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Old 11-15-2010, 01:04 AM   #1
Robertie
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Problem of the Week #83: Solution

Problem of the Week #83: Solution

Cash Game. Black owns the cube. Black on roll.





(a) Black to play 2-2.





(b) Black to play 2-2.





(c) Black to play 2-2.


Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. No gammons can be scored unless the cube has been turned.


Position 83a was submitted as a tournament play question a couple of weeks ago, but it’s a very interesting problem which bears on a number of back game issues, so I’ve translated it into a cash game position and added a couple of variations. Before we look at the 2-2 roll, let’s start by looking at the three positions and see how Black is doing in each one.

The Positions

In Problem 83a, Black is playing an ace-deuce back game with two additional checkers back. Unfortunately for him, he’s trapped behind a full six-prime, and White still has a number of checkers to bring around the board. The ace-deuce back game will generate the most shots as White tries to bear off, but it’s by far the hardest back game to time properly. Black trails here in the race by 102 (!) pips, 213 to 111, but even that isn’t enough timing to have a good game. If White were on roll in this position with a centered cube, he would double and Black would have a huge pass.

In Problem 83b, Black’s chances have improved because White doesn’t have a full prime and isn’t likely to get one. The gap on the bar point gives Black some useful options. If he rolls some fives, he can just hop out and improve his timing. If he doesn’t roll any fives but rolls some sixes instead, he can choose to abandon the back game and rely instead on a very well-timed two-point game. If White were on roll with a centered cube, he would still double and, interestingly enough, Black would still pass. This will probably surprise many readers, but ace-deuce back games are very treacherous, and conditions need to be just right for Black to take.

Problem 83c is very different. The switch from a 1-2 back game to a 1-2-4 back game changes Black’s position in several ways, all positive.

(1) It’s now harder for White to clear points without leaving shots.

(2) Black often gets a triple shot, rather than a double shot.

(3) Because he has a high point, Black is very hard to prime, and he can recirculate checkers to the outfield more easily.

(4) Black retains the option of abandoning the 4-point to preserve his timing, while still leaving behind a good 1-2 game with an open 4-point that causes White problems.

If White is on roll is Position 83c with a centered cube, he’s still a long way from a double and Black has a trivially easy take, almost a beaver.


The Plays

Now let’s go ahead and look at Black’s possibilities with the 2-2 roll. We’ll consider for the moment only the position on Black’s side of the board; later we’ll look at the whole board and decide how each play fits into the broad scheme of things.

Play (1): 8/4(2). This is the main non-contact play. By not hitting anywhere, Black minimizes White’s shots and tries to maintain the timing status quo. While the play looks craven and unimaginative, it may be best if Black feels that more contact is unfavorable for him. Another play with the same idea is 8/2 8/6, but among these two plays, making the 4-point will always be dominant.

Play (2): 8/2 6/4. This play avoids hitting White but allows White a double shot to send a Black checker back. With this play, Black avoids slowing White down, but is willing to go backwards himself.

Play (3): 13/11*(2) 9/7* 6/4. This play attempts to move forward in the most direct way, hitting two checkers, making the 11-point, and covering the 4-point. Black, however, sacrifices a lot of time in the process. He’s moved forward 8 pips and sent White back a total of 18 pips; that’s a 26-pip swing in timing. If this play doesn’t trap White and force him to break his prime soon, however, Black will find himself with a ruined position and no timing. Remember that Black only has nine checkers to play with right now, so at most he can make four points of a prime.

Play (4): 13/11*/7* 6/4. This is similar to Play (3) except that Black leaves one checker on the midpoint and plays 11/9 instead. The good news is that Black picks up aces to hit White’s last free checker. The bad news is that Black now has five blots, so if White enters right away, Black’s game is a little harder to clean up.

Play (5): 13/11* 9/7*/5 6/4. This play hits two checkers and makes the 4-point, but then goes ahead and slots the 5-point. It’s a play that tries to build the board more quickly, but at some risk.

Play (6): 13/11*/7*/5. Called by some the banzai or kamikaze play, the idea here is to hit White and force him to hit back. This may gain timing if White in fact hits and Black then dances for a couple of turns. If White doesn’t hit, or Black reenters quickly, Black’s timing could be worse than when he started. A variation on this play is 9/7*/5 6/2, which hits only one checker. It’s a weaker variation because of the checker deep on the 2-point, which may never get back into action.

