94
money game
Blue
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Problem 1
| 66 94 | White money game Blue |
Chuck Bower: 7/2*.
Blue needs to keep White's trapped checker shackled for several rolls. Asecondary consideration is sending back a second White checker as it both carries insurance for winning AND bonus points for a gammon.
The passive approach (8/6 8/5 or 7/5, 7/4) gives White either 9 or 11 escapingrolls, 8 safe pointing rolls, and some loose hits. If Blue survives that he isprobably going to need to attack next turn. Why not attack now and take awaymost of White's escaping rolls?
Giving up the 4-point (4/1, 4/2*) puts White checker on the bar but degrades Blue's board. 7/2* maintains or improves Blue's home boardand leaves 5 1/2 points of the outside (3-point thru 8-point) prime.
If White escapes Blue will be forced to pass the cube (barring joker returns).7/2* leaves White only 4/36 immediate escapes. There are certainly some badparlays for Blue (White hits, Blue fans) but then it is not clear thatWhite can even recube. The active play looks best: 7/2*.
Steve Clark: 8/5, 8/6.
When I don't know what to do, I try to eliminate some of thepossibilities. In this problem I will do away with 7/5, 7/4. 8/5, 8/6seems similar and keeps a 5 point prime. The value of this prime is notimmediately apparent but in variations were there is a variety ofhitting, I would much rather have the prime than a gap. Also maybe Iwill make the 2 point next roll. If I keep the 7 point, I will have afull prime again, but not if I keep the 8.
Next to go is 7/2*. I am not excited about leaving 3 blots for noreason. This play destroys my prime without any compensation that I cansee. My position is too good to give my opponent the opportunity to beplaying on for the gammon after my next roll.
4/1, 4/2* has some apparent value. I am way behind in the race. Thisplay puts a man on the bar where he might not come it. That has to bethe right idea. Unfortunately I am well behind in the race and I amwrecking my prime. He will have a few chances to escape and be wellahead in the race. Furthermore to some degree I am duplicating my own5's and 6's next roll. Suppose he flunks and I roll a 6-4. Thealternatives would be to escape or to cover. I would not be able to doboth. I lack enthusiasm for all this.
What about keeping the prime as best I can. He has a few good rolls,such as 2-1 even when he does not roll a 6. Even so he will have toperform or I will have him. It is scary to leave the opponent at theedge of a 5 point prime. But most of the time remains stuck and theprime will be able to expand. I think it is wrong to panic and give upthe prime for little compensation. I will play 8/5, 8/6
Malcolm Davis: 7/2*.
I guess I hit, Must be "off my game." Did not even see the play at first. A few years ago, I would not have seen anything else - breaking the 8-point makes me too nervous.
Ray Fogerlund: 7/4, 7/5.
Initially I answered 7/2* but that wasbothering me. I think better is 7/4, 7/5. Limiting White's good numbersand maximizing the bad ones. It is important to break the bar for morebuilders and to eliminate 51 as an escape number. Also, this doesn't allowWhite to win a lucky gammon nearly as often by picking up multiple blots. Ican't afford to hit and leave 4 blots because white's board deservesrespect, and holding the cube is a tremendous advantage for white when sheenters and hits. Often there is a gammon threat inherent in hitting loose,but here that is not a factor. Over the board or online I probably wouldhave hit... But upon reflection it just seems wrong.
Hal Heinrich: 4/1, 4/2*.
White is ahead in the race, has as many inner board points as Blue, andowns the cube -- Blue is skating on thin ice here. Breaking the eightor bar points gives White too many options -- White can win immediatelyby escaping or by tying up Blue's back man and then running out. And ofthe hitting plays, breaking the four point is clear because it leavesfewer blots -- White's board is as strong as Blue's!
Ron Karr: 4/1, 4/2*.
This preserves a good block; if White enters with a hit, he's still primed,and there are only 4 numbers that escape immediately, as opposed to 11if I break the 8 or 7 points. Keeping White on the bar also robs himof some of his good pointing numbers. But hitting 7/2* seems tooloose, giving up the bar point.
George Klitsas: 7/2*.
Play a (8/5 8/6) The good thing about this play is that it keeps a five-point prime. A five-point prime is good for it's owner, in many positions that are far from similar in nature. So, keep a five-point prime is a sound rule in a vast number of positions in backgammon even if one does not quite understand why. Here I could explain this �why� by an example. Suppose that White's first roll is a 3-2, making the ace point in Blue's head and that Blue counters with a 6-3, played B/19 5/2*. The power of the five-prime which includes the bar point (compared to a broken six-prime including the eight but not the bar point) becomes obvious: if White hits on the ace point his sixes are blocked and he is obliged to roll first an ace and then a six to escape (if in the meantime Blue has not made a six-prime which is rather easy here) and if White hits on the two point, Blue has the spares to re-hit loose. In 108 games Blue lost 0.19 points per game on a two-cube (Blue won 38 plain games, 8 gammons and lost 60 plain games and 2 gammons).
Play b (7/4 7/5) Much weaker than play a as explained above. Thirty-six games were enough to make up my mind. Blue lost 0.5 points per game on a two-cube.
Play c ( 7/2*) When White dances, Blue has a very good chance for a closeout (noticing, though, that his rear checker creates a small number of breaks of his board). When White enters (by hitting, of course) he is not finished. Some of his rolls (like 1-4 and 2-4) leave three blots, others two of them, a few only one. Sometimes White has a very strong redouble, sometimes he is lucky enough to roll a joker and then he is entitled to go for the unredoubled gammon. This is one of these positions that cannot be solved by arguments. A rollout was urgently needed, 108 games, and the result was a surprising plus equity for Blue, 0.13 points per game on a two-cube, the best so far. For the history, Blue won 57 plain games and 5 gammons, White 32 plain games and 14 gammons. This equity might be somewhat biased against White, because it's been very difficult (at least for me) to decide when White should redouble and when he should go for an unredoubled gammon. Still I believe this difficulty did not affect the final equity by much.
Play d (4/2* 4/1) Apart from the immediate winners for White (4-5 and 4-6), the gap created by this play on the four point, is going to harm Blue not only in the subsequent rolls, but in the games that will reach the bear-off, too. Also, if White flunks and Blue covers the two point with a non-ace, this fact will create other liabilities in his position (look also how badly a 4-3 plays for Blue when White flunks). In 36 games, Blue lost 0.5 points per game on a two-cube.
Play c (7/2*) is my choice with a high probability of being correct, I believe.
Laila Leonhardt: 8/5, 8/6.
Breaking from the back keeps a 5 point prime, with the potential of recreating the 6 prime which will give a few gammon wins for Blue.
Rob Maier: 8/5, 8/6.
Plays like 4/1, 4/2* look a lot better in the short term than they work inthe long term. 7/2* makes White do two things, but he is a favorite to dothe first immediately, and we are opening ourselves up to some gammons.Of the two quiet plays, breaking the eight point is more sound, as the barpoint will block White if they come in again on the ace, and is the lastpoint in the new potential six man prime.
Snowie: 7/2*.
Something has to give, so I might as well play for the best position on theassumption that my play works.
Kit Woolsey: 7/2*.
I don't like the idea of giving White a full roll here by breaking one of theback points of the prime without hitting. He will have large numbersto escape and small numbers to point on me. 4/2*, 4/1 invovles too muchmess cleanup. The simple loose hit on the two point gives me a decent shotat completing the closeout, and even if White enters he still has to crawlover my blockade..
Chris Yep: 7/2*.
7/2* leaves 4 blots, but I think it's called for here. 8/5 8/6 and 7/4 7/5 allow white to escape in one roll. Blue will be behind by 23 pips after this roll. White's actual race advantage is misleading since he will have a lot of wastage in the bear off. Still, White is ahead by enough that if he escapes his back checker next turn, he will be a big favorite. Blue has a strong 4 point board, while White has a weak 4 point board (the 6 point is open and the 5 point is stripped). After 7/2*, while 1-1, 1-6, and 2-5 are jokers, 1-4 and 2-4 are anti-jokers. Also, by hitting, Blue duplicates White's 1s and 2s.
Another approach is 4/1 4/2*. Although it leaves 2 blots instead of 4, this doesn't compensate for its awkwardness in my opinion. Although almost everything covers next turn (3-4 and 4-4 (played 8/4(2) 7/3(2)) don't cover, but at least make a 5 point board), Blue is behind by enough that he really needs to contain white's checker. For this, he'll need the 4 point. Also, 5s and 6s cover the blot on the 2 pt., but Blue also needs 5s and 6s to escape his back checker.
