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| 106 84 | White money game Blue |
Ken Arnold: 6/1, 4/1.
Do not volunteer more than 12 shots versus a gin board.
Chuck Bower: 6/1, 4/1.
With a centered cube and a race lead, Blue might be close toa double. (Before seeing the roll I think Blue should have doubledthis turn. Since 1x, fan were the market losers, Blue got awaywith his conservatism.) IMO, unless White gets parked on the rail,Blue won't have a cash until he clears the 10-point. He may ormay not have a double, but White's take looks clear. However, if Blue can hit and White fans, then Blue probably has a cash with as few as four home board points. If White leaves the checkeron the midpoint (which I think he should after 6/1, 4/1) thenBlue will get some pick-and-pass and pick-and lift rolls. IfBlue hits White but has to leave a blot in the home board, canWhite double? Surely not--it looks like a beaver. Thus if I'mgoing to leave White a direct shot I want to have reasonablechances that if it is missed, I can cash.
One of the rules-of-thumb for for the 'Fram Law' ("pay me now orpay me later") is: "if I volunteer the shot now and it survives,am I pretty darn sure I won't have to leave a shot later?" HereI cannot say that, so paying now isn't the obvious choice. AnotherFram question is: "is opp's home side improving or deteriorating?"Here it's in a steady state but it's going south in two or threerolls.
If this were doubles I'd have my partner make the decision. :)Since it's not, and leaving a voluntary shot isn't obviously the better play, I'm going with chicken instead of beef.
Steve Clark: 13/10, 13/8.
6/1, 4/1 looks safe. White will have to run away next roll so maybewe will be able to play off the midpoint without having to leave adirect shot. Besides maybe we will get lucky and not have to leave ashot at all. Paying now is for people who want to look good in front ofbig crowds. The wimps take all the money.
Well that is the way I used to play. However, if you take a closerlook, you will see all sorts of thing wrong with playing safe. First,you are starting to lose your pip lead. 2 men to the ace point is a lotof wasted pips. Second, If you tear up your board, White doesn't haveto run away. He can stay around fearlessly waiting for you to exposeyourself. Third, paying now does kinda solve all your problems. Cuzyou will have a big double to go with your big play so long as youdon't get hit.
Suppose you make the little play. Are you going to have an easydouble? No way. Bring the crowd around me; I am ready to be a star!
Hal Heinrich: 6/1, 4/1.
This is a good problem because it pits two fundamental rules againsteach other in a critical situation. It's "Do not leave fatal shots"versus "Do not trash your home board". I would play safe with 6/1, 4/1 here. Getting hit results in losing a third of the gamesimmediately -- discounting the thirteen hits to twelve because of 6-1and 1-1 as returns. So after being missed you're fighting for yourshare of the remaining two thirds in a position where your opponenthas a straight-forward take. It's ugly, but Blue has good chances tostumble home activating the cube along the way.
Ron Karr: 13/10, 13/8.
If I leave a shot, White hits 13/36 of the time--I lose most ofthose, except when I hit a lucky return shot. The rest of the time I candouble, and I don't think he can take--even if he can, it can't be by much. Sobasically I win 23/36 of the time. Could I have better winning chances byplaying safe? I doubt it. (Logically, if I could have better than 2/3 wins byplaying safe, I should have doubled prior to this roll, since most numbers(except 6s) could play safe, and I have a bunch of market-losers with my 1s.)If I break the board, it's easy for him to leave his blot on the midpoint, whichmakes it hard for me to clear my midpoint.
George Klitsas: 6/1, 4/1
play a (13/8 13/10). One can roughly calculate the equity of this play as follows (assuming a set of 36 games):
*In 13 games Blue is hit. In 3 of them (White rolls 63 or 33) Blue can resign without rolling. In the rest 10 Blue can hit with a lucky shot from the bar becoming the favorite. Without going into details, it seems logical to give Blue one of these 10 games. So, in this subset of 13 games, Blue is minus 11 points .
*In the rest 23 games ,when he is missed, Blue has a strong double (except when White rolls 66 or 55 perhaps) and White has a narrow take (he is behind enough in the race in order to have only slim chances of taking his men off first, but not behind enough in order to keep always his anchor- which will give Blue some pick-and-pass rolls in some games). Lets give him plus 19 points in these 23 games.Plus 19 minus 11 is plus 8 (in 36 games). So Blue's equity if he adopts play a, is +8/36, around +0.22points per game.
Play b (6/1 4/1). Here a straightforward calculation is out of the question but the play surely has merit, since, after White's roll (nothing much happens, White must only take care not to move his checker on his midpoint) , Blue is obliged to leave a direct shot only if he rolls 65,63,62,51 and 41. The five big doubles are game-winners or very good rolls anyway and the same is true for pick-and-lift or pick-and-cover rolls, if this can be said, namely 61,31,21 and 11, depending on White's response. Also good is 64, remaking the 4-point. The rest 12 rolls (54,53,52,43,42,32) break the 6-point but nothing is lost - in a way. Once more, one is left with a proper rollout as the only means to see what's going on. This is what I did, 108-games, taking care to give White the theoretical percentage of hits, when Blue was exposed to hits. The result of this rollout was +0.32 points per game for Blue, so I have a strong preference for play b.
Laila Leonhardt: 6/1, 4/1
White's board, is too strong to leave a volunteer shot here, and he will be moving the blot from the midpoint next turn, leaving a nicer option for Blue, to clear with only an indirect shot.The basic motivation for playing 2 from the midpoint is: If not hit, you have to able to cash the position, and the clearing options don't look like they are going to improve in the new few moves.Giving away 13/36's here, seems like a bit too much when the clearing options are improving next turn.
Rob Maier: 6/1, 4/1
Our goal in this position is to clear our midpoint and ten point leavingas few shots as possible. We have two choices, either to start theprocess now with what we've been given, or we can throw it back, and hopeto do better next roll. We can compare the possible rolls next time withthe 5-3 we rolled this time, and if we find that 5-3 is a better thanaverage start, we play 13/8 13/10, and if not, we play 6/1 4/1. Thisis complicated somewhat by the fact that the cube is in the middle. The first question to ask is, "If I bring two down and am missed, what are thecorrect cube actions?" This looks to be a strong double, but in view ofWhite's fine board, I think it still a take. This alone is usually enoughto make "paying later" correct. However, "paying now" could still becorrect if, on average, we do worse in our attempts to clear afterwaiting.
If White elects to remain on the midpoint, any ace will be an improvementfor Blue. Even though 1-4 and 1-5 leave shots, when White misses they arealso a favorite to remain on the roof, an easy cash. Add the other fivesets, 4-6 which remakes the five point board, and we have 18 numbers whichare better starts than coming down with the 5-3. On top of this we stillhave 3-4, 3-5 and 3-6, which combined are the same as coming downoriginally (actually slightly better, 3-6 leaves two less shots, while 3-4leaves only one more shot, as compared to the original 3-5.) So it wouldseem clear to play safe on this roll.
White may elect to leave the midpoint, but I think this is still betterfor Blue, as we can run from the midpoint, leaving only indirect shots, less than half the number we would leave by bringing two checkers down.
While not my usual philosophy, in this case, the ace is the place.
David Montgomery: 13/10, 13/8.
Usually you don't volunteer, especially against a perfect board.But after 6/1, 4/1, Blue's position is quite fragile, and it's unlikelyhe'll be able to get home without giving White better hittingopportunities. 13/10, 13/8 appears to give Blue a good cube on themisses, and I think this is enough to make it the right play.
Tony Moutzouris: 13/10, 13/8.
