought downcheckers from the midpoint, but in this case White already has hisbuilders in place, and by splitting I do little but give him additionalattacking possibilities (5-5, 5-3, etc.). In addition, after 24/22 I'dhave to either leave the blot on 11, giving White 6-4 and 5-4 to hit,or clear it, reducing my offensive potential.
Strangely enough, keeping the anchor and focusing on offense seemsbetter, even though I have to break the midpoint. The 11 point is sortof a new midpoint, and I get maximum coverage for my bar point, whichI'm dying to make. Most of White's 1s make a good offensive point, sohe'll have to give up the point if he hits; and the 66 and 65 which hitare already excellent numbers for White. If I get hit, I shouldn't havemuch trouble recirculating. If I make the 5-prime I'll be in greatshape, and if I don't I should be able to play flexibly.
I don't like any of the 6/1* plays because I don't think I have enoughammo to blitz. But after my play, I'll have more checkers in place, sothere may be blitz options next time.
George Klitsas: 13/8, 11/9.
Play a (24/22 13/8) Blue reinforces the eight point which is always a good idea, but with the other half of his move exposes himself to an attack by White, giving him the chance to get rid even of his buried checker on the four point (which presumably got there by an ugly four earlier) . There is some duplication on White's good rolls, but this partial duplication is not sufficient to turn an anti-thematic play into a plausible consideration. Blue should build on his strength, which is his priming potential and (try to) lead the game in a priming battle rather than a blot-hitting contest. In 72 games that I played, Blue won 0.19 points per game.
Play b (24/22 11/6) Looks to me slightly inferior to play a. The checker on the eleven point could handle some awkward sixes.
Play c (24/22 6/1*) It's seldom correct to hit on the guff when the closest cover is an indirect seven that, in this case, strips the eight point as well. I believe that White's immediate threats are not so dangerous to justify such desperate measures on Blue's part.
Play d (13/8 13/11) An interesting idea. Blue notices that rolls that contain aces (with the exception of 5-1) are already between the best rolls for White (duplication). Still, the loss of the midpoint will be a serious liability in Blues position for the rest of the game whether White rolls an ace or not.
Play e (13/8 11/9) That's the thematic play. Blue keeps his anchor on the twenty-four point in order not to be disturbed by White hits there and tries to make his bar point completing a strong five-point prime. If he succeeds in that, he will usually have the much better position (notice that at the moment none of White's back checkers is on the edge of this imaginary prime - so they will have first to go there in order to escape), for it's not that easy for White to do the same - his front position is not compact and his buried checker on his four point is an additional liability especially in a priming battle. In 72 games Blue won 0.29 points per game .
Play f (13/11 6/1*) Colorless and weak.
Play g (11/4) More of a liability than an asset. Wrong game plan, semi-burying a man at the same time. Such a play is always a sure sign of the inexperienced player. A novice or a beginner naturally tries various plays. After months or years (depending on the frequency of playing and, naturally, on his talent) one notices that plays that put a spare on the four or three point, tend to create difficulties later. Although at the moment there seems to be no problem, a subsequent awkward roll (which, before realizing the concept, looks like �unlucky� or �anti-joker�) forces us to bury another checker, or the same checker deeper - suddenly the position is ruined out of the Blue (!). So, the player, as he gets more and more experience, abandons a blitz-oriented style adopting instead a prime-oriented style. Here, as told earlier, Blue should try to make a prime rather than attack. Of course, play g like any play, could succeed sometimes. But what will usually happen is that Blue will have difficulty playing his numbers (especially sixes), and he will not be able to make a prime (barring a series of jokers). Especially, if White anchors on the twenty-three or the twenty-two point, Blue will often lose without realizing why.
My vote is for play e.
Rob Maier: 13/8, 11/9.
The 5 is easy. The spare on the eight point can be used to build anyof three useful points. As for the 2, we aren't going to leave a blot onthe midpoint, or split our back checkers, close our eyes, and hope. Thisleaves us with either 6/4 or 11/9 for the deuce. While 6/4 leaves twofewer shots and gives us better coverage of our outfield, it gives usfewer opportunities to make another point on our side next roll, and isalso quite distastefull from an asthetic view point. Beauty may not bethe goal in backgammon, but the pretty plays are quite often the correctplays.
Dave Montgomery: 11/4.
Should Blue hit? No. Blue is poorly placed to attack deep, and althoughWhite has many productive rolls, depriving White of half a roll is not ahigh priority.
Should Blue split? Unclear. Blue would love to make an advanced anchor, butsplitting does allow White to attack, and to put the dilly builder on the 4point to good use. I don't feel strongly about it, but I would not split.
13/8 11/9 looks like a natural play, leaving three builders for the 7 and 3points. However, it does leave six costly shots. 11/4 moves a tad deep,but this isn't so bad since Blue will be happy to make the 1 or 2 points onWhite's head. Probably several of the candidates here are close. I'll votefor 11/4.
Snowie: 24/22, 6/1*.
Standard hit and split play, with my stronger board to back me up. I wouldlike to get an advanced anchor out of this. White has too many goodnumbers for me to let him play his whole roll.
Kit Woolsey: 11/9, 6/1*.
I have the bigger board and he has all the threats, so it looks right tohit loose on the ace point and try to gain some time. Splitting the backcheckers doesn't appear productive and the 11 point isn't particularlyvaluable, so I'll try bringing in a builder where it might be productive.