I prefer 7/2* which forces White to enter quickly and roll a 5 (if he enters on the 23 point) or a 6 (if he enters on the 24 point) to escape.
Compare this problem to Problem 3 in last month's quiz. In this month's quiz problem, Blue's board is stronger than White's, playing "safe" does not provide any outfield coverage, and White does not have an outside point to clear (in last month's quiz, if Blue got stuck on the bar after a hit, White could clear his 10 point without leaving any direct shots). These factors all swing the balance toward the hit. While I preferred the conservative move last month, I prefer the aggressive move this month.
Summary.The old-fashioned walk the prime home pure play won out. Risky, but so isanything else. Quite likely to be the right choice.
Play Votes Score7/2* 6 1008/5, 8/6 3 804/1, 4/2* 2 707/4, 7/5 1 60
Problem 2
| 145 115 | White money game Blue |
Chuck Bower: B/24, 10/8.
Blue has two goals: escape the back checker and complete the prime (4-point).Escaping seems to be the higher priority, since merely building the prime leaves White with better timing in the ensuing prime vs. prime battle.
B/23 has one advantage--it puts pressure on the 8-point. But since White hasa spare there currently, the only immediate White response which makes B/23valuable now is 31.
B/24 has three advantages: 1) White's subsequent loose hit on Blue's 24-point is both less likely and less advantageous than on the 23-point; 2) if White leaves return shots (for example, on the 7-point) Blue will have more hitting numbers; and 3) if White succeeds in making both his 5- and 7-points, 13 Blue numbers advance 24/21 compared to 11 from the 23-point.
No need to decide how to play the 1 on the homeside! B/24, 10/8 looks like the play.
Steve Clark: B/24, 10/8.
I really want to come in on the 24 point. White will have lessopportunity to hit me there and he will be making the poorer point. IfWhite rolls a 3-1 I will be sorry, but I really belong on the 24 point.
Suppose I play B/24, 10/8 I will have four spares aimed at the 4 point.If I play B/23, 10/9, I still will only have 4 spares aimed at the 4. Iwill not want to leave a blot on the 8 in order to make the 4. Furtherthere is no pressure for me to avoid outfield blots because if Whitehits one of them he will have to leave a wreck for me to shoot at.Finally B/23, 5/4 pretends to be aggressive but all you would really bedoing is aggressively running of the nearest cliff. I will play B/24,10/8.
Malcolm Davis: B/23, 7/6.
Looks pretty good, but B/24, 10/8 could be right. Just like the way that B/23, 7/6 looks.
Ray Fogerlund: B/23, 10/9.
White is trying to build a strong forward position byslotting points, so... we can take some liberties to create 4 builders forthe four point. The builders are safe for this turn, and next turn we cansecure the 4 point or escape our back man according to the dictates of thedice. We counterpunch Whites lead, and recognizing the flow of the game, weseize an opportunity to secure a decisive advantage.
Hal Heinrich: B/24, 10/8.
It's immaterial whether Blue enters on the twenty-four or twenty-threepoint, so Blue can focus on his home board. Slotting doesn't workbecause if White misses the blot, White will attack Blue's back manmaking it tough for Blue to cover. So 10/8 is the way to go because itcreates four builders to make the four point with, while leaving lessexposed than B/23, 10/9
Ron Karr: B/24, 10/8.
I'd just as soon enter on the 24 point, because it gives White less incentive toattack. And there are just as many escaping numbers as entering on 23,as long as White has his 8 point, which is likely to be the case for awhile. 10/8 diversifies the front position pretty well with littlerisk.
George Klitsas: B/24, 10/8.
Play a ( B/23 10/9) Having many blots strewn around is bad in a vast number of (types of) backgammon positions, even in innocent-looking positions like the one that results after play a. Although White has only a two-point board for the moment, he is poised to attack and if things start getting bad for Blue, they can get worse and much worse. Blue gets maximum (theoretically) probability for making his four point, but it's not clear if by breaking his ten point (which is in itself a concession) he creates builders or targets. Many of White's rolls point on Blue's blot on White's two point and some more cover the five point and hit loose. Blue, in a sample of 36 games won 11 plain games and 8 gammons, White 17 plain games for an overall equity of 0.56 points per game for Blue on a two-cube.
Play b ( B/23 7/6) This play is visibly cramped. Keeps the ten point which is important , but only seemingly creates a new builder, since Blue will be reluctant to break his bar point to make his four point and consequently the checkers on his bar point cannot be thought of as real builders, only half-builders perhaps. In 36 games Blue won 14 plain games and 6 gammons, White 15 plain and 1 gammon for an overall equity for Blue of 0.5 points per game on a two-cube.
Play c ( B/23 5/4) The main danger is not that the slot on the four point might be hit here (White should have a hard time escaping with two checkers from the broken prime in that case) but another, somewhat subtle and hidden : the pending Blue slot on the four point will permit White to slot freely on his own side, since with many rolls Blue won't be able to hit White's slot AND cover his own at the same time. By slotting freely, White will be able to play often an effective prime vs prime game, which, although it has the disadvantage of two checkers back versus only one, has the advantage in timing. In 36 games, Blue won 15 plain, 2 gammons and White 19 plain with zero overall equity. Seems that variation c is the worst of the four candidates.
Play d ( B/24 10/8) A compromise is (not always but) often the best move. I think this is a case in point. Apart from creating a real builder (not a half one as after play b) Blue leaves only one outfield blot compared to play a and - most important - enters on the twenty-four point , where he gets pointed on or hit loose with a fewer number of rolls and with much less efficiency by White. The only liability of this play is that it breaks the ten point, but something but be given. All in all, play d looks best, which was supported (there is seldom proof in backgammon!) by a short rollout of 36 games. Blue won 16 plain games and 6 gammons, White 14 plain games for an overall equity of 0.78 points per game for Blue on a two-cube.
Laila Leonhardt: B/24, 10/8.
White will not hit the blot on the 10 point if he rolls a 6-2. Blues priority now is to create extra builders so he can make the 6 point prime. If faced with a # that escapes to the outfield or makes the 6 prime next turn, Blue should run, since White threatens to prime Blue and will most scenarios have a better timing. 7/6 would remove a builder to create one. 5/4 is much to risky it will give White a chance to move up and double hit or prime and bar/23 10/9 will provoke White to attack Blue on the 2 point and the 2 outside blots could become a problem instead of an asset.
Rob Maier: B/23, 7/6.
Blue has a large race lead, and a strong blockade. There's no need to getfancy by slotting or breaking the ten point.
Snowie: B/23, 5/4.
I'm going to want my four point, and what better time to slot it then whenWhite's game is in disarray. He hits at his own risk.
Kit Woolsey: B/23, 7/6.
The ten point is a valuable point. It serves as a backstop in case Whitecan advance to my four point. Slotting is possible, but it doesn't appearto be necessary. After B/23, 7/6, I should be in good shape pretty muchregardless of what White does.
Chris Yep: B/23, 7/6.
Blue has two main priorities in this position: (1) escape his back checker (and avoid getting any more checkers sent back) and (2) mobilize his front men to make the 4 point. Of these, I believe the first is more important. B/23 7/6 leaves White no immediate shots at hitting a 2nd checker. At the same time, 7/6 is comfortable, putting a builder where it belongs and retaining 3 builders for the 4 point. Next turn, if Blue gets stuck he will break the 10 point to create more builders for the 4 point. Blue will be ahead by 33 pips after the roll and have one man back to White's two. This argues for a safe play. I believe that the cost of getting hit outweighs the increased chances of making the 4 point after 10/8, 10/9, or 5/4.
Summary: The panel was willing to give up the ten point. I don't see it. That pointis a valuable backstop in case White gets up to the four point. And what'sthis? Snowie is the only one brave enough to out and out slot the four point.Quite the role reversal.
Play Votes ScoreB/24, 10/8 6 100B/23, 7/6 4 80B/23, 10/9 1 60B/23, 5/4 1 60
Problem 3
| 133 139 | White money game Blue |
Chuck Bower: 18/10(2).
This nice roll gives Blue the race lead. 18/10(2) does two good things:advances the back checkers to avoid future timing problems and adds a nicepoint in Blue's prime (and/or builders for the 4-point). No need to getcute or greedy here. 18/10(2) allows Blue to put all his future effort intoimproving the homeside structure, and White's winning options arereduced in the process.
