Bearing In Against 2 Point Anchor (Part 1)

	is Professional score: 0 pip: 117 Money session Jacoby Beaver pip: 90 score: 0 is Me_v_Bot
XGID=–bBBBCBBB–a-a—abbbbb–:1:-1:1:53:0:0:3:0:10
to play 53

eXtreme Gammon Version: 1.21

The natural play here seems to be 9/6 9/4, which gives

	is Professional score: 0 pip: 112 Money session Jacoby Beaver pip: 82 score: 0 is Me_v_Bot
XGID=–bBCBDBB—a—–acbbbb–:1:-1:1:00:0:0:3:0:10
on roll, cube action?

eXtreme Gammon Version: 1.21

Now the issue with clearing from the 9 is apparent, a 65 forces a blot on the 7 point!

The correct play is the awkward looking 8/5 8/3

	is Professional score: 0 pip: 107 Money session Jacoby Beaver pip: 82 score: 0 is Player 1
XGID=–bCBCCB-B—a—–cbbcb–:1:-1:1:00:0:0:3:0:10
on roll, cube action?

eXtreme Gammon Version: 1.21

Now the worst role for white is 55, this still forces a blot but it is an indirect that can only be hit with 4 rolls rather than a direct.

I was hoping this could be generalized into a rule such as never leave 2 checkers each on the 7 and 8 points when bearing in against a two point board, but it is not that simple.

	is Professional score: 0 pip: 107 Money session Jacoby Beaver pip: 88 score: 0 is Player 1
XGID=–bBBBCCBA—a—–cbbcb–:1:-1:1:62:0:0:3:0:10
to play 62

* 1.	XG Roller+	9/3 7/5	eq: +0.724
	Player: Opponent: 85.87% (G:5.65% B:0.09%) 14.13% (G:0.45% B:0.01%)
2.	XG Roller+	9/1	eq: +0.704 (-0.020)
	Player: Opponent: 85.00% (G:5.38% B:0.08%) 15.00% (G:0.52% B:0.01%)
3.	XG Roller+	7/1 6/4	eq: +0.666 (-0.058)
	Player: Opponent: 83.29% (G:5.57% B:0.11%) 16.71% (G:0.73% B:0.02%)
4.	XG Roller+	9/3 6/4	eq: +0.634 (-0.090)
	Player: Opponent: 82.25% (G:4.77% B:0.09%) 17.75% (G:0.83% B:0.02%)
5.	XG Roller+	7/1 3/1	eq: +0.384 (-0.340)
	Player: Opponent: 73.09% (G:7.05% B:0.19%) 26.91% (G:6.20% B:0.15%)

eXtreme Gammon Version: 1.21

Here the answer is to do just that! To see why let’s examine the alternatives

	is Professional score: 0 pip: 100 Money session Jacoby Beaver pip: 80 score: 0 is Player 1
XGID=–bCBCCBB———-ccbcb–:1:-1:1:00:0:0:3:0:10
on roll, cube action?

eXtreme Gammon Version: 1.21

This is the position after the best play. There are 3 bad rolls for white in this position, 65 as in the position above leaves a blot on the 7, 55 is even worse in this case as it leaves a blot on the 6 point.  But what are the options?

9/1 is the second best option, after 9/1 we have:

 

	is Professional score: 0 pip: 96 Money session Jacoby Beaver pip: 80 score: 0 is Player 1
XGID=-AbBBBCCB———-cbbcba-:1:-1:1:52:0:0:3:0:10
to play 52

eXtreme Gammon Version: 1.21

At first pass this looks about the same as 9/3 7/5, 55 blots, this time on the 8 instead of the 6 and 64. Both plays leave 3 blot rolls this time, so the difference seems to lie in what happens with the none blotting rolls.  After 9/3 7/5 the non blotting rolls play pretty well. But after 9/1 some of the non-blotting rolls are problematic. For example to avoid leaving a blot with 44 will force a gap on the 5, 66, 65 and 63 all leads to blotting numbers on the next roll

 

One has to look even deeper to see way 7/1, 6/4 falls so far behind. It leaves only 65 as an immediate blotting number, which would entice one to make the play on a quick analysis.  However, after 7/1 6/4 playing 6s creates a lot of problems for future rolls.