Tricky opening problem, my initial reaction was to play 6/1 4/1. Generally speaking I don't like volunteering shots in these kinds of positions unless absolutely necessary. However closer inspection of the position made me change my opinion. Playing 6/1 4/1 will leave Blue with a blot in his inner board and a position that's completely stripped. White will probably be able to hold his position without breaking his inner board for at least one more roll, possibly two rolls. He will leave the blot on Blue's 12 point applying pressure on the 13 point. Chances are unless Blue rolls doubles on his next roll he will lose his 6 point in his quest to continue playing safely or if he rolls a 6 White will get a direct shot immediately. Whatever happens unless Blue gets lucky his position will go down fast if he plays 6/1 4/1.
The fact that the cube is centered is important in this position. Cube access argues for the bold play. If Blue is not hit after 13/10 13/8 he will have a very efficient cube. White probably has a take but after playing 6/1 4/1 Blue may never get the opportunity to double or he may roll a big market loser.
Putting it all together it seems correct for Blue to give the shot and pay now rather than later.
Snowie: 6/1, 4/1.
I'm not giving away 12 game-winners when I have the advantage. When in doubt,pay later.
Kit Woolsey: 13/10, 13/8.
Dumping two checkers to the ace point both costs considerably in the race andstrips away the important builder on the six point. If Blue survives leavingthe shot, he will have a very efficient cube coming up. White's cube if theshot is hit isn't nearly as efficient.
Michael Zehr: 6/1, 4/1.
If Blue volunteers a shot and White misses, Blue isn't homefree, so it isn't worth giving up the shot. White will likely have toclear the midpoint next turn relieving much of the pressure.
Summary: The majority voted for paying later, which may well becorrect considering White's strong board. However I wonder if cube accessmay be enough to swing the decision.
Play Votes Score6/1, 4/1 8 10013/10, 13/8 5 80
Problem 2
| 108 119 | White money game Blue |
Ken Arnold: B/20, 5/2*.
Hit the guy! "When in doubt, close him out."
Chuck Bower: B/20, 8/5.
Blue is only a few pips behind in the race, so White's escapewon't necessarily result in a cube turn. Therefore I don't seethe need to put it all on the line with 5/2*. Why give White 20rolls to take a commanding race lead when only 13 is an option?Besides, I like a 5-point board better than a 4 and 2 halves! Even if the hit works, you still have to put humpty dumpty back together again.
Steve Clark: B/20, 8/5.
KG calls plays like B/20, 5/2 "banana split plays" because you haveto be bananas to consider them. My own rule of thumb is that you haveto be in a desperate position to consider a banana split. They kindawreck your board if they don't work. Here I don't feel that kind ofdesperation. I will still have many chances even if he hits me on my 8point. Further, any roll which doesn't get him out of my board willleave me in great shape. This all is a little tough to quantify, but Iwill play 8/5.
Hal Heinrich: B/20, 8/5.
B/20, 5/2* is a reasonable try in this position, but I don't believe itis quite there. Breaking your five-point home board to put your opponent on the roof against a four-point can be very effective --especially if you are vulnerable to attack otherwise. But that isn't the case here. Look at it this way: White is just as likely to remain stuck behind the four-prime as to dance. And after either good sequence, Blue has about equal chances to win the game. Hitting does provide extra gammon chances because of White's dangling blot, but what happens if White escapes or comes in? In a cubeless game, Blue has better chances with a stronger board -- it could be tough to put back together after being hit from the roof. But here, Blue can expectsome difficult take/pass decisions after White escapes -- so the cubeless results may be misleading. However, Blue retains some racing chances if White escapes with 5-2, 5-3 or 5-4. I evaluate thesetwo plays as close, but would hang onto my assets with B/20, 8/5.
Ron Karr: B/20, 5/2*.
A tough one. Positionally, 8/5 makes sense, because my 5-pointboard is my best asset, and by breaking the 8 point I create new builders forthe 2 point, which I'd like to make. However, tactically I have a problem. 20of White's numbers escape his checker, and 13 of those hit, after which I'll behard pressed to take a cube, because I'll have poor racing equity and, I think,poor chances to hit a shot. If he escapes without hitting I still have racingequity.
The good news comes if he can't escape; then I can attack next time & maybeclose him out. But he probably will have been able to safety his blot, so therewon't be many gammon chances.
So should I hit 5/2*? Even reducing my board to 4 points, I still have the edgein board strength. If he happens to fan for a while, I may be able to snag theother blot and close the board. That will still take some work$B!>(Band White willstill have a couple of chances to enter and possibly hit back. White has 20numbers to hit right away (the same as his chances of escaping if I don't hit),although I may be able to enter and return hit, etc. In general, though, itseems like contact is in my favor. White's board is kind of awkward, and if Iget a few checkers hit, it might be hard for him to come home safely. So I'mnot sure, but I'll vote for the hit.
George Klitsas: B/20, 8/5.
A short rollout (36 games each case) was enough to make up my mind. The actual gap between the relevant equities is unusual and unfair according to my feeling, still it was sufficient to make me vote for play a without further investigation.
Play a (b/20 8/5). If White hits with 13/36 numbers, Blue is practically lost. If White escapes without hitting (7 numbers) Blue is still in the game. If White does not escape (16 numbers) Blue can attack White on his 2-point with excellent chances of closing him out, since he already has a 5-point board. What is not obvious in this case, is a fair amount of gammons won by Blue, even without hitting the second White blot. Equity for Blue =+0.19 points per game.
play b (b/20 5/2*). Sort of panic. If White hits with 20/36 numbers, Blue is practically lost (often White is entitled to go for the gammon for a while). If White dances, Blue is not finished. Threes and sixes cover, threes are duplicated , but, strangely enough, double threes break the board. Equity for Blue =-0.50 points per game.
Laila Leonhardt: B/20, 8/5.
After moving the 8 pips, Blue has almost an even race.If White fails(16/36) to hit or pass the blot on the 8 point, then Blue will have a great advantage and become a huge favorite in the game. If Blue hits on the 2 point, it could be difficult for Blue to remake the 5 point, and the moment White reenters he would be back in the game. And if White hits one of the 2 blots, Blue will be facing a recube that he probably won't be able to take.
Rob Maier: B/20, 8/5.
Over the board, I'm sure I would quickly snap off 8/5 in disgust. We cancompare the two plays by grouping White's responses. Although the rollsaren't the same, we can group them such that the number of rolls is thesame. After 5/2 hitting, I've split White's fanning rolls across groups Aand B, and Blue's entering rolls across C and D. Likewise, after 8/5,White's rolls that don't come out are split between rolls that safety thesecond blot (Group B), and those which don't (Group A). The rolls that docome out are split between hitting numbers (Group D), and non-hittingnumbers (Group C).
Group A - White fans vs. White unable to leap OR safety his second blot (6rolls) - A slight edge to the hitting play here. Blue can choose to coverthe blot on the two point with the blot on the five point, rather thancovering one and leaving the sixth point slotted. Trying to cover aslot may be awkward on the following roll, as Blue needs to worry aboutjumping a checker. Hitting the second checker is almost as good as acloseout, so Blue doesn't need to make an entering roll for White anybetter by leaving a blot there to hit if he can avoid it.
Group B - White fans vs. White unable to leap BUT CAN safety his secondblot (10 rolls) - In this group, the hitting play is easily superior, asBlue's gammon chances are greatly diminished with the second blot nolonger in jeopordy.