Putting It All Together

In Position 83(a), Black labors under two handicaps: his game is poorly timed as is, and he’s trapped behind a full 6-prime to boot. The hitting plays are now all gambits of a sort. By sending White back, Black sacrifices more timing, in the hopes that he will either trap White and make him crack his prime, or force White to hit and thereby recover all the timing he has sacrificed, and then some.

Either goal is possible, but neither is likely. With only nine checkers to deploy, Black cant build much of a prime, so the trapping and cracking variation isn’t likely. Even if he can crack White’s formation, White will still have a 5-prime with six Black checkers behind it. White might have to hit a Black checker to get his men out, but hitting one checker only restores the timing status quo, while hitting two is unlikely.

Black’s best plan in 83(a) is just 8/4(2). Leaving White alone at least allows him to keep moving, and minimizes the chance that even more men will go back behind White’s prime. It both wins the most games and loses the fewest gammons compared to the more aggressive plays, not a bad combination. In general, when your back game timing is poor and you’re already behind a full prime, you’re in damage control mode. Getting off the gammon while preserving some few winning chances is your best bet.

In Position 83(b), Black is doing better. His timing is still poor, but he’s not completely trapped anymore, so he’s entitled to take a chance on going forward. His best play is to hit twice but not slot anything: 13/11*(2) 9/7* 6/4. Now he has some opportunity to spring his back checkers and win a forward game, while preserving some back game chances if the main plan doesn’t work. The slotting play, 13/11* 9/7*/5 6/4, actually wins a few more games, but loses too many more gammons and backgammons.

Position 83(c) is completely different. White isn’t nearly strong enough to be doubling, and Black can play completely freely, going forwards or backwards as things develop. The very pure play of 13/11* 9/7*/5 6/4 now becomes best. If White hits, Black just keeps recirculating, but if White gets stuck, Black will try to block him by releasing the checkers on the 21-point. Owning the cube, Black is now almost even money in what promises to be a fun game.


Solutions:

(a) 8/4(2)

(b) 13/11*(2) 9/7* 6/4

(c) 13/11* 9/7*/5 6/4
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Old 11-15-2010, 05:25 AM   #2
Bjornar
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Re: Problem of the Week #83: Solution

Is there any way you can comment on the crawford matchplay position also? We have done some really massive rollouts on the position and my play, 6/2 6/4(2) has thus far come out on top. You dont even mention that move here.
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Old 11-15-2010, 08:40 AM   #3
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Re: Problem of the Week #83: Solution

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Originally Posted by Bjornar View Post
Is there any way you can comment on the crawford matchplay position also? We have done some really massive rollouts on the position and my play, 6/2 6/4(2) has thus far come out on top. You dont even mention that move here.
In your original problem, black was 1away, white 2away, right? Then black was on gammon safe, white on gammon go. So referring to Bill, we are in damage control mode. If a gammon loses the match, the move with most gammon saving potential could be best. And that is probably yours. Maximum dodging.
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Old 11-17-2010, 12:31 PM   #4
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Re: Problem of the Week #83: Solution

Quote:
Originally Posted by Bjornar View Post
Is there any way you can comment on the crawford matchplay position also? We have done some really massive rollouts on the position and my play, 6/2 6/4(2) has thus far come out on top. You dont even mention that move here.
I didn't actually consider this play at first, but I should have, because it does have a point. It's the only play that doesn't hit and blocks 1-1, thereby giving White a cracking number. However, the cost is high (a ruined board). I did some 3-ply rollouts matching this play against 8/4(2) and it did significantly worse (although better than any hitting play), so I'll stick with my original recommendation.
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Old 11-21-2010, 08:56 AM   #5
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Re: Problem of the Week #83: Solution