Chris Yep: 11/4
Of the plays which try for the 22 point anchor, I prefer 24/22 6/1*. With 3 builders bearing on this point, I think Blue needs the tempo gain from a hit to protect the 22 point blot. 24/22 6/1* is a very serious contender. However I think dumping Blue's only inner board spare from the 6 point to the ace point compromises Blue's position a little too much. If Blue had more attack material in range, he would have the option to attack in the next few rolls if the dice favored him, but in the actual position he has no direct covers for the ace point and his attack material is far away. In addition, while the 22 point is a semi-advanced anchor, it's only a moderately good anchor - Blue would much rather own the 20 or 18 point anchor. Of the plays which hit loose on the ace point, I again prefer 24/22 6/1*. Blue's attack forces are far away, so attacking is not yet a serious option. If Blue hits loose with 6/1*, I think he needs to do it in conjunction with trying for a better anchor. Of the remaining plays, 13/8 13/11 breaks the midpoint (leaving a direct shot) in order to make the 11 point and add a spare to the 8 point. Otherwise it doesn't do much for the position. 13/8 11/9 brings maximum builders to bear on the 3 point. On the other hand, it decreases outfield coverage and strips the midpoint, which could be costly. What about 11/4? 11/4 decreases outfield coverage, but has several advantages. First, it reduces White's shots from 4 to 0. Second, it keeps the spare on the midpoint. Third, it brings more attack material in place. Since White's back men are split, he may be vulnerable to an attack once Blue gets his attack forces in place. With Blue having the 3 best inner board points and a better board than White, he will have both priming and attacking options over the next few rolls. White can either make new points on his side of the board or protect his blots, but he usually can't do both. Blue will often be able to make an advanced anchor later. If White chooses to concentrate on offense next roll, it may get too dangerous for Blue to try to split to an advanced anchor. However, as compensation, he may be able to successfully attack White's split men.
Summary: What a variety of choices! The concensus was clearly in favor of quietlybuilding. I wonder. Should White really be permitted to have his wholeroll here?
Play Votes Score13/8, 11/9 3 10011/4 2 9024/22, 11/6 2 9024/22, 13/8 1 8013/8, 13/11 1 8024/22, 6/1* 1 7011/9, 6/1* 1 7013/11, 6/1* 0 60
Problem 5
| 149 176 | White money game Blue |
Chuck Bower: B/24, 23/18.
White would much prefer making his 5-point over his barpoint, whileBlue would be tickled to get either one. This argues for B/24, 23/18.And if White succeeds in landing a punch, the anchor on the 24-pointmay keep Blue off the canvas. It's tempting to duke it out for White's5-point, but I'll opt for a long bout where I can wear White down rather than open myself up for the quick knockout.
Steve Clark: B/20, 23/22.
This is the editor's favorite problem. Not this problem exactly butproblems like this; 19 reasonable moves and we are expected to find a gemamong the dross. At the table I would be very inclined to play B/20,23/22. I believe moving up to the 20 point is quite important in thistype of position. I won't like if he points on me at his 5 point, butotherwise I will be glad to be there. If he fails to make a point, oftenhe will have to hit loose; for instance with a roll of 5,1. Hitting onthe 5 point is his best play, but it is not very strong for him and Iwill be happy to see it happen.
What about the alternatives? B/20, 24/23 makes the wrong point. If hehad more ammo in range, our safety would be a more pressing issue. Inthis position. B/20, 6/5 is not as good because the 22 point is a secondchance to make an advanced anchor. I much prefer coming up to the 22.If you make the banzai charge of B/20, 8/7 you are likely to have yourhead handed to you.
All of the plays which start with B/24 are too passive. We are not yet inbad enough shape to hit on the ace. B/24, 23/18 tries for an advancedpoint but puts the blot at a point where White will be much happier to hitit.
We are behind in the race and badly need an advanced point. White willnot be able to put his position together and point on us at the sametime. All these concepts point in the same direction. I believe myfirst reaction was correct. B/20, 23/22.
Malcolm Davis: B/24, 23/18.
Another tough play. B/24, 23/18 looks like the best alternative. Coming in on the 20 point seems a little risky, so if I am resigned to entering on the 24 point, playing 13/8 with the five looks too disjointed, and hitting on the 1 point does not accomplish enough.
Hal Heinrich: B/24, 23/18.
First, let's reject hitting on the ace point. While it's true that White hasbuilders poised to do something useful, the cost of taking away a half rollhere is too high. Stripping the six point and risking a fourth man back to oppose something that White will probably achieve anyway is wrong. Steppingout to the eighteen point distracts White from making inner board points --and if White ignores that blot, Blue has a great chance to establish adefensible position. The risk/reward ratio is strongly against slotting thetwenty point. The cost of losing the battle for the twenty point is muchhigher than that for the eighteen point -- while the gain from making eitherpoint is roughly equal. This play also leaves just one blot which is a plusconsidering White's initiative and cube access. My second choice is the quietB/24, 13/8 which hopes to win by out-devloping White from behind. Plausible,but a more active approach is needed here to avoid having three men hemmed in.
Ron Karr: B/24, 23/18.
A typical action play, challenging White, who's aheadin the race & is threatening to safety his blots. I'll probably gethit, but then he won't be making an inner point nor escaping his otherback checker, so I'll have some return shots and may be able to makethe bar or other advanced anchor. The question is: is it better toenter on the 20 point and try to make it? I'm not sure, but myinstinct says no: it's too dangerous to let White point on me, and notnecessary since I have this alternative.
George Klitsas: B/20, 23/22.
Play a (B/20 24/23) Anchoring on the twenty-three point could be the right idea if Blue owned already the cube, where the anchor would efficiently defend against the gammon danger. Here it seems a little overcautious, reducing Blue's options. It's actually kind of commitment, since Blue quite often will be obliged to resign a two-point game. Even if Blue anchors on the five point, which is against the odds, given that White plays aggressively as he should, White has some very strong doubles, if in the meanwhile, he manages to make his bar point and activate his runner. Almost all of White's rolls play well. In 72 games Blue lost 0.50 points per game.