Steve Clark: 18/10(2).
If I were in a hurry I would play 18/10(2) and hit the clock as fast as Ican. Since this is in the problem set I suppose I should think aboutit a while. Hmm. This is the safest play. It clears the points inorder. Other plays might win more gammons but there won't be many ofthem in this position. I expect that 18/10(2) has the highest winningpercentage; with low gammon potential this has to be the most importantfactor. A well known backgammon editor once said, "Clear from the rearand don't ask any questions." When you are ahead and have the opponenttrapped, that is the right idea. Play it fast and hit the clock.
Malcolm Davis: 18/10(2).
Just looks too good to make another play. Would really like to make the 4-point,but seems as if that or any alternate play is just getting too cute. I am not sure if I domake the 4-point what my other 2 4's would be. Making the 2-point is too deep. If the responseallows a split with a 2, I don't want to attack against the 3 point board. And I don't want to leave a direct shot. Have enough racing lead after the 16 pips to play very simply.
Ray Fogerlund: 13/5, 8/4(2).
Mostly in positions such as these, the tendency formost players is to clear out from the opponent's bar point, feeling thatthey have won the game. However, this allows White to build her position ather leisure, and holding the bar point is a much more threateningalternative. Now it might be difficult for White to avoid shots, and evenif she does avoid them she won't be able to take dead aim at her 5 pointbecause she will have to be careful! By making the offensive 4 point,Blue's prime becomes more "offensive". Breaking the midpoint to add to theforward advantage will be next, and White will have a thorn in her side asshe tries to build a position to win from, in the even that she can hit.Blue should take this game by force, and be thinking how can I gammon White?instead of, "Boy, I sure hope that I can run away!".
Hal Heinrich: 8/4(2), 6/2(2).
Blue has a lot of plays which leave a comfortable position. The question is how to squeeze the most out of this opportunity. I likemaking two inner board points and pinning White to the twenty-fourpoint. It does leave Blue without builders in the home board, but lookat it from White's point of view. Would you, as White, split to yourtwenty-two point if you rolled a deuce? I'm not sure how I'd play it --but that confirms the strength of the play. The most likely result ofthis is play is that White will wind up in a poorly-timed ace pointgame. Blue will get some gammon chances when White breaks the mid point.
Ron Karr: 8/4(2), 6/2(2).
I have a slight racing lead after this roll, but reducing contact isn'tnecessary. It's a good roll for increasing the pressure on White; I'llhave a good prime, an anchor, and good timing. He'll be hard pressedto avoid exposing another blot and/or destroying his board. Next I'llplay from the midpoint; even if I have to leave a blot there it won'tbe too bad. I should have plenty of time to get off the 18 point.
George Klitsas: 8/4(2), 6/2(2).
Play a ( 18/10(2) ) Creates the most compact position for Blue from all the listed alternatives, in the meaning that all of Blue's checkers are in the closed interval [5,13] mathematically speaking. The resulting position looks easy to play from Blue's angle, but the same is true for White - he is virtually undisturbed in his effort to build a strong board and he can split his rear checkers with a two or a three with little danger, trying for an advanced anchor, a plausible plan given his good racing chances. Playing the position out, I was thinking that, in order to fill smoothly his inner board, White should abandon the midpoint soon - sometimes even at his first roll (with a 6-5 or even a 5-4 perhaps) - and that fact should give Blue a free hand in the outfield. Summing up, a quiet variation that resulted in Blue winning 44 plain games and 9 gammons, White only 19 plain games [in 72 trials] for an overall equity for Blue of 1.19 points per game on a two-cube.
Play b ( 18/14(2) 13/9(2) ) Compared to play a, a less compact position, a blot left but in the plus side, a five-point prime instead of a broken six-point prime. The five-point prime is always stronger than one might think (!) but the blot left by this play could give White the time, the timing and the tempo to go forward by splitting his rear checkers and eventually make Blue's three or four-point and play from there, if he is lucky enough to hit with an ace on his first roll. White is well advised, here as well, to split with a two or, even better, with a three, before he is hemmed in . In 36 games Blue's equity was 0.84 points per game on a two-cube.
Play c ( 18/14(2) 8/4(2) ) Even less compact a position compared to variations a and b. Blue gets a stronger board in return, but with no spares in the front battlefield - so, White should not be particularly reluctant to split there. Blue has difficulty bringing his position home in variation c. Despite these observations, his strong inner board permits him to win a number of gammons. In 36 games, Blue won 1.17 points per game.
Play d ( 13/9(2) 8/4(2) ) An overextended position with a vulnerable blot could not easily be the winner here, a fact convincingly supported by a short rollout of 36 games - Blue won only 0.62 points per game on a two-cube. Blue often gets stuck on White's bar point.
Play e ( 13/9(2) 13/5) A five-point prime that will shrink in all probability in the very next roll.
Play f ( 13/5 8/4(2)) Better than play e in my opinion, but, still, weak.
Play g ( 8/4(2) 6/2(2) ) Strangely enough, this position, which is the less compact from all the candidates, could be best in equity terms. A feature that is good for one game plan (as is compactness for a priming-type kind of game) often becomes neutral or even bad for another game plan (building a strong board and trying to play aggressively). In other words, play g finds itself in the opposite side of play a, in the spectrum of all conceivable plays. Play a is the most prime-oriented, creates the most compact position which results in minimum contact as well and it's the quietest of all. Play g instead, is the most attack-oriented and pressure-oriented, creates the most disjoint position , retains maximum contact and it's the most sharp. The in-between plays (b through f) share some of the characteristics ( in varying degrees) of these two edge plays, but do not deploy a clear theme. This is not an argument in itself, a mixed strategy often is best. Plays b through f have just been proved ineffective in these short rollouts of mine. White has a difficult time both in splitting his back checkers with a two (it could work but could also backfire ) and trying to avoid leaving blots in the outfield - at the same time he must do his best to form a �reception committee� (one notices that if White breaks his eight point first, then all sixes must be played from the mid, a fact that will present Blue with a single or double shot against White's left checker on it and, in case of success, will considerably increase his gammon chances). All these objectives simply are not to be achieved unless White is very lucky. Summing up, Blue, by staying back, creates for himself the problem of clearing eventually White's bar point, but at the same time he creates probably more problems for White and it's the algebraic sum of this trade that will decide the equity of play g- which seems to me after a rollout of 72 games favorable to Blue (Blue : 41 plain, 13 gammons, White : 17 plain, 1 gammon), +1.33 points per game on a two-cube.
So, plays a and g, occypying the two edges of the spectrum of all plausible moves for this problem, seem to fight for the election, being very close in equity terms. I resist the tempation to feed Snowie or Jellyfish (a man should keep his word, after all!) until after the results of the Quiz have been posted in next month's issue. As I have to vote for something and in spite of the fact that I feel more comfortable with the priming play, I'll go with the typical winner of my rollouts (I would be not the wiser if I performed twice as much, I guess), which is the aggressive play g ( 8/4(2) 6/2(2) ).
Laila Leonhardt: 18/10(2).
I prefer clearing the midpoint and creating another builder/attacker for the 4 point. By clearing the 18 point Blue avoids some awkward 6's and also the scenario where White with eventually hit Blue on the 18 point and use this to counter prime, or to move up to the edge of Blue's prime.
Rob Maier: 18/10(2).
Bring the back checkers home. White isn't going to be leaving us any moreblots most of the time, and hanging back to wait for them may give us moreproblems than it gives to the opponents.
Snowie: 8/4(2), 6/2(2).
This pins White back on his ears. My back checkers are in no danger. I playto win rather than playing not to lose.
Kit Woolsey: 8/4(2), 6/2(2).
Backgammon is a game about space. By making the four and two points Irestrict White's space to maneuver. I can then leave the midpoint in comfort,and his game is likely to crumble. My checkers on the bar point are in nojeopardy at all. They will simply be an obstacle for White to get by safely.My play will generate far more gammons than a running play.
Chris Yep: 18/14(2), 8/4(2).
Blue will be ahead by 10 pips after this roll, so the natural instinct is to race (18/10(2)). I believe that Blue can do even better though. Since the race is still somewhat close, White has good chances if he can split to and eventually make the 21-anchor. If instead Blue plays 18/14(2) 8/4(2), the best White can do is the 22-anchor. Blue will still have good chances to safely clear the 14 and 13 points. (if he rolls a lot of 2s he may have to clear the 13 point first). In the meantime, Blue will have excellent control of his outfield.