Group C - White enters vs. White leaps BUT DOES NOT hit. (7 rolls) - Inthis case, the non-hitting play is superior. Blue will still have a fivevs. a four point board, will probably have eight or more hitting numbersvs. one or zero, and will be only slightly behind in the race vs. beingwell behind in the race.
Group D - White enters vs. White leaps AND DOES hit. (13 rolls) - A slightedge to the non-hitting play here, as at least it maintains a five pointboard, and doesn't leave a second blot at risk.
So, have we learned anything? Summarizing the above results :Group A - 6 rolls - small edge to hittingGroup B - 10 rolls - more gammons for hittingGroup C - 7 rolls - more wins for not hittingGroup D - 13 rolls - small edge to not hitting
Since increasing the number of wins is twice as important as increasingthe number of gammons, the above (obviously crude) analysis would suggestthat not hitting is correct. I would never attempt a more exact analysiswithout a robot, so this will have to do.
David Montgomery: B/20, 5/2*.
Break both plays down into three cases and estimate equity wins for Blue.After B/20, 8/5, I gave Blue 1.5 wins for the fourteen hits+55, 2.5 wins for thesix other running numbers, and 11.5 wins for the sixteen numbers that failtojump, for a total of 15.5 wins. After B/20, 5/2*, I gave Blue no wins after32, 3 wins after the other eighteen hits, and 13 wins after the sixteendances,for a total of 16 wins. I'll go with B/20, 5/2*.
Tony Moutzouris: B/20, 5/2*.
This was quite a tough one. Initially I favored B/20 8/5. I was loath for Blue to hit in his inner board, losing his 5 point in the process and creating two blots where there were none. The biggest downside to this play is the possibility of Blue losing his 5 point board which is his strongest asset. However, this may not be as bad as it appears. If for example White enters, hitting Blue's blot on the 5 point Blue can still make his 2 point and have a 5 point board for future backup. If Blue is hit on the 2 point he may make his 5 point before White hits his blot there.
The big upside to the play is if White fails to enter from the bar he is paralyzed and therefore cannot safety the blot on his 13 point or make another inner board point. If Blue picks up a second man and closes both checkers out he has very good gammon chances. This together with White's overall position i.e. only a 2 point board and pretty cramped position convinced me that hitting 5/2* is correct.
Snowie: B/20, 5/2*.
White has good sixes and fives if I don't hit, as opposed to good sixes andtwos if I hit. So, I might as well get something for my money if he doesn'troll a good number.
Kit Woolsey: B/20, 8/5.
Breaking up the board looks like it is carrying things too far. Blue's positionis ok even if White escapes with a hit, and if White doesn't escape Blue canattack with the stronger board. The problem with the bananas hit is thatBlue doesn't have enough ammunition in place to complete the closeout.
Michael Zehr: B/20, 5/2*.
Even after hitting it's a 4 point board vs. a 2 pointboard, and since Blue has three back to White's one back, it's time toattack.
Summary: A close vote between the two very different plays. I wonder which is right.
Play Votes ScoreB/20, 8/5 7 100B/20, 5/2* 6 90
Problem 3
| 144 160 | White money game Blue |
Ken Arnold: 7/1*, 6/1.
White's next roll is almost certain to make a key point, so whack him andtake away half the roll.
Chuck Bower: 7/1*, 6/1.
24/18, 13/8 gives White the best of two good options: hit orbuild a point. In fact, all 36 rolls hit and all 36 rolls make agood point! (They don't necessarily do both.) How could this be the right play?? If Blue brings two off the midpoint (13/7, 13/8), 36/36 rolls will make at least one of his 4-, 5-, or 7-points. If I choose not to hit, I'd rather have only one checker back. So 24/13 is my choice among the "nonmolesting" plays.
6/1* gives Blue three candidate 6's. After 24/18, all but 66return hit somewhere. If Blue really feels it's necessary to splitthe back checkers then 24/13 looks better.
Making the 1-point at least has a game plan--attack, attack, attack until you haveno attack left in you. 13/7 creates a needed builder, but theloose checker on the 1-point is an eyesore. You don't really wantit to get hit but you don't want to cover it, either.
Of the two remaining hitting plays, 6/1*, 5/1 leaves fewer shots,is more likely to keep White from playing this turn, and seems to bethe best road to a quick win via the blitz. Waiting around for goodthings to happen favors White.
Although 24/13 looks cleaner, White will have both the racinglead and probably a structure lead. Blue won't have much to beproud of. Making the 1-point may be ugly, but it focuses on White'sweakness--no anchor, no new points, and three total blots. 7/1*, 6/1is my choice.
Steve Clark: 24/13.
God gives you a 6-5 and you don't run? If you run, you must be thefavorite. The other non-hitting plays do not seem to me like the arewell directed.
So what about the various hits? 13/7, 6/1* seems the weakest. The wholepoint of hitting loose would be to get a back checker going. 24/18, 6/1*is better, but I usually reserve such plays for when I am well behind inthe equity of the position or when I am really anxious to prevent Whitefrom making an inner point. This could be all right if I didn't have abetter play but I do.
Finally we get to the real alternative, 7/1*, 6/1. This could be theright play. It puts White where he belongs (on the bar) and preventsWhite from making any points unless he rolls doubles. It gives me a 2point board. Of course it does tear down the 7 point and does notescape any of my back men. In balance I will take what god gave me,24/13.
Hal Heinrich: 7/1*, 6/1.
This problem is simple enough -- make the ace point on White's head.This solution is a typical result of imitating how bots play. Learningfrom the bots can be tricky -- if you've ever tried making the deucepoint with an opening 6-4 because the bots do it, you know what I mean! The bots either overrate deep plays or follow them up better than the humans. Here, however, it's easy to see why the bots are right -- assuming the bots make this play. You put your opponent on the bar with you having the stronger board, and you disrupt all those sexy point-making rolls. Hitting loose isn't right -- you've startedthe ace point, so make it. And the other plays allow White to build aboard to go with a racing lead.
Ron Karr: 24/18, 6/1*.
White is about to make a new point, so I have to interfere.The most straightforward way is to hit 6/1*, and I think it's right. 24/13seems too passive given White's racing lead & builders; 24/18 13/8 at least hasthe merit of provoking action on the bar point, when White might prefer to makethe 5 or 4 points.
After hitting, simply covering could be right, to cut down return shots & leadto a possible blitz. However, it costs the bar point, and leaves White's otherblots out of immediate danger. I'd prefer 24/18 to attack those blots, despitethe risk of getting hit twice.
Laila Leonhardt: 24/13.
A simple leap, seems to be the most sensible play here, allowing White to make a priming point. The postion is still very open and the race even.
George Klitsas: 13/8, 13/7.
play a (24/13) Our hand moves the checker all the way. When we start thinking it is landed on the midpoint-dice picked up. In most early positions a roll of 65 is played fast (and correctly) 24/13. Here, tho, things are not so clear. White has many builders in position (including two blots in his outfield) and the quiet approach represented by play a could not be the indicated one. Blue is somehow cramped on his own side, although he has made his bar-point. This means that he must take some risks bringing down builders (for example with a roll of 32) instead of stacking further. White, on the other hand, is poised to make a new point on every roll, leaving only indirect shots in the process. Important, also, is the 5-pips lead in the race for White ,which will count in a number of games. I performed a rollout of 108 games to see what happens and the result was -0.19 points per game for Blue.