Play b (B/20 23/22) White has many rolls that hit at least two checkers here, but Blue could hit back or anchor on the three or the five point after some other initial sequences. It looks that Blue's checker is better placed on the twenty two point rather than in the twenty three one, for, if Blue anchors, he will make the better and more advanced anchor and for the purpose of return-hits with a six on the White blot on the ten point. In general, Blue has more options (because of the diversification of his rear checkers) here in comparison with play a , which was reflected on a sample of 72 games that I played. Blue lost only 0.30 points per game, a great improvement over play a.
Play c (B/20 8/7) Another blot in such a vulnerable position does not look the right idea.
Play d (B/20 6/5) Worse than play b-see comment there.
Play e (B/24 23/18) Kind of �action� play. Semi-action, actually. In the typical action play, the opponent has the option of hitting on the bar point with a roll (say a 6-1) with which he could make alternatively an important inner point (the five point with 6-1). Here, this feature is absent and the play is far from a thematic action play. This fact alone should not make us preoccupied against it. Let's see, though. After playing a number of games, I came to the conclusion that if White plays calmly, not overdoing himself in hitting on the bar point while leaving blots strewn around, Blue is in a difficult situation. If he does not roll a linking six, to make his opponent bar point, he is well advised to move his blot preferably to the midpoint or, failing that, to the outfield. Then his rear checkers will have remained unsplit on the worst possible point on White's inner board. The main point for Blue to realize is that, even if he manages to make his opponents bar point, this is not a decisive improvement in this position, especially if White has been able in the meantime to activate his laggard, or (even worse) land it on his midpoint. Then White's racing advantage will take full credit in most cases. In 72 games, Blue lost 0.52 points per game and the play must be rejected.
Play f (B/24 13/8) Even more quiet a variation than e. Blue's game plan (one should have always one - number one consideration in choosing a move at any phase) is to try to contain White's runner, leaving his three back checkers out of harm's way (in order to concentrate in the front battlefield, where, admittedly, is only threatening to threaten ), alas out of progress's way at the same time (barring a 4-3 or a 6-5 if White has not made the relevant point himself earlier). In 72 games the result was -0.47 points per game for Blue.
Play g (B/24 6/1*) Unthinkable - I would be very surprised if such a play came up as a winner here and I would be not at all reluctant to defend my belief as a prop even against God (with fair dice, though!) .I did not waste any time to rollout the resulting position out. I just had the following passing thought, looking at the play - that as Blue I would pray for White to hit rather than miss my blot on the ace point. If the blot is missed, it will be a decisive liability in any kind of backgame that Blue might be lucky to find himself at, later.
All said, play b (B/20 23/22) emerges as the clear winner. An important lesson, also, emerges from problem 5 : that, when you have not the upper hand, when the natural course of things (after a series of small plays by both rivals) is going to lead usually to a marginally untakable or to a very strong (takable) double by the opponent, then one must react with a bold play before it's too late, and trade some games in which this bold play will be justified for him with some overkills (doubles by his opponent and clear passes). The net result will be favorable compared to any other plan that adopts a strategy based on small plays. In backgammon, in the war and in many other situations in real life as well.
Rob Maier: B/24, 23/18.
While coming in on the five point might be nice, we would like to havean anchor to protect us from misfortune, and 24/23 is just not worthcontemplating. Coming in on the ace point not only gives us some measureof safety, but it also allows us to come out and challenge White's blots.Another consideration is that if we are pointed on, it would be lessdamaging on the bar point than on the five point.
Dave Montgomery: B/20, 24/23.
White has a very flexible position. She will almost certainly accomplishsomething good next turn. Blue has to try to stop White from improving orgive himself chances to keep up.
The direct route to stopping White is to hit 6/1*. If Blue had fivecheckers on the 6 point, this would be the answer. But here, thecombination of a stripped 6 point, no direct covers, and no slotted advancedanchor make this play unpalatable.
With three back against one, Blue needs an advanced anchor. B/20 24/23 andB/24 23/18 go after this while holding a deeper anchor to prevent a completeblowout. Blue may get pointed on, but he can't worry about this. He has tochallenge White before she consolidates her position. I prefer B/20 24/23because the defensive 23 point is much better than the 24 point.
Snowie: B/20, 24/23.
I need a security base in White's home board in case something bad happens.With the anchor nailed down, I will be able to play more agressively onthe other side of the board.
Kit Woolsey: B/24, 23/18.
Coming in on the 20 point looks too dangerous. I wouldn't like beingpointed on there. I'll come out to the enemy bar point to challengeWhite and force him to use some of his good rolls to hit rather thanbuild a board.
Chris Yep: B/20, 24/23.
Black has 3 men back and will be down 21 pips after his move. White has only 1 man back and two checkers looking for safe places to go. At the moment, both players have roughly equal boards. This argues for a bold play. B/24 6/1* takes away half of White's roll. However it is very ugly and doesn't accomplish much on either side of the board. I believe that b/24 6/1* is the worst choice for all the reasons discussed in problem 4. It is very important for Blue to split to an advanced anchor. By splitting to the 20 or 18 point, Blue puts pressure on both of White's outfield blots, while at the same time fighting for an advanced anchor. If White hits loose, Blue may be able to hit back, equalizing the position. For this reason, I also reject b/24 13/8. Of the remaining plays, b/20 8/7 seems too loose. It strips the 8 point and gives White too many hitting numbers. It's usually not right to slot when your back men are split. Also, b/24 23/18 is inferior to b/20 23/22. Not only does b/20 23/22 slot the more valuable anchor, it also secures a more valuable anchor (the 23 point). That leaves three plays to consider: b/20 24/23, b/20 23/22, and b/20 6/5. All 3 are probably about equal.
B/20 23/22 is the most aggressive. It slots both the 22 and 20 points, and provokes a lot of contact. If White hits loose and Blue hits back, Blue will have an almost equal game. On the other hand, provoking contact is a mixed blessing. If White points on Blue's head and then Blue flunks, White may be able to carry out a strong attack.