If White can't escape his back men, he won't be able to hold onto the midpoint for much longer. This might mean that Blue should stay on his anchor and work on his offense. 13/9(2) 8/4(2) makes a broken 5-prime but leaves a blot. However, even if White hits the blot, Blue will have a fair number of return shots from the bar. Also, White only has a 3 point board with the 5 point still open. There's a good chance that even after a hit, White may not be able to make his 5 point. Still, there's some danger of Blue getting stuck after a hit.
I don't like 13/9(2) 13/5 or 13/5 8/4(2). 13/9(2) 13/5 leaves a stripped and awkward position. In particular, 6s don't play well next turn. 13/5 8/4(2) is better, but is inferior to 18/14(2) 8/4(2) in my opinion. Compared to 18/14(2) 8/4(2), 13/5 8/4(2) is slightly better for the immediate prospects of making the 3 point, while significantly worse for outfield coverage.
8/4(2) 6/2(2) makes a broken 5-prime, including the important 4 point. It preserves Blue's timing -- if White can't spring at least one back checker, White will probably have to break his midpoint before Blue has to break the 18-anchor. The major disadvantage of this move is that it strips the 6 point, making it easier for Blue to split to and make the 22 point. Also, the spares in front of White's anchor could come in useful to handle future awkward rolls. In addition, Blue loses the 8 point, which is a landing spot for the checkers on the midpoint.
Probably 18/14(2) 8/4(2), 13/9(2) 8/4(2), and 8/4(2) 6/2(2) are all close. When in doubt, play thematically. In general when one is ahead in the race it is thematic to disengage contact in order to race. In addition, moving all 15 checkers as a unit allows Blue more flexibility, which may help him to extend his prime from the back as well as the front. I'll choose 18/14(2) 8/4(2).
Summary: It was a close vote, but the concensus appears to be against running. I agree.Gammons still count double.
Play Votes Score8/4(2), 6/2(2) 5 10018/10(2) 5 9013/5, 8/4(2) 1 6018/14(2), 8/4(2) 1 6018/14(2), 13/9(2) 0 5013/9(2), 13/5 0 4013/9(2), 8/4(2) 0 40
Problem 4
| 125 147 | White money game Blue |
Chuck Bower: 13/9, 11/9.
White has much the better of this position. Blue owns security in thedeep anchor and needs to concentrate on keeping White's back checkertrapped. Building the 9-point goes farthest in that plan. AlthoughBlue doesn't want a third checker back, any other play gives Whitetoo much freedom in waltzing home.
Steve Clark: 11/5.
Plays involving 7/3* are too wild for me. Take it from me; don't leave 5blots when your opponent has the stronger board. You might not beleaving 5 blots but it sure could seem like 5 in a roll or two.
13/9, 11/9 makes 5 point of the prime, but it does leave a double directshot. I am reluctant to make this play for reasons that I can'tentirely quantify. I think the problem is that White is likely toescape no matter what I do. If this is the case I will be poorlypositioned to play big number because I will be overrunning my 5 point.Unfortunately this line of thought is not very convincing, at least notto me. Well if White is likely to escape in any even, why not 11/5.This tries for the point I really want. It keeps the rest of myposition together. If I get hit, maybe I will be able to make the 20point, something which is rather unlikely at the present. As a matter offact, I would be much less inclined to to slot the 5 if my rear checkerswere placed differently. That fact that they are rather blocked on theone hand but that they are advanced enough to avoid major gammon dangeron the other hand makes slotting the 5 point very attractive. Anotherplay with a similar idea is 13/9, 13/11, but I like slotting the 5. Itis the play that goes after what I really want.
Malcolm Davis: 11/5.
Where do these plays come from?! Very tough. I slot the 5 point. I almost never slot, as I haven't figured out when it is right thematically, and I know it is often wrong, but I'll tryit this time. Would like to make the 9 point, but don't want to leave the double shot.
Ray Fogerlund: 11/5.
I don't know what the best play here is, but maybe the bestthing about this position is it is hard to do something really wrong. Maybeit is best to block 6s, but the timing argues against that. Other playsseem to try to minimize danger. I like to exert psychological pressure whenI play, and I think slotting the 5 point here does it subtly. White has tosee that if he doesn't get a 2 that I am threatening to get a 5 prime. Thisis the biggest threat that Blue can generate in this position, I think. Ithreaten to win with a prime, and if I get hit, it is no big deal, itimproves my timing and I can fall back on the deuce anchor game with littlefear of getting gammoned.
Hal Heinrich: 11/7, 8/6.
Blue is in bad shape in this position, and should play conservatively.None of the plays which leave a shot gain enough to justify the risk.
Ron Karr: 11/7, 8/6.
First, I'll rule out the attacking plays: too risky with a weaker board, lowchance of gain: even if I manage to make a good board and avoid gettinghit, I'll still have to escape the back checkers. My strategy is:hope for some luck in the priming battle, and fall back on the anchorgame if necessary. The question is: should I play safe and try toavoid getting more checkers sent back, or try hard to improve theposition? Making the 9 point is good, but it leaves a double shot, andthe 5 point is still open. Slotting the 5 is tempting, but even ifWhite doesn't hit he'll still have 6s to escape. So safety seems best,and 11/7, 8/6 seems like the smoothest play.
George Klitsas: 13/9, 13/11.
Play a ( 13/9 13/11) Conceding the midpoint in a somewhat everyday position like this one, is out of our basic patterns as human-nets (should I risk the term human-bots?). In each position, one should consider all plausible moves, though : often the best move is out of these basic patterns. Play a certainly has merit. White is hard-pressed to roll a six (or a 2-5 at least), otherwise things could start becoming dangerous, for Blue is almost ideally placed for attack and/or a priming game. The true priming potential of this position (after play a) is �hidden�, in the meaning of �much more than one thinks, before playing the position out�. Combined with his attacking chances against White's runner and White's difficulty in making his five point (White must be careful in leaving blots in the outfield), this play results in a very low negative equity for Blue, around minus 0.33 points per game on a two-cube (Blue won 16 plain and one gammon, White 14 plain and 5 gammons in 36 games). One notices the unusual difficulty of White to bring in his checkers (something common in slightly varying degrees after all the other initial plays, it's a characteristic of White's structure) with five's the most awkward numbers and two's following in the ugliness list.
Play b (13/9 11/9) White has more hitting numbers here that slow down Blue's game. The good-looking blocking position of Blue is kind of an illusion, somewhat cramped as it is. It's true that Blue will score some wins because of the escaping difficulties of White's runner and that White has some awkward initial rolls (4-6, 5-6), as well, but, overall, play b is less dangerous for him compared to play a. Blue won 16 plain games, White 12 plain and 8 gammons for an overall equity of -0.67 points per game for Blue on a two-cube.
Play c ( 13/11 7/3*) So many blots strewn around just can't...
Play d ( 11/5) Not so bad. Could work on a good day, but notice the duplication of threes for Blue if White rolls something like a 3-1, taking his chances and making boldly his five point, which is in general difficult to make naturally later on. After this sequence, Blue needs threes to cover his five point, to hit on his three point and to hit on his ten point. Only double threes qualify for doing everything. White has some awkward rolls after play d (including a hitting-awkward roll, namely 2-3*), but the conclusion is that Blue's position has not big priming potential , it has more attacking one, which is not high either, so my feeling about play d coincides with the result of a rollout of 36 games (14 plain for Blue, 18 plain and 4 gammons for White) for an overall equity of 0.67 points per game for White on a two-cube.
Play e ( 11/9 8/4) I can't see how this play could be better than play d for example. It creates seemingly more builders but at the cost of burying a checker at a moment when making the five point is number one priority for Blue.
Play f ( 11/9 7/3*) I wonder how much should I ask to be paid to make such a play : half a point perhaps? A little less?
Play g ( 11/7 8/6) The only alternative that does not leave a shot - only for that reason one should take the time to have a look at it. Ok, I looked : Blue has considerable difficulty playing sixes and, in general, does not rate to make progress here barring miracles. What is hidden and of utter importance here is that if White does not hit any Blue checkers (something quite expected ) then Blue's timing is such that his own board breaks usually before White is obliged to leave any blots during the bear-in and bear-off. In variations a, b, d and e Blue does not want to be hit, of course, but, when this happens, it's a blessing in disguise, giving him good timing for a two-point game.