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Originally Posted by Robertie View Post
I didn't actually consider this play at first, but I should have, because it does have a point. It's the only play that doesn't hit and blocks 1-1, thereby giving White a cracking number. However, the cost is high (a ruined board). I did some 3-ply rollouts matching this play against 8/4(2) and it did significantly worse (although better than any hitting play), so I'll stick with my original recommendation.
I did also some rollout. Your explanation of 11 from white in the next gives a little light. I did a 10k RO with 3ply checker/cube, variance reduction. 8/4(2) came in as 6th, near whopper range. And to decide between first and second, we have to extend to even 40 or 80k, if we look at the confidence interval. I played several deep backgames from both sides against XG and he played in my opinion like a human. He tries to solve the game at protobackgame otherwise, but also has no fear to go in full back game modus. And then, i was really stunned about his understanding of timing.
Position 83a is as deepest as i could imagine to stand in a backgame. So i think the philosophical question (or epistemological) is, what can we really know for certain in complex backgammon positions. I think, if we use equity estimations from bots as a reference, then this is the archimedic point. But if we are not sure, that there is a flaw in the bot estimation and the move doesn't fit in our conceptual framework of the game, then we have to admit, that there is no certainty. My opinion is: there is so much order from noise, which can't be analyzed, that only with a really massive simulation we can see a little light. And if we think, that the bots are way off in deep back games, then this is south pole exploration. And for sure a "goal line stand". That is in my amygdala, since i've read advanced backgammon.

XGID=----A-CaBA-aaB---bbbbbbDB-:1:1:1:22:0:0:3:0:10

1. Rollout¹ 8/4 6/4(2) eq:-0,812
Player : 29,97% (G:0,68% B:0,03%)
Opponent: 70,03% (G:44,15% B:12,11%)
Confidence: 0,010 (-0,822<E<-0,802)
Duration: 5 hours 45 minutes

2. Rollout¹ 9/7* 7/5 6/2 eq:-0,815 (-0,003)
Player : 31,73% (G:0,98% B:0,05%)
Opponent: 68,27% (G:45,27% B:16,11%)
Confidence: 0,014 (-0,829<E<-0,801)
Duration: 9 hours 33 minutes

3. Rollout¹ 6/4(2) 6/2 eq:-0,836 (-0,024)
Player : 28,23% (G:0,73% B:0,03%)
Opponent: 71,77% (G:43,76% B:10,38%)
Confidence: 0,009 (-0,845<E<-0,827)
Duration: 4 hours 31 minutes

4. Rollout¹ 8/2 6/4 eq:-0,853 (-0,041)
Player : 27,91% (G:0,70% B:0,03%)
Opponent: 72,09% (G:44,44% B:10,50%)
Confidence: 0,010 (-0,863<E<-0,843)
Duration: 4 hours 28 minutes

5. Rollout¹ 8/6 8/2 eq:-0,877 (-0,065)
Player : 27,05% (G:0,55% B:0,03%)
Opponent: 72,95% (G:44,83% B:10,26%)
Confidence: 0,009 (-0,886<E<-0,868)
Duration: 4 hours 00 minute

6. Rollout¹ 8/4(2) eq:-0,888 (-0,076)
Player : 26,62% (G:0,51% B:0,02%)
Opponent: 73,38% (G:45,16% B:10,00%)
Confidence: 0,008 (-0,896<E<-0,880)
Duration: 3 hours 05 minutes


¹ 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply


eXtreme Gammon Version: 1.21

Last edited by higonefive; 11-21-2010 at 09:05 AM.
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Old 11-21-2010, 03:48 PM   #6
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Re: Problem of the Week #83: Solution

Very interesting rollout. 9/7*/5 6/2 is thought to be the best play by the best backgame player in Norway(he is known to LOVE and think pretty uniquely about these positions).
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Old 11-21-2010, 04:27 PM   #7
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Re: Problem of the Week #83: Solution

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Originally Posted by Bjornar View Post
Very interesting rollout. 9/7*/5 6/2 is thought to be the best play by the best backgame player in Norway(he is known to LOVE and think pretty uniquely about these positions).
Thanks. I am going to loose the trust in my scientific estimation. And if you know him, you can tell him my estimation of the general course. I believe, in 83a there are to general plans, dodging, abandon win and trying to save gammons. And playing pure with the "phantom prime". I believe, if you want to save a gammon, you have to play anyway to hit a shot and contain him. And i believe this is to be achieved by playing pure, containing a checker with a semicrunched position, sometimes with Kit Woolseys "random play". The "weired" computer moves i think, are playing to reach this semicrunched position, because this is the best we can achieve. And the pure play is as good. If we don't hit and contain, there is no way out.
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