Play b (24/18 13/9) The type of play that we usually call �action play�. Most of the rolls that hit and/or make the bar-point could be used to make other, more significant points-this is the reasoning behind an action-play strategy. Remains only to see how this play works in this particular setup. Almost any number hits (except 54 which makes the 5-point and 44, a good roll anyway). Some hit two checkers (like 51), some make the bar point as well, some leave a lot of indirect shots . When White is hit back, it's practically anybody's (long) game. When Blue just enters or flunks, White has a tremendous front firepower that is decisive immediately or very soon . In this last case, White has gained further in the race, so he has practically three ways to win : blitz, prime or race (If he manages to escape with his back checker). In 108 games, Blue's equity was -0.28 points per game.
Play c (24/18 6/1*) One can reject this play with little risk of being wrong, I guess.
Play d (13/8 13/7) Another plan-here Blue actually tries to play a kind of priming game against White's back checker, a plan that does not exclude the attack on this checker, If the right conditions are present. It would be much better for Blue If White had two rear checkers instead of one, but a minor compensation for this fact is that Blue is behind in the race and , due to this fact, ahead (=better) in the timing battle. Sometimes Blue is lucky enough to escape with one of his own rear checkers and then his timing advantage takes full credit and makes him a slight favorite. I played this position 108 times noticing to my surprise that a 5-prime , even a 6-prime was forming in many games for Blue quite naturally, giving him easy wins and an overall equity of -0.11 points per game, the best so far.
Play e (13/7 6/1*) Same comment as in play c.
Play f (7/1* 6/1) Still another plan. Sacrificing practically any chance of a future priming game in favor of an immediate attempt to seize the initiative and prevent White from consolidating. White has for a start 4 bad numbers (the dancing ones) plus some other awkward ones(62 is the worst of this group, I think). On the other hand, all entering aces (anti-duplication?!) cover both outfield blots. A rollout is a good way to see what develops in that case, as well. 108 new games, result =-0.15 points per game for Blue.
I am not at all sure, but, according to these rollouts, I have to vote for play d, the typical winner, with all my heart I must say, for It is based on a sound theoretical point (advantage in timing). Play a (the unanimous choice in a chouette, I figure) is close, and the same is true for play f ( I believe that it could be even closer in a slightly modified position for White, If we moved his checker from his 10 point to his 11 point (anti-duplication mentioned above).
Rob Maier: 24/13.
If we aren't going to run, the only reasonable alternative is making theace point. Presumably, we are doing this to prevent White from buildingnext roll. Even so, White still has 20 numbers which will build at leastan outside point, 4 numbers which hit the new blot on the bar point, and 6additional numbers which threaten to escape. So, unless White fans orrolls 2-6, 6 out of 36 numbers, White is still going to be able toaccomplish something constructive with the roll we have "taken away."Meanwhile, we haven't escaped a checker of our own, and we have given awaythe bar point in return for the ace point, not a fair trade I think. LetWhite make something, our back checker will be in no worse shape thantheirs, and we can hit, escape, or work on building ourselves the nextroll.
David Montgomery: 7/1*, 6/1.
The five looks clear. Hitting stops White from making a point andtightening up his position. 24/18 with the six gives White toomuch initiative. 13/7 doesn't appear to accomplish much. Once the aceis started, it is usually better to just make it, so 7/1*, 6/1 is my play.
Tony Moutzouris: 7/1*, 6/1.
This play seems clear to me. White has too many options, Blue definitely wants to take one of his rolls away. White has some very awkward entering numbers, specifically those that contain a six. White is well positioned to improve on his next roll and Blue wants to disrupt his development. There is also the possibility of White dancing on his next roll.
Snowie: 7/1*, 6/1.
It is thematic to attack the lone back checker, particularly with all thoseother blots strewn around. Nothing wrong with making the ace point in thissort of position.
Kit Woolsey: 7/1*, 6/1.
Blue is behind is the race, and if he leaves White alone White will almostcertainly make an inner board point and Blue will be in trouble. The bestbet is to attack and keep on attacking, hoping to be able to hit one ofWhite's blots before White has a chance to consolidate.
Michael Zehr: 7/1*, 6/1.
Blue has to hit to keep White from making a point, so 6/1* is part ofthe move. With two blots on the other side, good thing could happenin an attack, so 7/1* 6/1. After the purer 13/7 6/1* if White enterswithout hitting Blue has a hard time following up because of the bloton the ace.
Summary: Making the ace point would not have been a popular choiceseveral years ago. The strong vote for the play indicates how our thinkinghas changed.
Play Votes Score7/1*, 6/1 8 10024/13 3 7024/18, 6/1* 1 5013/8, 13/7 1 5024/18, 13/8 0 4013/7, 6/1* 0 40
Problem 4
| 157 170 | White money game Blue |
Ken Arnold: B/20, 6/5*.
Looks super close to me. Any match score considerations would swing thisplay.
Chuck Bower: B/20, 6/5*.
Before Blue rolled, I was thinking: "look at all those White blots.BLAST 'em!" Is making the 20-point worth changing thatplan? I bet if there were TWO spares on the 6-point Kit wouldn'thave even put this to a vote.
Blue is a bit behind in the race and has a better home board; Whitehas no anchor and three blots. If Blue makes the 20 point then White hasalmost no bad rolls. 4's, 6's, and 1's cover key points and/or hit.55, 22, 33 are good. 32 makes the 4-point. (Maybe 53 and 52 are bad.)All of this argues for hitting.
If Blue makes the 20-point, then this game is probably going to be a 2-way holding game or a 1-way with Blue doing the holding. In eithercase Blue is behind in the race, and that means behind in the game. I'd rather try to take the lead in the game (and risk being quitea bit of an underdog) than just settle for being a little behind.B/20, 6/5* is my play.
Steve Clark: B/20, 6/5*.
There are a number of good rules to follow in these positions. First, assets matter. When in doubt, make a valuable point, likeopponent's 5 point. Second, when you have the stronger board, hit, likeon your 5 point. Third, When you are going to leave a direct shotanyway, hit him first, like on your 5 point.
Is it now 2 rules to 1 in favor of hitting on my 5 point? I don'tsuppose so but I would hit. If I make his 5 point, he seems to have toomay ways to equalize or become a favorite. A fourth rule, hit if youare behind in the race, tips the balance.
Actually each of these concepts has merit, but you have to fit them tothe position. I think it is relatively close, but I definitely wouldhit.
Hal Heinrich: B/20, 6/5*.
Another easy problem -- hit on the five point. If you're the first oneto be hit in the early going, it's usually correct to make a decentanchor instead of slugging it out with a hit in your home board. Thisis an important exception! Here the reasons are compelling:
1. Blue has the stronger board -- look at the cube turn after a dance.
2. Blue is fighting for the biggest point in the home board.
3. Blue's blot on the eleven is exposed after making the twenty.
4. While's blot on the seven is harder to safety from the roof.
5. After being hit on the five, Blue still rates to form a defence.
Ron Karr: B/20, 6/5*.
Everything points to aggression: racing deficit, better board,White's extra blots. Anchoring is too passive, allowing White to anchor himselfor hit the blot on my 11.
George Klitsas: B/20, 6/5*.
play a (b/20 21/20) Usually it is good to grab the asset, make a concrete progress, something that will remain practically for as long as we want - a point. This principle, tho, must not be overdone. Blue must ask himself what will be a common scenario if he plays conservatively - the answer is: A mutual 5-point holding game with Blue having the better structure and White in most cases the race preponderance.
Play b (b/20 6/5*) Building on his advantage in inner board points and going for the throat. Using the last spare on his 6-point is not very important here. White's best responses (the ones that hit two checkers + small doubles) are far from real jokers. On the other side the 4 dancers are immediate winners for Blue. Most of the rolls that hit on the 5-point give Blue a bunch of return-hits on the 18-point and then White's position will be toothless for a long period. The rest of White's rolls simply enter giving Blue the opportunity to close the 5-point and/or hit any blots. I am pretty confident voting for play b.