Play h ( 8/6 7/3*) If I was eager to take something less than half a point to adopt play f, I would probably not settle for less than that here.
Bottom line : I vote for play a (13/9 13/11).
Laila Leonhardt: 13/9, 11/9.
Blue is in a lot of trouble here. By creating the 5 point prime, he might be able to counter prime White while trying to escape. If the blot on the 13 point is hit, it does not deteriorate Blue's position further.
Rob Maier: 13/9, 11/9.
While counter priming may seem to be an unlikely route to victory, makingthe nine point also prepares for an attack should that avenue become morepromising. While we don't wish to be hit, it could turn out to improveour timing, even allowing us to anchor on the 20 point with a bit of luck.
Snowie: 11/5.
With so few checkers to play with, I have to make sure every checker goeswhere it belongs. If White doesn't roll a two or a six, I will be in positionto do some serious damage. If I am hit, I will still have a playable position.
Kit Woolsey: 11/7, 8/6.
Making the nine point is not consistent with the position. White has too manymen in the outfield for me to win a priming battle. I need to attack. Hittingloose would be nice, but there is no convenient way to do so. My best bet isto bring the firepower into range with the safe 11/7, 8/6. By keeping themidpoint I put pressure on Blue's outfield checker, and I may be able to attacknext roll.
Chris Yep: 13/9, 11/9.
I don't like attacking (7/3*). Blue's game will be too hard to put back together after breaking the bar point. I think that Blue's game plan should be to try to win a priming battle by containing White's back checker. With that in mind, 13/9 13/11, 13/9 11/9, and 11/5 are the top contenders. 11/7 8/6 reduces builders on the 5 point and decreases Blue's chances of making the 9 point. 11/9 8/4 slots the 9 point, but brings in a builder past the 5 point.
Between 13/9 13/11, 13/9 11/9, and 11/5, 13/9 11/9 makes the 9 point, while the other two moves only slot a key point (the 9 and 5 points respectively). Even though 13/9 11/9 gives White a lot of shots, it prevents White from escaping in one roll (except 2-5; 2-6 escapes but leaves a double shot). Getting hit is not that costly, since Blue already has two men back and is behind 16 pips with White on roll. In fact, with a 3rd checker he may be more likely to make the 20-anchor, while with 2 checkers back it will often be too risky to try for an advanced anchor by splitting 23/20.
Summary: A variety of choices resulting in a virtual 3-way tie. It is not clear what the proper game plan hereshould be. An interesting position.
Play Votes Score11/5 4 10013/9, 11/9 4 9011/7, 8/6 3 9013/9, 13/11 1 7011/9, 8/4 0 5013/11, 7/3* 0 5011/9, 7/3* 0 508/6, 7/3* 0 50
Problem 5
| 142 186 | White money game Blue |
Chuck Bower: 22/21, 15/10.
Compare the current position with the opening setup. White has madetwo new points (9- and 7-) and gotten one of his back checkers intoBlue's outfield. Blue has moved 24/23(2) and gotten three checkerssent back! It's time Blue trowel some mortar between bricks. 22/21makes a good defensive point which is not blocked (unlike 23/22).
Now it's down to 15/10 or 8/3*. Hitting takes away half of White'sroll, and finishes the cliche' "when in doubt...". Is that enough?15/10 takes a checker off the point White most wants to make andbrings a builder for the point Blue really wants--the 5-point. Twoanchors won't put much fear into an opponent, but an efficient homeboard might. I like the pure play here: 22/21, 15/10.
Steve Clark: 15/9*.
It is not clear what I am trying to accomplish here. Do I want to playa backgame? If so, I still don't quite know how to accomplish it. I amnot really far enough back to make it work. If I play 22/21, 8/3*, I amnot putting my checkers in the right position. When playing a back gameI must have prospects for a prime or the backgame is worthless,particularly when I am not far enough back. 22/21, 16/11 has the sameproblem.
Plays involving 23/22 don't look right because I really want the 21point, not the 22. Furthermore these plays also suffer from the factthat I am not putting my other checkers in the right place.
21/15 has some attractions. This play builds a very useful point. Thedisadvantage is that my back checkers are poorly place. I want a betteropportunity to make a more advanced anchor. However, my opponent has nospares which can be used to make inside points safely. I will have areal chance to make a more advanced anchor in the roll or two. Thisroll looks more attractive that the backgame plays.
Another real possibility is just to play 15/9*. Why not? He does nothave the better board. This play will drive him back. If he hits me, Imight have better timing to play a back game, or possibly the hittingcontest will just go on. 21/15 might be right, even one of the backgameplays could be correct, but I will go with 15/9*.
Malcolm Davis: 22/21, 8/3*.
Finally! May not be right, but I like it. Can't imagine not making the 21-point,and a bland 5 like playing to the 10-point is just not my style. Let's play some backgammon!
Ray Fogerlund: 15/9*.
In general, when you get a chance to hit you should do so. Idon't think this position is any exception. Also, you never want to settlefor a back-game when there are other options available, so making the 21point is too passive. White will not be able to prevent us from making asecond anchor should the need arise later. When you hit, you never knowwhat might happen, and in this position it happens to place a Blue builderin a favorable position. If White hits from the bar, then make a secondanchor, but for now... keep hitting.
Hal Heinrich: 22/21, 15/10.
21/16 is the kind of play that is too often overlooked -- it escapes aback man creating outfield control and gaining timing. However, in thiscase it leaves Blue's defense too weak. So we make the twenty-one point. That leaves as 15/10 as the natural play. It gets off a pointthat White wants to make and aims at developing a home board.
Ron Karr: 22/21, 8/3*.
My first thought is to hit 15/9*: buried in the race, and White has no board, sowhy not? I should be able to make a second anchor at my leisure,right? Well, maybe not. White will have small doubles to blast mewith, even from the bar, and he'll have them for several rolls if Ican't roll an ace right away (and even if I roll an ace I may want touse it to attack). So I'm thinking maybe I should just make the anchorright away and then hope to have some attacking chances, falling backon a reasonable 2-4 game if nothing works out. And by hitting 8/3*maybe I can prevent the other blot from getting away after all.
George Klitsas: 21/15.
Play a ( 23/22 15/10) Why Blue is not anchoring on the twenty one point if he wants to play half of his move there? Why Blue wants to risk being hit loose with a two from White's heavy stack on the six point? Why is he leaving three blots strewn around for no visible plan?
Play b ( 23/22 8/3*) Same questions.
Play c ( 22/21 15/10) Effective or not as it might (or might not) prove in practice, at least this play is made with a clear plan - locking a second anchor in order to have at least the skeleton of a backgame and try to make the best of it in the front battlefield. This plan looks not bad. Having secured the second anchor back, Blue can hit or slot freely in his inner board. If he is hit, his timing for a backgame becomes better, if not he's poised to make points and try to win forwards. In practice, in a set of 36 games, Blue won 14 plain games, White 13 plain games and 9 gammons, for an overall equity of -0.94 points per game for Blue on a two-cube.
Play d ( 22/21 8/3*) A little better contact, control, flexibility and smoother positions compared to those after play c for Blue, resulting in somewhat better timing in general. Other than that, plays c and d are quite similar in nature. Hence, the difference in equity terms between these two plays has to be small.
Play e ( 21/15) Making a crucial point, one that White would be more than willing to make himself in order to extend his four-point prime backwards and restricting efficiently Blue's back checkers. Like in the tale of the naked King, White's position suddenly shows all of it's weaknesses - his cramped front game, his two blots that even if they get connected temporarily (say with a roll of 5-1) will have a hard time trying to join the main body of their brothers - along with some immediate awkward rolls (like 6-4). On the other side of the picture, Blue is well positioned to make progress. True that Blue with only three checkers back in this variation, won't find himself often in a backgame, reducing in a way his �ways� of winning but we have seen that such an argument is actually not an argument in itself, should be co-evaluated with other considerations. Here, for example, the reduced number of White gammons more than compensates for that loss. In 36 games that I played, Blue won 16 plain games, White 15 plain and only 5 gammons, for an overall equity of -0.50 points per game for Blue on a two-cube, much better than c (presumably d, as well) and the best so far.
Play f ( 15/9*) This is actually similar in nature with plays a and b, perhaps a little better than those, far from a candidate for the best move in any case.. Here as well (not to mention some crushing small doubles from the bar), White will hit loose on his four (even three, sometimes) point [from his heavy six-point, of course], planning to make the point and deprive White permanently of these anchors - if he's hit back, he won't have much trouble recirculating and making some important points of his own in the outfield.