B/20 6/5 keeps the back men spread out maximizing indirect shots at any blot White leaves in the outfield. If White hits loose on the 5 point, Blue will have 23 numbers (5s, 1-3, 2-4, 3-4, 2-2, and 3-3) to hit back. If White doesn't hit loose, Blue will have 29 numbers to make either the 20 or 18 point anchor (3-x, 4-x, 1-2, 2-2, 2-5, 2-6, and 5-6). On the other hand, it moves the spare on the 6 point to the 5 point (only a very minor consideration), and doesn't secure an anchor. If White points on Blue's head and Blue stays on the bar for 2 or more turns, or if Blue stays on the bar one turn and then enters without anchoring, White suddenly may be able to launch a successful attack.
B/20 24/23 at least gets everyone off the 24 point and secures the 23 point anchor. If White hits loose on the 5 point, Blue will still have 18 numbers to hit back (only 5 fewer numbers to hit back than after b/20 6/5 - all 5s, 1-3, and 3-3). If White doesn't hit loose, Blue will have 15 numbers (3-x, 1-2, and 2-5) to secure the 20 or 18 point anchor. It's a very difficult decision, but I value the security of the 23 point anchor. I slightly prefer b/20 24/23 to b/20 23/22 and b/20 6/5.
Summary: On a tough choice, the plurality chose to anchor and make a bid for theenemy bar point. Seems sensible, as entering on the 20 point is very dangerous.
Play Votes ScoreB/24, 23/18 6 100B/20, 24/23 3 80B/20, 23/22 2 70B/24, 13/8 0 60B/20, 6/5 0 50B/20, 8/7 0 40B/24, 6/1* 0 40
Problem 6
| 121 96 | White money game Blue |
Chuck Bower: 7/1*.
There's an old BG cliche' for this position: it's easier for Whiteto roll a single 1 than two of them. Go for the throat. A closeoutis worth a lot of gammons, and although White's acepoint game (if heanchors up) won't be so well timed, the 24-point outpost will still bea thorn in Blue's side. Blue should invest aggressively instead oftrying to sit on his modest profits.
Steve Clark: 7/1*.
Christmas is coming and I am without a clue. Maybe somebody will leave meone under the Christmas tree.
I would not play 13/7. That leave a rear man exposed and two checkersawkwardly placed on the 8 point. I don't particularly like leaving atrailer on the 20 point. Opponents have a bad habit of rolling double 1'swhenever I do that. I do, however want to get a hitter in range so 8/7,8/3 draws my attention. Overall all, however, the checkers seem badlyplaced so I would not make that play.
The real question is whether to play 7/1*. In general hitting is strongerthan making a prime because the opponent gains so much by making my acepoint. I seem to remember some rule about hitting so long as the opponenthas not made more than 4 points. But somehow that rule did not take intoaccount the alternative of making a prime. Nor did it mention the factthat I do not have any other blots nearby. That point about preventinghim from making my ace is pretty persuasive, even so. Even if he rolls anace, I will be relatively happy that I hit him, 7/1*.
Malcolm Davis: 7/1*.
I like hitting on the 1 point. This makes it more difficult for your opponent to make his 24 point, and you do have 9 covers, in spite of having no direct covering numbers.
Hal Heinrich: 20/15, 8/7.
The choice looks close between 20/15, 8/7 and 6/1*. White's 1-1 roll is a huge swing, and Blue doesn't have any direct covers to complete the closeout.If Blue doesn't attack and White comes in right away, White's timing for anace point game is poor. And if White dances, Blue can then play for a closeout. Considering all this, it doesn't seem that Blue gets two extra gammon for each additional loss.
Ron Karr: 8/3, 8/7.
First question: to forgo the prime and play 7/1* inquest of a closeout? Sometimes it's right, but in this case theproblem is that there are no direct covers for the ace point, whichallows White at least a couple of chances to hit back. The nice thingabout making the prime is: if White enters immediately, then his boardfigures to crash, reducing his chances of winning even after hitting ashot. And if he doesn't enter, I can always attack later with betterchances of success.
So after making the bar point, which 5 is best? 20/15 gets out of theway of the dreaded double 1s, but doesn't seem aggressive enough. I'llgo with 8/3: it's not the ideal spot for a spare, but it maximizesattacking potential in case White doesn't enter, and shouldn't be aproblem if he does.
George Klitsas: 7/1*.
Play a (20/15 8/7) I think that the checker on the twenty point is an asset rather than a liability for Blue. The worst case for him is when White rolls 1-1 from the bar, but, even then, Blue remains the favorite. On the other hand, White has some awkward entering numbers, like 1-6, when he is obliged to leave an additional blot. This checker impedes also White from slotting his five point and obtaining a smooth �reception committee� if Blue leaves a blot during the bear-off. By moving this checker, Blue loses the opportunity to bring more firepower down, which could be crucial.
Play b (13/7) Bringing down the firepower I was speaking about above. The fight for the ace point might last for a while and this bunch of men on the bar and eight points might be needed in a prolonged battle like this, for repeatedly hitting on the guff with direct and indirect shots until someone makes the point. I played 72 games in this variation and the result was +2.30 points per game for Blue on a two-cube.
Play c (8/3 8/7) I am not sure, but I feel that the resulting position is slightly worse than the one after play b. Looks that if White does not roll an ace, Blue has slightly more hitting numbers. If White does roll that ace, though, Blue's checker on the three point will be badly placed, a fact that might play a role later, especially in the bear-in and the bear-off. But even if one was to assure me that White is not going to roll that ace on his next roll, I would not play 8/3 with the five. It's just a feeling, that the greater flexibility retained from not advancing to the three point, would compensate for the small immediate gain. Anyway, plays a through c don't seem to have big difference in equity terms between them.