Laila Leonhardt: B/20, 21/20.
Making a solid advanced anchor, will give Blue at least an even game for a very long time. The anchor also offers a nice duplication; White's 6's, to make the 7 point and to hit the loose blot on the 14th point.If Blue hits loose on the 5 point, he will strip the 6 point and risk having 2 checkers hit, and could lose much ground in only a few moves.
Rob Maier: B/20, 6/5*
This is no time to give White a chance to breathe. Making our five pointwill put White in quite a hole, so hitting there is a must. We have abetter board, so we should be thinking offense, not defense. I'll bequite surprised if this one is not unanimous.
David Montgomery: B/20, 21/20.
The hit strips the 6 point, leaves five blots, and lets White double hitwith any five. Better to just make the 20 point, duping White's sixes,and leaving a solid position that should be easy to play from next turn.
Tony Moutzouris: B/20, 6/5*.
Hitting seems right here. There is a big upside if Blue can secure his 5 point and the downside of having another man sent back or two checkers on the bar is not enough of a deterrent.
Snowie: B/20, 21/20.
A five point in the hand is better than two in the bush. Let's see White clean thismess up.
Kit Woolsey: B/20, 6/5*.
With the stronger inner board, it looks thematic to hit loose. The potentialgains are huge, and the cost doesn't figure to be great. This is not the timeto give White a chance to consolidate.
Michael Zehr: B/20, 21/20.
There are too many double hits for B/20, 6/1*. Also aftermaking the 20 point, Blue puts the three White builders on the 19 outof play.
Summary: The loose hit won, largely due to the stronger board. Howevermaking the anchor sure is tempting.
Play Votes ScoreB/20, 6/5* 9 100B/20, 21/20 4 70
Problem 5
| 172 143 | White money game Blue |
Ken Arnold: 13/11(2), 6/4(2).
5 and 11 points; seems the clearest of the bunch.
Chuck Bower: 18/14, 6/4(2).
Blue is at least 37 pips ahead in the race after playing this roll.Leaving blots around plays into White's hands. Pointingon White's head [7/3(2)*] leaves Blue searching for an encore. Making the 5-point (with ALL THREE checkers) just trades one valuable pointfor another. I like ADDING a NEW valuable point--6/4(2).
After that, leaving a checker on the 18-point allows Whiteto hit and start a point he really wants, so 18/16 is the third 2. Now I'm down to 16/14 or 24/22. 24/22 communicates, but makesit easier for White to hit TWO. It also leaves a checker on anotherpoint White wants--his 9-point. Finally, White's back checkerscan't move 3 and his spares on his 6-point are looking for a goodpoint to start. The continuation 16/14 is safer this roll, is inbetter position to build my outfield if missed, and is closer tosafe haven. So, my full play is 18/14, 6/4(2).
Steve Clark: 13/11(2), 6/4(2).
I would not make the 3 point. The checkers are too badly placed evenif White is put on the bar. Such hits just tend to drive White forwardto my more desirable 4 or 5 point.
There is something attractive about making the 4 and 5 points, but theplay does leave a lot of shots. It may be right but I have talkedmyself out of it. Of the other plays, 6/4(2), 13/11(2) jumps out at meas the most attractive. The alternatives each have merits and demeritsabout where the blots are left, but 13/11(2) has a plus that the otherplays don't have. 13/11(2) makes a very useful point and I would makethat play.
Hal Heinrich: 7/5(2), 6/4(2).
I can't imagine what sequence of rolls led to this position! In addition to the plays given; 6/4(2), 7/3* and 7/5(2), 7/3* and 7/5(3), 18/16 are worth considering. The solution to this problem falls into the category of "Grab the assets and hold your breath". What I mean by that is make the five and four points at the cost of letting White attack. White has 6's, 4's, and 1's to initiate one --hoping to continue attacking and escaping the back men. Blue might nothave a checker decision for the rest of the game. However, any return hits by Blue are potentially devastating. There is a case to be madefor playing 18/14, 6/4(2). It builds a good inner board point andduplicates White's twos. With the cube in the middle, Blue only needsto reach a potent double -- any equity past the drop point won't berealized. If Blue had already doubled, making both inner points would definitely be my play. As it is, I make the same play with much lessconfidence.
Ron Karr: 18/14, 6/4(2).
Making the 4 point is clear; pointing on the 3 point gives upthe valuable bar as well as numerous return shots. Then 18/16 to reduce shots;no point in leaving a target on the bar point. Finally, I'll keep going tominimize shots further, and also cover my outfield better. 24/22 gives Whitetoo many numbers to attack, which is what he wants to do; 13/11 gives me a newbuilder, which is nice since I only have one spare, but I don't think it's worthhaving the extra blot.
George Klitsas: 7/5(2), 6/4(2).
There are a number of principles in life and backgammon (some are common in both games). In life, the mother of all mottoes is, in my opinion, �possible is what usually happens� (this could help a steamer sometimes, in bg !). In bg, among others, a solid principle is �do first what seems to be the most difficult task�. In this position, which possibly resulted after an early 64 played 8/2 6/2 , Blue must see the roll of 22 as a golden opportunity to fill nicely the gaps in his inner board by playing 7/5(2), 6/4(2) putting maximum pressure to White to roll immediately something good. Any other play leaves much to be done in the future and puts remarkably less pressure. This play fulfills another aspect, an aesthetic one, which has been reported by a number of grandmasters in chess. �Abstract beauty�.
Laila Leonhardt: 7/3(2)*.
Money game, the cube is centered, and the 6's and 1's will be duplicated.This is a great oppotunity to gain a big advantage in the position.If White fails to hit, Blue has builders on the 7 and 6 points, and when White dances, Blue has a strong cube. It is a nice position, with lots of options, (maybe 6/4(2) 7/3* should have been added.)
Rob Maier: 24/22, 18/16, 6/4(2).
Lots of choices. If White had other blots, then 7/3(2) would be apossibility. Here, it should be rejected. So, we will make the fourpoint with the first two deuces. Making the five point with the othersgives White too easy a road to getting back into the game, by hitting onand making the bar point, not to mention reducing our racing lead by quitea bit. Leaving a blot on our eleven point should be rejected also, weshouldn't be leaving extra targets at this stage. Making our eleven pointhas some merit, but the downside is that we remain on the point Whitewould most like to make, and there is some danger of being primed. This leaves either running to the fourteen point, or moving both checkers forward. These plays seem quite close, I slightly prefer 24/22 18/16.The position after 18/14 seems somewhat awkward when we are not hit. By moving both back checkers it will be easier to extract the back checker, and we have more control of the outfield as well.
David Montgomery: 7/3(2)*.
Not hitting strips the six point and doesn't give White any dances.The duplication of sixes after 7/3(2)* is a plus. The big gap on the4 and 5 points is ugly, but I'll go with the hit.
Tony Moutzouris: 13/11(2) 6/4(2).
The solution to this problem did not come instantly. As is common with 2:2 there were many options available. I don't like playing 7/3(2)*. I think this play overextends Blue's position and makes it too easy for White to anchor on Blue's 4 point or 5 point. I think Blue should play 6/4(2) with the first two 2's. Playing 6/5(2) with the other 2's is tempting since sixes are duplicated but I think that play leaves Blue too vulnerable. I would simply play 13/11(2) with the last two 2's. This play nails down Blue's 11 point which is a good point to have when his 5 point is open. This play also keeps Blue's back checkers in touch with each other. While the other plays have their advantages I think playing the last two 2's from the 13 point is correct.