I think that play e (21/15) steps out as the clear winner here.
Laila Leonhardt: 22/21, 8/3*.
White has solid outside prime but still no board. Blue is in an excellent position to go for a backgame. 4-2 is not a strong backgame to hold, but there should be lots of possibilities for Blue to create yet another point inside White's homeboard, making it very hard for White to bear his checkers in and possibly leave several shots very early.
Rob Maier: 22/21, 8/3*.
The ace is easy. We haven't committed to a backgame yet, but the securityis nice. Unstacking the eight point doesn't have a downside. If thechecker is hit, we improve out timing for the backgame. If not, we havestarted a point in our board. Taking half the roll away is nice as well.
Snowie: 22/21, 8/3*.
Lock up the anchor first, and see what happens. I can win this positionfrontwards, backwards, or sideways, and it is important to avoid any bigaccidents while things develop.
Kit Woolsey: 15/9*.
Since White has no inner board, making an advanced anchor isn't vital rightnow. I should have plenty of time to do that later. Right now it is importantto send a second White checker back. This way I am not so buried in therace, and it is much easier to contain White if he has two checkers back.
Chris Yep: 22/21, 15/10.
I prefer 22/21 15/10 over 23/22 15/10 and 22/21 8/3* over 23/22 8/3*. The 23/22 plays spread out the back men in the hopes of establishing an advanced anchor or getting more indirect shots at any blots White leaves in the outfield. However, the potential gain is small. The extra indirect shots are minimal since White can often play safely onto his 4-prime. Blue can already establish an advanced anchor by playing 22/21. It's not even clear whether the 20-anchor is better than the 21-anchor. The downside, the lack of a second anchor, is significant. If White rolls doubles for instance, Blue could quickly find himself in trouble.
I like making the second anchor. This shores up Blue's defense and avoids the "accidents" that would occur if White rolled doubles, pointing on Blue's head. Although outside primes are generally weak, they're only weak if the opponent establishes an advanced anchor. If White grabs his 5 and 4 points before Blue can anchor there, Blue will be in trouble. 22/21 solves this problem now -- the attack can wait. After making the anchor, Blue can win both forwards and backwards, depending on the dice.
For the 5, I prefer 15/10. 8/3* brings a checker in too deep and making the 3 point later on is no bargain. Blue doesn't have many checkers to spare and so should instead try to concentrate on the 4 and 5 points. 15/10 feels comfortable and if hit, Blue can either drift toward a backgame or continue to try to win forwards, depending on the dice.
Summary: A difficult position which can take a lot of different branches. It is hardto fault the choice of the panel, which keeps many avenues open.
Play Votes Score22/21, 8/3* 5 10015/9* 3 8022/21, 15/10 3 8021/15 1 6023/22, 15/10 0 5023/22, 8/3* 0 50
Problem 6
| 166 146 | White money game Blue |
Chuck Bower: B/21, 14/13.
This looks like a textbook position from Magriel's "Safe Play vs. BoldPlay" chapter. Blue leads in the race, has fewer checkers back, noanchor, and a weaker home board. Play safe. B/21, 14/13.
Steve Clark: B/21, 14/13.
Our advantages in this position are that we are well ahead in the raceand we only have one checker back. Our disadvantage is that we don'thave as strong a board as our opponent. We can play to his advantage byleaving multiple blots around for him to hit or we can play to ouradvantage by playing safe and trying to escape. B/21, 14/13 looks likea beginner's play it is my play also.
Malcolm Davis: B/21, 14/13.
Too much racing lead to hit on the 5-point, although it's great when you get away with it. This type of play was not in my vocabulary a few years ago.
Ray Fogerlund: B/21, 6/5*.
I think it is too early to quit playing and try toprotect the 20+ pip lead. Fight for the 5 point, and 5s are duplicated allover the board. At least if White throws a 6 there won't be much that shecan do. If I am not hit, I am close to a double with my men optimallyplaced to escape and or make the 5 point and a four point prime. 5s willplay well for White anyway, so why not challenge her to do it? Make theplay that works best when she FAILS to get her five! I don't want to besitting back on the ace point while she is deciding whether to make a fourprime or hit my outfield blot. Hitting places my back man on the ace pointand leaves 5s and 2s and 4s, so put your checkers where they belong andplay some backgammon!
Hal Heinrich: B/21, 14/13.,
Blue is up in the race and has a weaker home board. Both of these factors argue against getting involved in a blot-hitting contest.Hitting on the nine point is very strong -- primarily because it workstowards splitting White's army in half. White can only hit the blot onfourteen point at the cost of the midpoint. It's a difficult choice,but I'd opt for safety here.
Ron Karr: B/21, 14/13.
It's normal to play safe here, with a racing lead and weaker board. It'stempting to attack 6/5*, trying to make the 5 point, which would begreat, but it leaves a ton of returns. 13/9* is tempting too, but italso leaves many return shots. So B/21, 14/13, leaving only 1 blot,seems like the play. It's a bit scary to leave White complete freedomto attack, but only 4s (which are duplicated) and 2s are really good,and if I'm pointed on it's still not the end of the world.
George Klitsas: B/21, 6/5*.
Play a ( B/21 14/13) The conservative approach - lifting the blot but ceding the initiative to White. Blue's position is undeveloped and not a menacing one and White's attack proves itself stronger than one might think at a preliminary glance - his prime exceeds surprisingly easily and puts Blue on the defensive. In a 36-game rollout I was hitting as White on the four point almost with anything (even with 3-1) and the result was a little bit surprising as Blue emerged only as a slight favorite, of only +0.06 points per game. I am not quite sure that all these hits were correct, so the actual equity could be even lower for Blue, perhaps around zero.
Play b ( B/21 6/5*) �You have to have the fighting spirit. You have to force moves and take chances�. The words of a World Champion in another great war game, chess. The words of Bobby Fischer. Blue tries to make his five point unstacking at the same time his six point and noticing that most of White's entering [not to mention the dancing 6-6] sixes are awkward. If he succeeds in that, he will usually double and White might or might not have a take. If, instead, he is hit back, he might anchor on White's four point with a decent game. A fact that should be mentioned is that games after play b are much shorter on average than after play a (for that reason one could adopt play a perhaps when his opponent is in time-pressure!). I believe that play b is slightly better than play a, a feeling backed up by a short rollout of 36 games, which resulted in +0.17 points per game for Blue.
Play c ( B/24 13/9*) I don't like the marooned checker, I don't like three blots strewn around and the stripped midpoint, as well.
Needless to say, my vote is for play b ( B/21 6/5* ).
Laila Leonhardt: B/24, 13/9*.
Money game and the cube isn't turned. This is not a race. In spite of Blue's lead in the pipcount, Blue's strategy should be to play aggressive and try to gain a positional advantage. By hitting the checker on the 9 point, Blue gains from 10 of White's rolls and avoids stacking his checkers in inflexible towers.
Rob Maier: B/21, 14/13.
With a nice race lead, and outboarded 2 to 1, now is not the time to getinto a blot hitting contest.
Snowie: B/21, 14/13.
Elementary safe play vs. bold play problem. Everything points to the safeplay.
Kit Woolsey: B/21, 14/13.
I have a racing lead, and he has the stronger board. These factors pointto a safe play, and B/21, 14/13 is it. I immediately threaten to escapethe last back checker, which puts pressure on White to perform before he isready.
Chris Yep: B/21, 14/13.
I don't like B/24 13/9* at all. It strips the midpoint, creates an extra blot, and leaves White a lot of returns. Blue is ahead in the race and only has one checker back to White's three. Furthermore, White has a stronger board. These factors mean that Blue shouldn't want to get into a blot hitting contest.
If Blue chooses to hit, I prefer B/21 6/5*. This at least unstacks the 6 point, fights for the 5 point, and cleverly duplicates 2s, 4s, and 5s all over the board. However, I believe that it still gives White too many returns. Also, some of White's numbers which miss the blot on Blue's 5 point hit elsewhere (2-1, 1-1, and 3-3), which will reduce the number of rolls for Blue to make his 5 point next roll. In addition, 2-2, 4-4, 5-5, 5-2, 5-3, and 5-4 hit twice which is very costly for Blue since White will often be able to pick up the third blot while Blue tries to enter from the bar.