Play d (7/1*) A radically different approach. If White flunks, Blue has 9 covers and much more to follow if Blue flunks again. Also, White might hit with an ace, but after that, he might flunk for a while and Blue would be able to bring ammo in the meantime and continue his attack. These thoughts are hardly a proof of the correctness of play d. As it happens often, a rollout was needed to see what happens. In 72 games, Blue won 2.48 points per game on a two-cube. This is not a proof, either, only a strong indication that play d is the winner here and I'll go with it.
Rob Maier: 8/3, 8/7.
If Blue had more cover numbers, I would be more interested in attacking onthe ace point. As it is, it gives White too many wins to compensate forthe extra gammons. Cover the blot on the bar point, and then bring inmore lumber. The aces joker is not that big a deal, as Blue has enoughtiming to weather that particular storm.
Dave Montgomery: 7/1*.
7/1* looks clear. Blue will have nine covers now and it gets much betternext turn. Blue won't like it if he gets hit, but he will still have a bigedge unless White rolls 11. Blue shouldn't be afraid. Go for the throat.
Snowie: 20/15, 8/7.
I'm not going to risk losing a priming battle if White rolls double-aces.The builders can wait. I don't quite have enough ammo up front to makehitting on the ace point worthwhile.
Kit Woolsey: 20/15, 8/7.
Hitting could win a gammon, but it could also lead to some ugly scenarios.Without having a builder in direct cover position, I don't think it isworth it. Even if White anchors, his timing for an ace-point game doesn'tfigure to hold out. I run the back checker largely to avoid the double-aces disaster.
Chris Yep: 8/3, 8/7.
First note that by staying back on the 20 point Blue gains a little when White enters with 1-6, but loses a lot (probably more than twice the magnitude of the gain when White rolls 1-6) when White enters with 1-1. For this reason, I believe that 13/7 is inferior to 20/15 8/7. 20/15 8/7 virtually locks up the game, but I believe Blue can do even better. 7/1*, putting two men on the bar, is a very strong candidate. However, Blue has no direct covers next turn and White still has a broken 5-prime to trap any Blue checkers he may hit. I prefer delaying the attack for one more roll. 8/3 8/7 locks up a 6-prime and prepares to attack next turn if White stays on the bar. If White's next roll contains a 1, Blue is probably slightly better off having made the 6-prime than he would be if he had hit. If instead White flunks, Blue will usually be able to attack (with more power) next turn anyway. For example, if White flunks I think Blue should attack next turn with 6-x and maybe even 5-1 (Blue should definitely attack with 2-x).
Summary: Greed may be a terrible thing, but our many of our panelists don't think so. The loose hitcould work, of course, but with no builders in position I'm far from convincedthat it is worth the risk.
Play Votes Score7/1* 5 1008/3, 8/7 3 8020/15, 8/7 3 8013/7 0 50
Problem 7
| 110 140 | White money game Blue |
Chuck Bower: 16/11, 5/1.
I was wondering when Kit's sadistic side was going to show up thismonth! Blue wasn't looking too bad until she birthed this demon. Breakingthe home board here is so impure that just thinking about it makes me feelthe need to go to Confession, and yet...
White is wanting to abandon the 18-point in the worst way. Breaking oneof the blocking points and leaving juicy targets besides would make thetask just that much easier. I'm not going to aid in White's escape. So 16/11 and try and decide which home board point to break.
Figure White is going to leave one checker on the 18-point and look forthe most hit+cover rolls. After 6/2, I see 61, 41, and 65. After 5/1,there's 62, 42, 22, 66, 44, 33. I'm not going to worry about the bloton the 1-point. That checker is "where it belongs". Besides 6/2 just looks uglier.
Steve Clark: 13/4.
If 16/11, 5/1 is the right move, why are we not considering 6/1, 5/1 as analternative? I guess I will have to leave such philosophical questionsto others. The reason such moves as 16/11, 5/1 are considered "ugly" isbecause it is difficult to find a way to win the game afterwards. If weroll well we might be able to put the position back together but the oddsare against us. Once we face that fact 13/4 becomes a standout. It isthe one move which threatens to make a strong board. In positions whereboth players have outfield points, there are two considerations. Leavefew blots and build as strong a board as possible. Here the alternativesall leave our board in a much weaker situation. The extra blot on the 23point is a further argument for taking a chance now. I believe 13/4 iscorrect.
Malcolm Davis: 16/11, 5/1.
16/11, 5/1, I suppose. Any five other than 16/11 just looks too terrible. As much as I hate breaking my board, I guess I must do it. I wouldn't quarrel with 6/2, but like 5/1 a little better. If Snowie does not agree, then maybe I have learned something.
Hal Heinrich: 13/4.
A difficult decision, but Blue has reasonable winning chances and shouldhang onto assets. This means rejecting any play that breaks inner boardpoints. So which shot(s) do we leave? 11/2 overruns the open four point, solets forget that. 16/12, 11/6 leaves a good structure, but the twenty-seven number double shot seems a little rich. 13/4 starts the point we most want ata cost of eighteen shots. I hate to break the blocking point exactly sixpoints away, but here we have to make a concession -- and none of them aresmall. The key to this position is seeing that it is not overly gammon-proneand that Blue has real winning chances. So don't play to avoid losing, playto win!
Ron Karr: 16/11, 6/2.
A lovely roll. It's going to be tough to win thisgame, so far behind in the race and behind a 5-prime, so I think mygoal should be to avoid getting any more checkers sent back andpotentially getting gammoned, rather than trying to preserve a pureboard. My outfield points are valuable (you never know when he'll roll44 or 66), and after 16/11 6/2 I should be able to play safely for awhile. I can probably put my board back together in case of hitting alate shot.
George Klitsas: 16/12, 11/6.
