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| Pip: 144 | ||
| Game 1 5 point match Green-White: Score 4-1 | ||
| Pip: 154 | ||
| # | Ply | Move | Equity | |
| 1 | R | 23/21 7/3 | -0.412 | |
| 0.2% 6.7% 40.3% 59.7% 10.3% 0.3% | ||||
| 95% confidence interval: - money cubeless eq.: -0.230 ±0.010. Rollout settings: Full rollout, 1296 games (equiv. 60887 games), played 3-ply (fast), random seed, with race database. | ||||
| 2 | R | 8/6 7/3 | -0.506 (-0.094) | |
| 0.2% 7.4% 38.4% 61.6% 12.9% 0.4% | ||||
| 95% confidence interval: - money cubeless eq.: -0.290 ±0.010. Rollout settings: Full rollout, 1296 games (equiv. 54630 games), played 3-ply (fast), random seed, with race database. | ||||
| 3 | R | 13/7 | -0.532 (-0.120) | |
| 0.4% 7.7% 37.8% 62.2% 13.6% 0.5% | ||||
| 95% confidence interval: - money cubeless eq.: -0.305 ±0.011. Rollout settings: Full rollout, 1296 games (equiv. 47685 games), played 3-ply (fast), random seed, with race database. | ||||
| 4 | R | 23/21 6/2 | -0.538 (-0.126) | |
| 0.3% 6.9% 37.5% 62.5% 13.5% 0.4% | ||||
| 95% confidence interval: - money cubeless eq.: -0.318 ±0.011. Rollout settings: Full rollout, 1296 games (equiv. 50531 games), played 3-ply (fast), random seed, with race database. | ||||
| A Special Backgammon Lesson |
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This posiiton arose in a 5-point match between Chicago player Phil Simborg and GGRaccoon (a computer player). Phil Emailed
Tim Mabee with the position and the problem he faced. Both Phil and Tim are accomplished
tournament backgammon players, but not of expert class.
They traded emails about the position. and eventually Nack Ballard and Jake Jacobs got involved in the discussion. Jake is "only" ranked in the top 15 in the world, while
Nack is the consensus #1 consensus player in the world. To give context to the position, I have included
Phil and Tim's original emails, which include some good-natured barbs.
What is most interesting, by far, are Nack and Jake's comments at the end. It truly is a rare treat to
get this kind of insight into the game of backgammon. We are all eagerly awaiting Nack's first book, scheduled to
be published later this year. [Phil] Black leads 4-1 in a match to 5, holds a 2-cube, and 4-2 to play. I blew it..... you? [Tim] It couldn't be wrong by much to make the bar. [Phil] Yes, it could be. You're as bad as me. [Tim] Need a rollout to convince me that putting a checker on the 3-point is better, down in the race. [Phil] It has been rolled out many thousands of times by Malcolm [Davis], and he, Neil [Kazaross], and Nack [Ballard] all make that play. Is that enough to convince you? [Tim] I may be convinced, but I haven't learned anything. Does Nack explain WHY the safe play is clearly superior to one that provides some structure? [Phil] Nope…neither did Jake [Jacobs}, Perry [Gartner], or Paul Weaver or others….they all simply thought is was a simple, straight-forward play. I’m with you on this one….I don’t like the recommended play either. My first thought was that winning 4-1 in a match to 5, you tend to stay away from plays that might get you gammoned more…but it looks like the gammons are about the same with the other plays. Because you and I don’t understand this very well, I am copying my email experts on this to see why Snowie’s play is superior and see if anyone can educate us on this one. Over the board, in a similar position, I would probably screw it up again. Nack Ballard's analysis of this position In mutual holding games, the order of the day is not to get hit outside. The object is to hit your opponent outside. Failing an outside hit on either side, the first player to roll a big doublets will have the advantage. (If it is the player who is already leading, it may be a decisive advantage. If it is the player who is trailing, it may be only a small advantage.) Another key feature of this position is the value of the midpoint. Outfield control is more important when one side or (especially) both sides have an advanced anchor. Black is a clear underdog in the game, but just considering the outfield control aspect, he has a chance to use his third checker on the 21pt to advantage; by running it, he can keep his timing, thereby keeping his valuable midpoint longer than White can keep hers. Right now, Black's midpoint inhibits White from making her 9pt with double 2's, and if White strips her midpoint, Black's midpoint will inhibit White from making her 7pt with 6-1 (she might do it anyway, but it leaves an expensive shot). And if White loses her midpoint completely, perhaps Black can combine his 21pt checker (after running it into the outfield) with a midpoint checker to make his 10pt or 9pt, saving his 8pt builders for his 7pt. (It leaves a blot on the midpoint, but White no longer has that hugely profitable hit with an ace.) By the same token, in mutual holding games, priming points are reduced in value because builders cannot be as easily positioned (without leaving a direct shot) to make the remaining priming points (in this case the 5pt) and a full prime cannot be made. Moreover, if you look closely, after 13/7, Black cannot use all his spares in front of White anyway. There are three builders (8pt 8pt 6pt) aiming at one point (the 5pt), a direct consequence of having "wastefully" used a midpoint builder to make the 7pt (the job of one of the 8pt spares). In short, putting a dilly builder on the 3pt is not nearly as bad as it would be if the 4pt were vacant. After 13/7, if Black is missed, he will presumably want to run his midpoint blot to safety. This means that next roll, Black will often have four builders overbuilding onto one point (the 5pt). Moreover, White can safely run both checkers out with 6-5, and in some later variations it will be a more reasonable risk to run out with one checker with 6, 7 (or 8) pips because Black will have lost the option to hit outside and his chances to go after both checkers is significantly reduced. The value of having the 7pt as a blocking point and a place to house 3-hitters does not come close to compensating. If White's anchor were not advanced, that would change everything. Move White's anchor on Black's 4pt to Black's 1pt or 2pt, and 13/7 becomes a better play than the ugly 24/21 7/3. (8/4 6/4 becomes the best play of all, but that is incidental.) Black's loss from getting hit is smaller and his gain from not getting hit is much larger. The swing is enormous. Given that gammons trade 1:1 with wins at this score, you were right when you said "...tend to stay away from plays that might get you gammoned more…" but in my view, it was quite sloppy to add "...but it looks like the gammons are about the same with the other plays." According to the Snowie-4 evaluation, 23/21 7/3 gets gammoned 3.5% less often (12.4% vs 15.9%) than the second best play (13/7). Since 23/21 7/3 wins only 2.2% more often (39.9% vs 37.7%) than 13/7, the reduced gammon risk is an even more substantial reason to prefer 23/21 7/3 over 13/7 than the superior winning chances. Jake Jacobs then weighed in with his review: A couple of points (besides the gammon issue) ... |
Output date: 8:34:41 PM, 1/31/2005(Export v2.10)