I prefer the simple B/21 14/13. As mentioned above, Blue has the weaker board, is ahead in the race, and has only one man back to White's three. This argues for a more conservative play. B/21 14/13 is my choice.
Summary: The majority of the panel clearly agreed that with a good racing lead the rightgame plan is to run away and win. We don't have to hit every time we seea blot.
Play Votes ScoreB/21, 14/13 9 100B/21, 6/5* 2 70B/24, 13/9* 1 60
Problem 7
| 133 130 | White money game Blue |
Chuck Bower: 7/1, 5/1.
The six looks like 13/7 and 4 looks like 7/3*, but playing the fullroll 13/3* is unappetizing. Note that White will be on roll down 13 ormore pips, and hoping for a hit to take steal the race lead. Why give himthe chance. 7/1, 5/1 gives Blue a stronger board to go along with therace lead, and leaves White no cheap shots.
Steve Clark: 7/1, 5/1.
7/1, 5/1 is a total weenie play. It leaves my men stacked up whileadvancing my position too far. It gives up all prospects for a prime.But it does make a third inside point which might be useful and it doesnot leave any blots. Also I get to keep my midpoint which is always agood idea when contact remains. Let's see if we can do better.
24/14 looks good except that it leaves 24 shots (Please don't tell me ifI have miscounted.). Do I get to claim 11/36's (Boxcars are also quitepoor for me.) of the time? Probably not. That seems like a lot ofshots when I don't get to claim when I am missed. 24/18, 7/3* leavesabout as many (This time I have not counted at all.). Ditto for 24/20,13/7 and 24/20, 7/1. We have to do better than this pile of junk.
That leaves 13/7, 13/9 and 13/7, 8/4. Both plays take risks whilereally trying to make something. If White escapes he will have a bigadvantage partly because we have abandoned our midpoint, but there is agood chance we can trap him. Of the two plays I prefer 13/7, 13/9 by afair amount. The other play attempts to duplicate aces, but even withduplication two blots are considerably worse than one. A good rule isto not leave gratuitous blots around unless there is some good reasonfor it. Furthermore it is generally easier to put the position togetherwhen a point has not been slotted.
So is 13/7, 13/9 better than the weenie play? I don't think so. Bigplays often have more defects than meet the eye. Even if I get awaywith the big play, he still will have lots of opportunity to trap myback checker. I only like big plays when they provide a clear solutionwhen they go well. In this position the big play could work withoutgiving me any real advantage. I will keep my position together with7/1, 5/1 and hope for better next roll.
Malcolm Davis: 13/7, 13/9.
Back to the tough ones. Just don't know. Seems as if you are in pretty good shape if you get away with it.
Ray Fogerlund: 24/20, 13/7.
This is the hardest problem! I would not be surprisedif making the ace point and awaiting developments is the winner, but it isnot my style. I want to escape, and I want to make a prime. I would haveliked to point on White, but that is impossible. So, I make my prime, andmove into position to run. Of course White will attack me, but aces areduplicated, and even though her builders are impressive, with any 2, 5, or 6she will not be able to point on me. If I do get pointed on, I will onlylose 5 extra pips in the race, much less than I would if I get hit in theoutfield. The subtle part of this play is that when White gets a 6 andruns, I have the best coverage possible from my midpoint and from her 5point.
Hal Heinrich: 13/7, 8/4.
24/14 is the natural play in this position, but a double shot is toohigh a price to pay -- especially considering how close the race is.Still, Blue has to leave White something -- so Blue should try to getgood value if White misses. After locking up the bar point with the sixBlue has two good choices for the four. Coming down to the nine is thenormal play -- and it might be right here. But I prefer duplicating aces with 8/4. It unstacks the heavy eight point, starts the importantfour point, and is not noticeably riskier than the alternatives.
Ron Karr: 13/7, 13/9.
With a racing lead, I'd love to play safe, but the only possibility is 7/1,5/1, and the resulting distribution seems too awkward. I could attack7/3* 24/18, but that leaves a ton of return shots. 13/7 13/9 hasseveral advantages: If White rolls a 6, he would have escaped anyway(while if I cleverly duplicate 1s with 13/7 8/4, White has good 1s and6s); and if White doesn't escape now, I'll have superb attackingchances on the next roll.
George Klitsas: 7/1, 5/1.
Play a ( 24/14) This play is conceivable, fulfilling a sound criterion : a clear route to victory. If White does not hit (but two thirds of all rolls hit) Blue is in very good shape, controlling even White's escaping trials in the outfield with double coverage. White has two awkward hitting numbers (the ugly 4-6) but on the other side the devastating 4-2 hitting both of Blue's blots. In 36 games, Blue lost 0.11 points per game.
Play b ( 24/18 7/3*) Breaking the potential four-prime and giving White several rolls that hit both checkers, does not look to me like the right idea here.
Play c ( 24/20 13/7) Making the four-prime but leaving less coverage of the outfield compared to (a) and, most important, failing to clear things up in case of immediate success, something that play a does, as we saw. Just compare the resulting positions (after play a and after play c) supposing that White rolls a 6-3 played 22/13. In 36 games Blue lost 0.17 points per game.
Play d ( 24/20 7/1) Looks clearly worse than play g (7/1 5/1).
Play e ( 13/7 13/9) If Blue is hit with any of thirteen rolls, he's practically lost. If he is not hit, he will encounter enormous difficulties bringing his rear checker all the way around - he just completely abandoned the outfield breaking his midpoint. Blue, in a sample of 36 games, lost 0.33 points per game. Seems that variation e is clearly worse than any of (a) or (c).
Play f (13/7 8/4) Duplicating aces but breaking the midpoint and leaving three blots strewn around - doesn't rate to be an improvement over the plays we've discussed so far.
Play g ( 7/1 5/1) Given his decent lead in the race, Blue adopts an appropriate strategy here, avoiding huge exchanges of equity that usually help the underdog in such a situation. A calm variation like g, which permits him to exploit often enough his race advantage is what Blue should strive for - if the position becomes a virtually no-contact one, then he should have a strong double or a claim in most cases. In a sample of 36 games, Blue won 0.11 points per game, so I vote for play g with both my hands.
Laila Leonhardt: 13/7, 13/9.
If White fails to hit the checker on the 9 point, Blue has a good position to start attacking/pointing on White next turn. Note that Blue cannot loose a gammon since the cube has not been turned yet, and should play to reach a position where he either loses a point or gets positional strength. This play leaves only 13 numbers for White to cash the game, while the 24/14 leaves 24 numbers for White to hit one of Blue's checkers.
Rob Maier: 24/20, 13/7.
I don't see a clear winner for this one. Making the ace point has theadvantage of not leaving any other blots, and we want to protect ourmodest race lead. On the other hand, the player that gets their lastchecker out first has a substantial advantage that usually more thancompensates for a small race lead, and making the ace gives our opponent agood chance to get out first. Of course, getting a second checker sentback would also do wonders for our opposition. Among the other plays, Ilean toward 24/20, 13/7, because it locks up a solid asset in exchange forthe risk of the second blot, and it also puts us in a position to try andescape. The more I look at the made bar point, the more I like this play,but I won't be putting any money on it.
Snowie: 24/14.
Simple game plan -- run home and win. The other game plans involve toomany complications.
Kit Woolsey: 24/14.
Anything leaves a shot except 7/1, 5/1, and that is too ugly for words.Given that, I might as well do want I want to do most -- get the back checkerout of hock. If I survive this play I will be in great shape, and ifWhite hits one of the blots I am far from dead.Other plays such as 13/7, 13/9 give White too many good things to do onboth sides of the board, and I still have to worry about escaping myback checker.
Chris Yep: 24/14.
Both players have a 2 point board, the race is close, and each side has one man back. In these types of positions both players have the same goal: escape one's own back man while preventing the opponent from escaping his. 24/20 13/7, coming under the gun and leaving a blot on the midpoint, doesn't look right to me. Similarly, 24/20 7/1, coming under the gun and dumping a checker out of play, doesn't look right either. 13/7 13/9 works well when White doesn't roll a 6 or 5-1. However, if White hits the blot (13 shots) it is disastrous for Blue. Note that many of White's misses do something constructive on the other side of the board. 13/7 8/4 duplicates 1s, but getting hit with a 1 is very costly (1-1 is very costly). 7/1 5/1 puts 2 checkers out of play and leaves Blue with a stacked, awkward position. On the other hand it doesn't leave any shots, which is important in a close race. However, the resulting position, with 5 checkers on the 8 point and 2 checkers out of play looks too awkward to me. If one of the checkers on the 8 point were moved to the 5 point, then I would choose this move.