Play a (16/11 6/2) Safe for just one roll, yet creating a difficult to close gap on the six point. Blue will need a series of almost perfect rolls to remake the six point without leaving blots in the outfield and, after (say) having made it not to break it (or some other crucial inner- board point) again . A short-sighted play. In 72 games Blue lost 0.94 points per game on a two-cube. When in doubt, keep a strong board!
Play b (16/11 5/1) I don't know if this is better or worse than play a, but I won't waste my time to find out.
Play c (16/12 11/6) Two blots that look vulnerable, but in fact are not. Only a few White rolls hit conveniently and without much risk from return-shots by Blue (between the good rolls for Blue are the four rolls that hit both blots [namely 5-4 and 4-1] because Blue will have to extract four checkers out of White's five-point prime). If not hit, Blue has no particular difficulty playing his upcoming rolls. Even if he will be obliged to leave a blot, the position will be such that White will not be able to hit it without some risk. White, on the other part, if he does not make a quick progress, is in danger of losing the timing battle, as his position will deteriorate by being obliged to break his eight and bar points, while Blue's position will become better by slotting and often making his four point. In 72 games, Blue lost only 0.16 points per game on a two-cube, a great improvement over play a.
Play d (13/4) The crucial feature of this play is that Blue has not a follow-up if he survives this roll (it's true that a fewer number of rolls, compared to play c, hit conveniently for White here). The problem is the follow-up. Blue will have great difficulty playing his numbers in the outfield and he will be leaving direct and indirect shots there for a while, a fact that will make the thought of clearing his outfield blots AND making his four point, a dream. Probably play d is better than play a, still much worse than play c.
Play e (11/2) I am not going to waste any time on this play, either. For the history, I think it's worse than d, since it buries a checker.
Needless to say, play c (16/12 11/6) comes out as the substantial winner here. I will risk the comment that, even if White had his two point made (and not slotted, as in the problem), even then, play c would probably be best here.
Rob Maier: 13/4.
Just when I was starting to enjoy this quiz. I'm not going to break myboard, or leave two direct blots. 13/4 puts a checker where it belongs,and 11/2 doesn't.
Dave Montgomery: 16/11, 6/2.
If Blue breaks his board, he's unlikely to win with a hit, but he may beable to preserve some racing chances and late shot vig. But if a thirdchecker gets sent back, Blue will be unlikely to win with a hit or from therace. It will be too hard to pump three checkers over the five prime. Bluemust avoid getting hit now and hope to get lucky later. I prefer 6/2 to 5/1because two inner board blots gives White a free hand. Blue wants to hitlater to improve his standing in the count.
Snowie: 16/11, 5/1.
Anybody who leaves a direct shot here must think they are wearing abulletproof vest. I will have time to put my board back together, andmy outfield points will make life difficult for White. If all else fails,I'll still have my three-point game in reserve. Leaving a shot increasesthe gammon danger considerably.
Kit Woolsey: 13/4.
I don't think I can afford to bust up my board if I am going towin this game. Since anything which keeps the board intact leaves a shot,I might as well start the point I know I must have eventually.
Chris Yep: 16/11, 5/1.
Between 16/11 6/2 and 16/11 5/1, I prefer 16/11 5/1. 16/11 5/1 gives Blue the best chance of making a 4 point board next roll. If White sits on his anchor, Blue has a surprising 21 numbers which make a 4 point board next turn: 15 numbers (6-1, 6-2, 6-4, 6-5, 4-2, 5-1, 3-3, 4-4, and 6-6) remake the 5 point while 6 numbers (4-1, 4-3, and 4-5) make the 1 point. After 16/11 6/2 only 9 numbers (6-5, 3-2, 4-1, 5-1, and 5-5) make a 4 point board next turn. If Blue plays 16/11 5/1, White will usually make a run for it if he rolls higher than 6 next turn, but since Blue has two different numbers to cover his inner board blots (4s and 6s), even though there is some duplication (Blue needs 4s and 6s to hit; after hitting he will then have 2s, 4s, and 6s to make a 4 point board) Blue still has a fair number of rolls which both hit and make a 4 point board. In addition, White's return hits are somewhat mitigated since he also has a blot in his inner board.
Of the plays which keep the 4 point board, I don't have a strong preference. 11/2, for example, seems to put the most pressure on White; however, it brings in a checker past the 4 point and Blue has precious few checkers to spare. 13/4 at least slots the 4 point, but gives up the valuable blocking midpoint. 16/12 11/6 gives up a double shot and decreases coverage of the outfield. I have a slight preference for 13/4 over 16/12 11/6 and 11/2, although I'm not very confident about this. The biggest drawback with these 3 plays is that they allow White to both hit (with at least 17 numbers), putting a third Blue checker behind a 5-prime, and make a run for it all in one roll. Of course the huge swing on either 4-4 or 6-6 (depending on which move Blue plays) is another factor. I believe that Blue is better off by sitting on the 11 point and the midpoint and waiting for events to unfold.
Summary: Can Blue really afford to blow up his board here? Maybe so, but it is avery difficult play for me to stomach. I'd rather go down fighting.
Play Votes Score16/11, 5/1 4 10013/4 4 9016/11, 6/2 2 8016/12, 11/6 1 6011/2 0 50
Problem 8
| 86 82 | White money game Blue |
Chuck Bower: 4/3*, 3/1.
White's racing chances are significant. The 8/5 play counts on neither side rolling a 6 (25/36 * 25/36 < 0.5). I don't like those odds. 8/6, 4/3* gives White only 13/36 good rolls, but those aren't just good, they'reVERY GOOD. After Blue plays 4/3*/1, White has no really good rolls. 16/36 fan, 11/36 hit but then leave White needing to impress with his triple-jump skills. The remaining 9 rolls put White back where he started, but with some ground lost in the race.
Steve Clark: 4/3*, 3/1.