Snowie: 13/11(2), 6/4(2).
Points are points. If White wants to break his eight point to hit, that'shis problem.
Kit Woolsey: 18/14, 6/4(2).
This natural escape and build play looks best. The duplication of deuces isquite real, and Blue should have a comfortable position to play from here.
Michael Zehr: 18/14, 6/4(2).
The builders on the 6 belong on the 3, 4, or 5, so putthem there. The checkers on the 7 belong there to block the acepoint, so keep them there. (What's wrong with 6/4(2), 7/3*?) 18/14effectively rescues one back checker since White must use a 2 toadvance the anchor.
Summary: So many choices, as is often the case with double-twos. Thesimple run and build play tied with making the 11 point, but there was plenty of support for other choices.
Play Votes Score13/11(2), 6/4(2) 4 10018/14, 6/4(2) 4 907/5(2), 6/4(2) 2 707/3(2)* 2 7024/22, 18/16, 6/4(2) 1 6018/16, 13/11, 6/4(2) 0 40
Problem 6
| 155 87 | White money game Blue |
Ken Arnold: 15/12, 11/6.
Even after losing a fortune in gammons to opponents who make theacepoint, I cannot leave 3 random shots. If White's 5 point were slotted andnot covered yet, I'd make the ace.
Chuck Bower: 6/1, 4/1.
I'm greedy. I want a gammon. 6/1, 4/1 makes that more likely, Ithink. If White rolls 65, Blue gets 15 return shots. 55 leaves 6 return shots. Even if Blue misses the returns, as long as he enters I don't think White can cube.
After making the acepoint, it looks like 1.5% of games Blue gets hit and then fans. Call these losses. About 3% of the time Blue get hit but re-enters, hitting. Call these non-gammon wins. About 4% of the time Blue gets hit and re-enters immediately without hitting. Say Blue wins half and loses half of these. So Blue will lose about 3.5% of games with 6/1, 4/1 that he would have otherwise won. Can Blue extract 7% more gammonsfrom this play?
After 6/1, 4/1, a full one fourth of the time White will stay on the bar this roll when he would have entered with the other plays. That's got to be worth quite a few increased gammons right there. And if White enters on the 1-point and remains there, sometimes that becomes a thorn in Blue'sside. I'm guessing 6/1, 4/1 garners more than 7% increased gammons so that is my play.
Steve Clark: 6/1, 4/1.
6. Should we go for the big bucks? 6/1, 4/1 has a lot going for it. A6-5 reply doesn't look too bad but the disaster roll of 5-5 could makeus quite nauseous. The only alternative that looks attractive is 15/12,11/6. The other 2 possibilities still pay off to double 5's while15/12, 11/6 get us to the verge of being in safely. Of course White maynow come in on the ace point and hit us from there, so maybe the safeplay isn't so safe. Besides the gain of having a 5 point board looksgood to me. I will make the ace.
Hal Heinrich: 15/12, 11/6.
I only see two candidates here: 15/12, 11/6 and 6/1, 4/1. It might beright to go for the gammon by making the ace point -- and at certainmatch scores that would be my play. Here, however, I'd simply play tobring my men home safely by playing 15/12, 11/6. It doesn't seem thatmaking the ace generates enough extra gammons to compensate for thelosses.
Ron Karr: 6/1, 4/1.
At the table I'd play the obvious 15/12 11/6. After all, I'mtrying to get home ASAP; this gives me two crossovers & leaves no shots.However, after thinking about it, I got more gammon-hungry. Am I really worriedabout getting hit now? White's board can't contain me & there's another blotthere. And making the ace point increases my gammon chances, particularly ifWhite rolls an ace. And if he rolls a 5 (other than 55 or 56) it's moredifficult for him to come out into the outfield.
George Klitsas: 6/1, 4/1.
From the plays that don't make the ace point, best looks 15/12, 11/6. So, actually the issue is between this play ( play a) and play d (6/1 4/1). In effect, one is trading some gammons with some losses. In a small rollout, I discovered that the number of additional gammons is much more than the number of occasional losses (23 gammons and 6 losses in play d, 18 gammons and 4 losses in play a), so, in all probability, seems that play d is better.
Laila Leonhardt: 15/12, 11/6.
With this move, White has no chance of hitting from the bar. The checker on the 12 point will be easily cleared. And it looks like easy win, maybe gammon from here.Making the 1 point doesnt really gain anything, and even leaves White a chance of hitting from the bar.Blue's position, when White enters from the bar on the ace point, is nowhere as compromising, as White hitting Blue from the bar with either 6-5 or 5-5, depending on the choice.
Rob Maier: 15/12, 11/6.
Ahh, finally, the kind of problem I like to have. Seems for the most partthat we always have the worst of it, it's nice to be considering gammonsfor OUR side for a change. Still, I don't think we should get carriedaway. Three shots seems like a lot to offer for the dubious gains frommaking the ace point. IF they come in on the ace point, we may make it inthe next roll or two. If on the other hand, they come in on the fivepoint, we will want our checkers closer to home. There is a danger thatwe may be forced to leave a shot on our ace point later, but I would judge that danger to be less than the immediate danger from making the ace pointnow.
David Montgomery: 15/12, 11/6.
11/3 and 11/6, 7/4 seem unlikely to be right. Blue should get something for anyextra shots he leaves. 6/1, 4/1 gets the ace point, and so will win moregammons. Is it enough to offset the additional losses? I don't thinkso. Blue may be able to make the ace point later, and he shouldwin many gammons in any event.
Tony Moutzouris: 6/1, 4/1.
I would make the 1 point. I want to keep White on the bar as long as possible in order to win a gammon and to prevent him from building his board. There is something to be said for 11/3 or 15/12 11/6, they do take away the 5:5 joker and leave Blue with a very flexible position and some outfield control but I would still go with making the 1 point.
Snowie: 15/12, 11/6.
The goal of backgammon is to bring all your men around and take them off.My play aims at that goal; making the ace point doesn't.
Kit Woolsey: 15/12, 11/6.
Blue really doesn't need the ace point that badly. 15/12, 11/6 not only issafe but prepares to bring the outfield checkers home comfortably which isthe highest priority. If Blue makes the ace point and White enters, Blue'sposition may suddenly become very difficult to play.
Michael Zehr: 6/1, 4/1.
The gammon is close and keeping White out an extra roll isprobably worth the 3 shots now plus a good chance at 6 indirect shotslater.
Summary: Purity and safety won out over greed in a close vote.
Play Votes Score15/12, 11/6 7 1006/1, 4/1 6 9011/6, 7/4 0 4011/3 0 40
Problem 7
| 131 127 | White money game Blue |
Ken Arnold: 8/2*, 7/2.
Chuck Bower: 8/2*, 7/2.
Assume White will break his bar-point with a 6 (which I thinkis correct) and shifts home board points with doublets (maybecorrect) and count the shots:
14/3: 3114/8, 6/1: 2414/8, 7/2*: 208/2*,7/2: 15
When you throw in the fact that after Blue makes the 2-point onWhite's head, 25% of the time White can't even enter, then this moveseems even clearer. This roll gives Blue a fair opportunity to takecontrol of the game (and then send back the cube) in a couple ofrolls. Why waste that chance? 8/2*, 7/2 is my choice.
Steve Clark: 14/8, 6/1.