The two remaining moves try to accomplish the goal of "escape while preventing the opponent from escaping" in different ways. 24/14 runs the back man as far as possible, while 24/18 7/3* runs the back man halfway while simultaneously knocking White farther away from escape. At first glance, 24/18 7/3* appears to be the "safer" move, since it only gives White one direct shot. However, appearances are deceiving! After 24/14, White has 22 single hit numbers (1-2, 1-3, 1-4, 2-3, 2-5, 2-6, 3-4, 4-5, 4-6, 5-6, 2-2, and 4-4) and 2 double hit numbers (2-4). After 24/18 7/3* White has 17 single hit numbers (1-2, 1-4, 1-6, 2-4, 2-6, 3-4, 3-5, 4-6, 2-2) and 8 double hit numbers (1-3, 2-3, 3-6, 1-1, 3-3). So 24/14 is safer in terms of White's immediate hit numbers. Furthermore, not all hits are equal. More of White's hits break the midpoint after 24/14 than after 24/18 7/3*. In addition, 24/14 provides more outfield coverage, which is important if White rolls 6-1, 6-2, or 6-4 (played 22/18* 13/7).
Summary: A variety of possibilities, from running, priming, playing safe, or acombination of these. Any of the panel's choices could well be right.
Play Votes Score13/7, 13/9 3 1007/1, 5/1 3 9024/14 3 9024/20, 13/7 2 8013/7, 8/4 1 7024/18, 7/3* 0 5024/20, 7/1 0 50
Problem 8
| 147 154 | White money game Blue |
Chuck Bower: 13/7*.
Blue is behind in the race and has a stronger board. 24/20 is solidand safe, but that play doesn't take advantage of Blue's strength or address his needs. 13/7* does.
Steve Clark: 13/7*.
24/20 looks obvious, unfortunately the 2 that goes with it is not.Furthermore if our opponent makes my bar point in return, he will havethe advantage with his lead in the race. It can't be right to leave agratuitous blot as well. This gives him far too many ways to getahead. Since 8/6 with the 2 stacks up my checkers rather badly, we willhave to look beyond the obvious start.
8/4, 6/4 has the clear advantage of making a third inner point. It hasa second benefit which is quite important but not so obvious, and thatis that most of his 5's play rather badly. He certainly would play 23/18but would not be too happy with most rolls of his other die. Of coursehe might make the 5 point on our head, but I make us a favorite afterthis play and it might be best.
Another good play is 13/7*. In general we should hit when we have thestronger board and are behind in the race. This is an attractive playand also might be correct.
When faced with the choice between a rather strange play (making the 4point) and a play with which I am familiar I tend to make the familiarone. If I have misjudged the benefits of the unusual play, I am morelikely to regret it. I could be wrong by a fair amount here but I willgo with the play we all know and love. When in doubt, hit him.
Malcolm Davis: 13/7*.
You've got to be kidding! It may be wrong, but if I don't make this play, I've got to give up backgammon.
Ray Fogerlund: 13/7*.
Just hit, and challenge White to hit back. Should Whitefail to hit me off of the bar I will tend to make a nice prime. In fact, toavoid that she will probably go ahead and hit me loose off of the 5 pointwhich will give me numerous shots to hit, or cover, or both! Don't settlefor holding games when you have a more forcing alternative. If you forceyour opponent to roll well to survive, they often fail to survive! Also, itis very important for them to feel pressured when they are playing againstyou. The added stress takes away from their normal deportment and orjudgment at the table and can yield dividends.
Hal Heinrich: 13/7*.
It sure is tempting to make the twenty point and then look around for atwo. The problem is that none of these deuces are very good -- I'd saythat 8/6 gets my vote. Hitting sends White back, starts an important point and uses Blue's advantage in inner board points. Why defend whenyou've got a good opportunity to attack?
Ron Karr: 13/7*.
Better board, behind in the race, opponent has two blots: seems like the time to hit. I don't see any point in anchoring, particularly since there are nogood 2s. Making the 4 point is worth considering, but I think it givesWhite too much freedom.
Laila Leonhardt: 13/7*.
Blue does not want to allow White a chance to create the important advanced anchor on his bar point. White still has no board and with a checker on the bar is not likely to point on Blue on the 20 point. Blue wants to be the attacker with a stronger board and an initial cube.
Rob Maier: 13/7*.
Making the bar point here is huge. We have the better board. We don'twant to give White his whole roll. Is there really anything to thinkabout here?
Snowie: 13/7*.
White's blot goes right back where it belongs. I want that bar point. Makingthe defensive anchor isn't very important since White has no board.
Kit Woolsey: 24/20, 6/4.
The security blanket of the defensive five point is very nice. White's positionis disjointed, and if he doesn't roll a five to anchor I can attack next roll.If he hits the blot my position is still very sound, and if he makes theanchor it is a very even mutual holding game. 13/7* leaves White a lot ofreturn shots on both sides of the board, and making the four point leavesWhite too many good numbers.
Chris Yep: 13/7*.
In the early stages, offense usually comes before defense. Here I especially believe that Blue should concentrate on his offense rather than make the defensive 20-anchor. Blue already has the stronger board. Both 13/7* and 8/4 6/4 strengthen his offense considerably. If Blue instead makes the anchor, he has an awkward 2 -- he will be forced to either leave a direct shot or strip the 8 point and pile a 5th checker on the 6 point.
Between 13/7* and 8/4 6/4, I prefer 13/7*. If this were Blue's first move in response to White's opening 6-2, 6-3, or 6-4 (played 24/18 13/x), 13/7* and 8/4 6/4 would be about equal. With that as a reference position, we can see that Blue has more incentive to play 13/7* here -- by playing 13/7* he protects his blot on the 20 point and increases the chance that he will make this anchor next turn. In addition, if White stays on the bar, Blue will have a very efficient double next turn.
Summary:The panel overwhelmingly says that offense comes before defense. We don'tneed the anchor. Ok, I'm convinced.
Play Votes Score13/7* 11 10024/20, 6/4 1 6024/20, 13/11 0 5024/20, 8/6 0 508/4, 6/4 0 50
1 2 3 4 5 6 7 8Chuck Bower 7/2* B/24, 10/8 18/10(2) 13/9, 11/9 22/21, 15/10 B/21, 14/13 7/1, 5/1 13/7* Steve Clark 8/5, 8/6 B/24, 10/8 18/10(2) 11/5 15/9* B/21, 14/13 7/1, 5/1 13/7* Malcolm Davis 7/2* B/23, 7/6 18/10(2) 11/5 22/21, 8/3* B/21, 14/13 13/7, 13/9 13/7*Ray Fogerlund 7/4, 7/5 B/23, 10/9 13/5, 8/4(2) 11/5 15/9* B/21, 6/5* 24/20, 13/7 13/7*Hal Heinrich 4/1, 4/2* B/24, 10/8 8/4(2), 6/2(2) 11/7, 8/6 22/21, 15/10 B/21, 14/13 13/7, 8/4 13/7* Ron Karr 4/1, 4/2* B/24, 10/8 8/4(2), 6/2(2) 11/7, 8/6 22/21, 8/3* B/21, 14/13 13/7, 13/9 13/7*George Klitsas 7/2* B/24, 10/8 8/4(2), 6/2(2) 13/9, 13/11 21/15 B/21, 6/5* 7/1, 5/1 13/7* Laila Leonhardt 8/5, 8/6 B/24, 10/8 18/10(2) 13/9, 11/9 22/21, 8/3* B/24, 13/9* 13/7, 13/9 13/7* Rob Maier 8/5, 8/6 B/23, 7/6 18/10(2) 13/9, 11/9 22/21, 8/3* B/21, 14/13 24/20, 13/7 13/7*Snowie 7/2* B/23, 5/4 8/4(2), 6/2(2) 11/5 22/21, 8/3* B/21, 14/13 24/14 13/7* Kit Woolsey 7/2* B/23, 7/6 8/4(2), 6/2(2) 11/7, 8/6 15/9* B/21, 14/13 24/14 24/20, 6/4Chris Yep 7/2* B/23, 7/6 18/14(2), 8/4(2) 13/9, 11/9 22/21, 15/10 B/21, 14/13 24/14 13/7*