When hitting at the front of a 5 point prime it is usually wrong toadvance the checker further because it then becomes much more difficult tocomplete the prime. In this circumstance the prime is not such animportant consideration All we really need is a modest improvement in ourracing lead to be quite happy. Thus playing 4/3*, 3/1 means that in order forour opponent to hit and escape we will have to roll a 1, a 2, and a 6 inthat order. Actually that is a fairly difficult task, rather moredifficult that his task if I hit on the 3 and leave my checker there.Hmm.
If I play 8/5, I have a small lead in the race; he has to roll a 6 toescape and if he doesn't, I probably will be able to point on him nextroll. Suppose I hit him and move on to the ace point. I will quite happy40 % of the time and fairly happy 30% of the time.. The other 30% I thinkI am still a favorite unless he rolls a 2,1. Suppose I play 8/5. I willbe fairly happy 70% of the time and a small favorite with one or twoexceptions the rest of the time. None of this is very clear to me but Ihave to make a choice and so I will play 4/3*, 3/1.
Malcolm Davis: 8/6, 4/3*.
I don't make plays like 4/3*/1. If I hit, I would at least consider 6/3*. A few years ago, I would have hit without even thinking about another play. I suppose I would play 8/6,4/3*, the argument being that your opponent has to hit 13 numbers and then roll a 6 before you can enter on his five point board. It's tempting to play 8/5 and let your opponent roll, as you are further ahead in the race than the pip-count indicates, and only a 6 is a good number. Ask yourself if you would really hit loose at double-match- point if you were in the finals at Monte Carlo? I opt for the hit. On second thought, 4/3*/1 does mean that your opponent has to roll a 1, then a 2, and then a 6 to escape. but I still wouldn't do it. 8/6,4/3* is my play.
Hal Heinrich: 4/3*, 3/1.
White has good chances in a race, particularly with cube ownership, so hitting has to be considered. Hitting and moving to the ace means that afterhitting, White still needs a two, and then a six or a closeout before beingable to claim with the cube. Advancing with 8/5 is quite reasonable becauseif White doesn't escape with a six, Blue has good chances to squelch furtherresistance by making the three point. Even so, I'll take my chances by hitting and moving on.
Ron Karr; 8/6, 4/3*.
I find this kind of play difficult because generalprinciples don't necessarily work; you have to really look at theindividual scenarios for each move, and try to calculate winningchances. My gut feeling would be that since the race is close, it'sbetter to attack on the 3 point and try to lock the game up. Let's seeif I can be more precise, realizing that some of my estimates could beway wrong:
8/5: If White rolls a 6, he'll be the favorite because of owning thecube. If he doesn't roll a 6, he can advance on his side, possiblymaking the 4 point. I'll have better attacking chances next time, butstill an underdog to point cleanly. (One good thing is that smallnumbers point, and big ones gain in the race.) If I'm not hittingloose now, I'm not hitting loose later, so he'll continue to havechances to escape. His total chances of escaping are 30% the firstroll, and maybe a total of 50%, and he's winning more than half ofthose due to cube ownership--say 30-35%. The rest of the time I makemy prime & win, with very few gammon chances.
8/6 4/3*. If White hits back (36%), I'm a definite underdog but I'llstill have a roll or two to enter and survive. I think he needs toescape or close the board before he can double. I'll estimate I'lllose 2/3 of these, or 24%.
If White fans, I can make a 6-prime by covering with 3s and 5s, and 4scover also. I might then be able to slot the ace point and pick up afew gammons, but these might be offset by the few times I can't cover. So let's just say I win a single game whenever I don't get hit back. So this play seems better than the safe play.
4/3*/1 is an intriguing idea. It has the advantage that if White rollsa 1 without a 2 (25%), he's not at the edge of the prime. His boardcould easily crash while waiting for escaping numbers, allowing me toenter and attack. I'll estimate he wins at most 10%. After 1-2(5.6%), he's in the same shape as hitting above, so let's say he wins4%. If he fans (44%), I'll probably cover the 1 point, but then it'llbe hard to make the 3 point. Most likely I'll gain sufficient racingequity that I can just tiptoe home; he figures to hit occasionallywhile I'm bearing off but won't win all of those; I'll estimate 5%. IfWhite enters right away on the 3 point (31%) it'll be hard for me toattack safely, so he'll again have racing chances. Maybe he'll win10%. Total is 29%; I think that's a high estimate but I'll still guessit's not as good as the other hitting play.
George Klitsas: 4/3*, 3/1.
Play a (8/6 4/3*) White hits with thirteen rolls, which are immediate winners when Blue flunks (I think taking the redouble is too risky in that case). Blue is not guaranteed to make the three point if White does not hit on his first roll (also 3-3 play awkwardly for Blue and some other covers along with the 6-2 that makes the ace point leave indirect hits). In 36 games I counted nine very strong redoubles for White (hit-flunk) and six redoubles and big passes (for example when White hit an early shot during Blue's bear-off). In 72 games Blue won 0.47 ppg on a two-cube in this variation. For the history, I am not convinced that the ugly-looking 6/3* is worse than play a.
Play b ( 8/5) If White does not roll a six, Blue is well positioned to point on him with the numbers one to five, while the sixes are good for the race. The bad case for Blue is when White rolls a six on his first roll. Then White (if he continues to roll better than Blue for a while), should be able to offer some strong redoubles (I counted seven strong and three untakable ones in a sample of 36 games) . In 72 games, Blue won 0.78 ppg on a two-cube.
Play c (4/3* 3/1) An interesting idea. If White hits with an ace, he will need first a two and then a six to escape. From the other side, Blue's position is not gin, the three point is difficult to make and there is a difficulty in playing five's. In 36 games I counted nine very strong redoubles for White and two more redoubles and big passes. In 72 games Blue's equity was +0.86 ppg on a two-cube.
It's difficult to be sure on such a small sample. I think that play a is a distant third but I am not sure about the others. I will vote for play c, the typical winner.
Rob Maier: 4/3*, 3/1.