Nothing looks very good here. 14/3 and 14/8, 7/2 seem aimless. Bothplays leave blots and don't provide much gain even if they are missed. If we were attempting to build a prime risking a blot would seem moreattractive. But here White will still have our 5 point. 8/2*, 7/2suffers from the same weakness, leaving 2 blots around to be hit. Furthermore, it seems wrong to hit a blot that is rather badly placed. If we hit him, he probably will end up in a place which he likes more. Of course, White may stay on the bar while we hit him again or maybeeven escape. This seems much more attractive than the 2 other playsconsidered. What about the weenie play? 14/8, 6/1. This play tries to avoid havingmore blots sent back with the hope that we can escape soon. If wedon't escape next roll, maybe we can hit him without leaving a blot. This seems like the right idea to me. All we need is someone to singthe Oscar Meyer Weiner Song.
Hal Heinrich: 14/8, 6/1.
Blue has taken the cube and would now be happy to pay a point and moveon to another game. White's inner board is very strong, White's defence is rock solid, and White's timing is reasonable. Blue's ambitions should be modest -- get off the gammon, and perhaps escapeinto a race. Any play that leaves a shot, risks getting gammonedwithout adequate winning compensation. 14/8, 6/1 is the way to go.
Ron Karr: 14/3.
My big problem is escaping the back checker from behind White'sbroken prime; eventually I'll have to roll a 2 , then a 5 or 6. Pointing on the2 point seems counter-productive: White has the better board, and I'd bebreaking my 8 point. 14/8 6/1 seems right for the short term, since Idefinitely don't want another checker hit if I get lucky enough to advance orescape the back guy. On the other hand, having the blot on my ace point willcause future problems: it'll be more attractive for White to attack, and I'llhave fewer builders to make the 3 and 2 points.
Looking at the position as a prime-vs-prime, White has a better prime, but 3 menback to my one. Long-term, the best strategy could just be to play 14/3: keepeverybody in play, slot the next point. If White hits, I won't like it, butmaybe it'll help my timing; and if he doesn't hit, I'll make the 3 point (and 2saren't duplicated). 14/8 7/2* is an interesting variant, since if White hitsback, that checker is still primed; but it's already primed, and 2s would beduplicated to cover.
Bottom line: I think I'll make the long-term play, despite the immediate shots.14/8 6/1 seems a bit too ugly.
George Klitsas: 8/2*, 7/2.
One can quickly reject play a (14/3) and play b (14/8, 7/2) . Both look inferior to play c (14/8, 6/1), for they risk a second checker sent back without much compensation and they both look inferior to play d (8/2*, 7/2), for they do not make at least an inner point and leave more hits. The position is very complicated and not very common, so a rollout was needed once more to decide between them.
Play c (14/8, 6/1) A quiet variation , leading usually to simple wins for either side. In about 25% of the games, Blue jumps in the outfield with a roll like 2-5 or 2-6 becoming a huge favorite or moves with a 2 on the 22 point and fights from there. In about 40% of the games White closes out one (usually) or two Blue checkers. Net equity for Blue=-0.22 points per game.
Play d (8/2*,7/2) A dynamic variation . Crucial are the 9 dancing numbers, in which Blue often goes for an un(re)doubled gammon and the same is true if White enters with a six (a 36 for example) and (correctly I think) goes for the throat by hitting on his ace point - in that case , depending on the eccentricity of the dice any player can score a gammon. Net equity for Blue =-0.02 points per game. Play d is my choice.
Laila Leonhardt: 14/3.
The cube has been turned, and Blue can lose a gammon if he plays too loosly.But leaving the blot on the 3 point has a great advantage. If White fails to roll a 1 or a 3, then Blue can make a 5 point prime with a 1, 3 or 4 and step up to the 22 point with any 2 next turn, and that way apply some pressure on White. A blot on the 1 point, would have no priming value and maybe become a hazard later on.
Rob Maier: 8/2*, 7/2.
The two choices would seem to be either making the two point or leaving noshots at all via 14/8 6/1. 14/3 aims at trying to win a priming battle,but Blue's position is too fragile for that to work often, and White has adangerous amount of ammunition on the other side of the board. 14/8 7/2is worse, leaving an extra shot, and losing most of what little primingchances there are. 14/8 6/1 temporarily solves the problem of exposing a second blot, but the blot on the ace point will still be a liabilityshould Blue manage to hit a shot, or wish to point on White later. Makingthe two point not only leaves less shots, but provides an excellent bonuson the 25% of the time when White fans, giving Blue more time to roll atwo to move up, or to put up a second blot with an ace. Even when White comes in without hitting, Blue may be able to recover theeight point, or point on White again if they come in on the ace or three point. Pointing on White's head is Blue's best chance toturn the game around.
David Montgomery: 14/8, 6/1.
If Blue gets hit, he is pretty much toast. 14/3 and 14/8, 7/2* look clearlywrong to me, since they don't gain that much for the direct shot theyleave. 8/2*, 7/2 is better, since it leaves fewer shots and gives Whitemore dances. But since White is not threatening anything in particularthis roll, I would play safe with 14/8, 6/1.
Tony Moutzouris: 8/2*, 7/2.
I think the play is clear. Blue makes another inner board point, puts White on the bar and gives his back checker better odds on escaping.
Snowie: 14/8, 6/1.
I don't need any more men sent back against that board. I'll just hope myback checker can find a way out later.
Kit Woolsey: 8/2*, 7/2.
Everything is scary, so might as well attack and hope for the best. The duplicationof odd numbers limits White's return shots.
Michael Zehr: 14/3.
This looks like the time for purity, as an attack is unlikely towork and dumping checkers will make Blue's position deteriorate toofast.
Summary: The attacking play won, but it is far from clear.
Play Votes Score8/2*, 7/2 6 10014/8, 6/1 4 8014/3 3 7014/8, 7/2* 0 50
Problem 8
| 146 170 | White money game Blue |
Ken Arnold: B/20, 24/18.
The best problem of the set. This type of position comes up frequentlyand nobody knows. If this discussion leads to some reference positionswhere the 3 plays cross over then even GO will be on its way to beingindispensible. I guess that it is best to fight for the good points here,but if White had a trace more ammo then 20/14.
Chuck Bower: B/14.
I was gonna vote for 8/2 but slotting the 2-point didn't workin last month's quiz... :) Let's take a look:
24/18 leaves 36 hitting numbers of which 25 are double hits and allthat without an anchor. If this is right I'm switching to tic-tac-toe! White should definitely double after this move. I don't know ifBlue has a take. I'm guessing it's a pass.
13/7 leaves 31 hitting numbers of which 5 are double hits. However, many of the hits are loose on the 20-point giving a lot of returns. Ifthere were four on the 13-point then I would like this play better.As it is we strip the midpoint with no advanced anchor. White mayhave a double here, too, but Blue surely has a take.
20/14 leaves 22 hitting numbers, none of which are double hits.White will be attacking a point which he wouldn't mind making, butit's not part of the home-board. Blue doesn't get many returnshots. Even so, I'm pretty sure White shouldn't double.
Counting shots and taking the play which leaves the fewest isn'talways right. But when you are under attack, it's probably a rareexception when this ploy is wrong. Is this the exception?
I'm concentrating on keeping White's last checker back. (Ofcourse a second one back would be great but let's not get greedy!)Surviving to play another roll is important in this kind of position.Spending a lot of time re-entering is not much of a survival plan.After 20/14, if this blot gets hit then at least White's last checker is staying back this turn. Also, sometimes Blue's re-entering rolls either return hit or make a better anchor. Most of the time Blue is left with a similar decision as the one being contemplated now.
In a chouette I wouldn't be opposed if the captain chose 13/7 but with no spare on the midpoint I'd rather be hit on the 14-point than the 7-point. B/14 is my play.
Steve Clark: B/20, 24/18.
I would play B/20, 24/18 without worrying about it very much. Insome similar positions 13/7 is ocassionally right, but I have difficultypicking those positions out. And I do not really think this is one ofthose positions anyway. B/14 just looks like a blot available to be hitis White needs it. B/20, 24/18 makes a strong attempt for an advancedanchor while leaving White just enough bad numbers so that the resultusually isn't too bad.
Hal Heinrich: B/20, 13/7.
Normally, slotting the seven point against one man back is wrongbecause it allows your opponent to escape while hitting with too higha probability. Here, though, it seems the best of a bad bunch. B/20, 24/18 gives White too many attacking numbers. B/14 is a playthat tries to divert White from building a home board or escaping, butdoesn't really help Blue. At least with B/20, 13/7 Blue has startedtwo good points with a decent chance of making one of them.
Ron Karr: B/14.
After entering, I'd like to keep the checker on the 20 point, to getmaximum coverage of the outfield. After all, I'm behind in the race, and Whiteis trying to safety his partially escaped checker. 20/14 isn't so attractive,because White figures to be able to either hit or play safely to his mid, 10 or9 points.
But then my other 6s aren't so great either. 24/18 provides the best coverage,but it leaves lots of shots, and many numbers that hit twice. We both have 2point boards, and I'm not so far behind in the race that I want to give White somany opportunities to crush me.
13/7 has the advantage of putting the checkers more where I want them, and givesWhite fewer double-hit numbers. If White rolls a 6 that doesn't hit twice, I'llhave numerous returns. Problem is, I've stripped my midpoint, and getting hitcosts more.
So I'm not really sure what's right, but my instinct says go ahead and play20/14, conceding the escape of White's checker. My board is better, I won'thave squandered too much racing equity, and I can concentrate on containingWhite's last checker.
George Klitsas: B/20, 24/18.
A common theme-position in the early going. In similar positions one automatically plays b/20, 24/18 and I don't think that this one is an exception. B/14 is leaving a big uncontrolled gap and a blot vulnerable to many hits. I would give more consideration to the third play (b/20, 13/7), If Blue had another spare on the midpoint, but not here. By playing B/20, 24/18 , Blue , If things go well, will secure an advanced anchor , sending perhaps one or more White checkers back. If things go unwell ( a common bad scenario is the one in which White hits two checkers and Blue fails to re-hit the crucial blot), Blue might face even an early cube. As already said, my vote is for B/20, 24/18.
Laila Leonhardt: B/20, 24/18.
It is vital for Blue to get an advanced anchor. He is down in the race, and it will not be long before he will have to face a cube from White if he fails to anchor.The open play, leaving 3 blots leaves a good chance that Blue can hit back or make an advanced anchor next turn.
Rob Maier: B/20, 13/7.
Coming out to the fourteen point just gives White a free shot to bringbuilders into the outfield, with or without hitting. Coming out to thedefensive bar point is asking for trouble, slotting the two pointsWhite would most like to make. Nearly all of White's numbers areplayable, and many leave Blue needing to roll well to remain in the game.The best chance is to leave the back checkers alone, and come down to ourbar point. If this checker is hit, we will often make the defensive fivepoint, which will give us a playable game. If not hit on the bar, thechecker on the five point covers the entire outfield, and we will haveexcellent chances to hit another checker and/or cover our bar point.
David Montgomery: B/20, 24/18.
Because of the many double hits, this kind of play is widely known to bebad, and it usually is. However, the alternatives are bad, too. B/14 leavesa double direct shot and tries for nothing, while B/20, 13/7 strips the mid andis also subject to double hitters. Plays like B/20, 24/18 are often not as badas most players have thought, and that is my play.
Tony Moutzouris: B/20, 13/7.
Rolling 6:5 from the bar can be awkward. After entering B/20, deciding which six to play is often a difficult decision. I don't like playing B/14 in this position because it isolates the two back checkers and gives White a double shot at the blot on the 14 point. Blue would like to make an advanced anchor so that he can play more freely up front in order to contain White's back checker. B/20 24/18 leaves White too many double hits and if Blue does not hit back he will be in trouble. That leaves B/20 13/7 as my first choice.
Snowie: B/14.
No reason to give White extra blots to shoot at. My position will be ok aslong as I don't get stuck on the bar.
Kit Woolsey: B/20, 24/18.
Since Blue is behind in the race but has as strong a board as White, it seemsthematic to spread the back checkers out. This both increases Blue's chancesto make an advanced anchor and to hit White's outfield blot.
Michael Zehr: B/20, 13/7.
Put the checkers where you want them. If Blue can come outof this with either the 20 point or the bar point next turn then Bluehas made a lot of progress.
Summary: A 3-way split between the candidates. Any of the plays might be right.
Play Votes ScoreB/20, 24/18 6 100B/20, 13/7 4 80B/14 3 70
Vote Summary
1 2 3 4 5 6 7 8Ken Arnold 6/1, 4/1 B/20, 5/2* 7/1*, 6/1 B/20, 6/5* 13/11(2), 6/4(2) 15/12, 11/6 8/2*, 7/2 B/20, 24/18Chuck Bower 6/1, 4/1 B/20, 8/5 7/1*, 6/1 B/20, 6/5* 18/14, 6/4(2) 6/1, 4/1 8/2*, 7/2 B/14Steve Clark 13/10, 13/8 B/20, 8/5 24/13 B/20, 6/5* 13/11(2), 6/4(2) 6/1, 4/1 14/8, 6/1 B/20, 24/18 Hal Heinrich 6/1, 4/1 B/20, 8/5 7/1*, 6/1 B/20, 6/5* 7/5(2) 6/4(2) 15/12, 11/6 14/8, 6/1 B/20, 13/7Laila Leonhardt 6/1, 4/1 B/20, 8/5 24/13 B/20, 21/20 7/3(2)* 15/12, 11/6 14/3 B/20, 24/18Ron Karr 13/10, 13/8 B/20, 5/2* 24/18, 6/1* B/20, 6/5* 18/14, 6/4(2) 6/1, 4/1 14/3 B/14George Klitsas 6/1, 4/1 B/20, 8/5 13/8, 13/7 B/20, 6/5* 7/5(2), 6/4(2) 6/1, 4/1 8/2*, 7/2 B/20, 24/18 Rob Maier 6/1, 4/1 B/20, 8/5 24/13 B/20, 6/5* 24/22, 18/16, 6/4(2) 15/12, 11/6 8/2*, 7/2 B/20, 13/7David Montgomery 13/10, 13/8 B/20, 5/2* 7/1*, 6/1 B/20, 21/20 7/3(2)* 15/12, 11/6 14/8, 6/1 B/20, 24/18 Tony Moutzouris 13/10, 13/8 B/20, 5/2* 7/1*, 6/1 B/20, 6/5* 13/11(2), 6/4(2) 6/1, 4/1 8/2*, 7/2 B/20, 13/7Snowie 6/1, 4/1 B/20, 5/2* 7/1*, 6/1 B/20, 21/20 13/11(2), 6/4(2) 15/12, 11/6 14/8, 6/1 B/14Kit Woolsey 13/10, 13/8 B/20, 8/5 7/1*, 6/1 B/20, 6/5* 18/14, 6/4(2) 15/12, 11/6 8/2*, 7/2 B/20, 24/18Michael Zehr 6/1, 4/1 B/20, 5/2* 7/1*, 6/1 B/20, 21/20 18/14, 6/4(2) 6/1, 4/1 14/3 B/20, 13/7