My original thought was that this was a good time to make the wimpy play.Thinking about the cube being with White has changed my mind. We shouldmake it more of a challenge for White to become a favorite than justtossing a six. Hitting and going to the ace point will give us time torecover if we are hit, and will take a huge chunk out of White's racingchances otherwise.
Dave Montgomery: 4/3*, 3/1.
If Blue plays 8/5 and White escapes, Blue may not even be the favorite.Hitting and continuing to the 1 point allows Blue to nearly lock up the gamein the good variations, while still retaining excellent chances when Whitehits or miss-enters.
Snowie: 8/5.
Even if White rolls a six, I'll still be a bit ahead in therace. If White doesn't roll a six, I'll be a big favorite to pouncesuccessfully next roll. White's five-point board must be shown somerespect.
Kit Woolsey: 4/3*, 3/1.
The race is too close to give White a chance to escape. However, I don'tthink I can risk White hitting back at the edge of the prime. Thecompromise play of hitting and moving to the ace point gives White decentthrees and aces, but except for 2-1 nothing is crushing. If he hits he willhave to roll well to avoid crunching.
Chris Yep: 4/3*, 3/1.
First, among the hitting plays, I believe that 4/3* 3/1 is superior. White has 13 numbers to hit after 8/6 4/3*, while only 11 after 4/3* 3/1. Also, more importantly, if White hits on the ace point, he still has to roll a 2 and then a 6 to escape, while if he his on the 3 point, he only needs a 6 to escape. Should White stay on the bar, Blue will usually make a 5 point board next turn without leaving a direct shot. After 8/6 4/3*, everything makes a 5 point board without leaving a direct shot except 6-1 (which awkwardly preserves a 4 point board, but with no direct shots) and 6-6 (which makes a 5 point board, but leaves a direct shot). After 4/3* 3/1, everything makes a 5 point board without leaving a direct shot except 1-1 (which awkwardly preserves the 4 point board, but with no direct shots) and 2-1 and 3-1 (which preserve the 4 point board, but leave a direct shot). So 8/6 4/3* is slightly better at building a strong board, should White stay on the bar. However, I believe the overriding factor is that for Blue to pay, White must roll a 1, 2, and 6 (in order) after 4/3* 3/1 while White only needs to roll a 3 and 6 (in order) after 8/6 4/3*.
If Blue were 6-8 pips farther ahead in the race I believe the conservative 8/5 would be absolutely clear. If White doesn't roll a 6 next roll, Blue will be able to point on White's head with everything except 6-x (even 6-x is not that bad for Blue, since he can use it for the race). If Blue plays 8/5 he will be 7 pips ahead with White on roll. The advantage is a little greater than this since White still has an open 4 point and 2 checkers each on his ace and deuce points, which could lead to slightly more wasteage than normal in the bearoff. We should probably penalize White a few pips for this. Still, if Blue plays 8/5 and White rolls 6-x, White will have an almost equal race. If Blue plays 4/3* 3/1 he knocks White away from the edge of the prime. White loses 3 pips immediately and each turn that he stays on the bar is a full roll wasted in the race. On average he will probably lose 10-12 pips in addition to the 3 pips that he loses from being hit off the 3 point. This is a significant factor in a close race. In order for Blue to regret 4/3* 3/1, White must hit back, then roll a 2 followed by a 6 before Blue can enter from the bar. White's chances are improved if he can close his board after hitting, but some of the numbers which close the board have to be used on the other side of the board. For example, if White rolls 2-3, 2-4, or 2-5, he has to play 24/22 rather than closing his board. Considering that the race will be close to even if I play 8/5 and White rolls 6-x before I can point on him, I'm willing to risk White rolling a 1, 2, and 6 in order to beat me.
Summary: And we thought it was the bots who over-attacked. Only Snowie was willingto sit back and wait patiently. Are we learning from Snowie, or is Snowielearning from us?
Play Votes Score4/3*, 3/1 8 1008/6, 4/3* 2 608/5 1 50
Vote Summary
1 2 3 4 5 6 7 8Chuck Bower 21/16 14/10, 7/5* 18/12 24/22, 13/8 B/24, 23/18 7/1* 16/11, 5/1 4/3*, 3/1 Steve Clark 8/5, 8/6 20/14 18/12 13/8, 11/9 B/20, 23/22 7/1* 13/4 4/3*, 3/1Malcolm Davis 21/16 24/18 18/12 24/22, 11/6 B/24, 23/18 7/1* 16/11, 5/1 8/6, 4/3* Hal Heinrich 8/5, 8/6 13/7 18/12 24/22, 11/6 B/24, 23/18 20/15, 8/7 13/4 4/3*, 3/1 Ron Karr 21/16 20/14 18/12 13/8, 13/11 B/24, 23/18 8/3, 8/7 16/11, 6/2 8/6, 4/3*George Klitsas 4/1*, 4/2 14/10, 7/5* 18/12 13/8, 11/9 B/20, 23/22 7/1* 16/12, 11/6 4/3*, 3/1 Rob Maier 21/16 14/10, 7/5* 18/12 13/8, 11/9 B/24, 23/18 8/3, 8/7 13/4 4/3*, 3/1 Dave Montgomery 21/16 14/10, 7/5* 18/14, 4/2* 11/4 B/20, 24/23 7/1* 16/11, 6/2 4/3*, 3/1 Snowie 4/1*, 4/2 14/10, 7/5* 18/12 24/22, 6/1* B/20, 24/23 20/15, 8/7 16/11, 5/1 8/5 Kit Woolsey 21/16 24/22, 14/10 18/12 11/9, 6/1* B/24, 23/18 20/15, 8/7 13/4 4/3*, 3/1Chris Yep 21/16 14/10, 7/5* 18/12 11/4 B/20, 24/23 8/3, 8/7 16/11, 5/1 4/3*, 3/1