 

It is relatively easy to analyze this type of position with the aid of XG or GNUBG, the dice distribution feature in XG and Temperature Map in GNUBG aid in determining the problematic rolls after a play. The real issue is seeing these problems OTB, and doing it fast enough to be able to make the right play. I have a long way to go on that, so it is time to practice, practice, practice.

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Rollouts from Magriel’s Backgammon

 

NOTE: THIS IS A WORK IN PROGRESS, ADDITIONAL ROLLOUTS ARE STILL BEING CONDUCTED AND WILL BE ADDED AS THEY BECOME AVAILABLE.

I recently started reading Paul Magriel’s classic Backgammon. I had avoid this book because I knew that it was prebot and contained some errors. However I was struggling—even with reading Trice—to put to get clear in my mind some of the guiding principles that were being used to drive plays in various positions. After reading some comments online about Magriel’s book I decided to give it a try. I wanted to know – beyond the openings—were Magriel was not in agreement with the bots. My search turned up the following link at Hardy’s Backgammon pages:  http://www.hardyhuebener.de/engl/magriels_irrtuemer.html.  This is excellent information, however the rollouts are all cubeless and GNUBG 0-ply. So I decided to use this list as a starting point and reroll these positions in XG.

I choose money play, no Jacoby, cubeful, 3-ply for the rollout parameters. Money play without Jacoby was chosen because I believe it will give the best overall information for checker play in most money situations as well as most match play situations where the checker play is not score dependent.  Using 3-ply was a practical consideration for doing the rollouts in a reasonable amount of time and still providing a high degree of accuracy. I screened the candidate plays using XG Roller + and included at least all the plays that were better than Margriel’s in the longer rollout. I used 1296 as the base number of games, but in some cases extended until the play either reached statistical significance (i.e. the confidence intervals between the top play and Magriel’s did not overlap) or until it was pretty clear that the plays were to close to call. For example in Position 12.1 the equity difference between Magriel’s play and the top play is 0.003, but both the top play and Magriel’s have confidence intervals of ±0.003 after 41,472 games, so this is a too close to call situation. Magriel’s plays are shown in bold italics in the rollout results.

There are some significant differences between these results and the GNUBG published at Hardy’s Backgammon Pages, undoubtedly due to differences in bots, plys, and choice of settings. This work is not intended as a criticism of the work done by the author of that site, therefore I will not go into a position by position comparison of the results from the two projects.

Position 12.1

1.	Rollout1	8/7 8/5	eq: +0.364
	Player: Opponent: 58.83% (G:15.71% B:0.59%) 41.17% (G:7.65% B:0.17%) Conf: ± 0.003 (+0.361…+0.367) Duration: 5 hours 49 minutes
2.	Rollout1	7/6 7/4	eq: +0.361 (-0.003)
	Player: Opponent: 57.97% (G:16.67% B:0.62%) 42.03% (G:8.56% B:0.23%) Conf: ± 0.003 (+0.358…+0.364) Duration: 5 hours 20 minutes
3.	Rollout1	8/6(2)	eq: +0.354 (-0.010)
	Player: Opponent: 58.09% (G:15.96% B:0.59%) 41.91% (G:7.94% B:0.19%) Conf: ± 0.003 (+0.351…+0.357) Duration: 4 hours 37 minutes
1 41472 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.13

Position 12.4

1.	Rollout1	10/9 6/4	eq: +1.000
	Player: Opponent: 78.72% (G:3.05% B:0.06%) 21.28% (G:1.31% B:0.01%) Conf: ± 0.000 (+1.000…+1.000) Duration: 1.9 seconds
2.	Rollout1	9/8 6/4	eq: +0.982 (-0.018)
	Player: Opponent: 78.29% (G:2.57% B:0.06%) 21.71% (G:0.94% B:0.01%) Conf: ± 0.006 (+0.976…+0.988) Duration: 45.1 seconds
3.	Rollout1	9/7 6/5	eq: +0.965 (-0.035)
	Player: Opponent: 78.94% (G:2.77% B:0.05%) 21.06% (G:0.88% B:0.01%) Conf: ± 0.005 (+0.960…+0.970) Duration: 1 minute 25 seconds
4.	Rollout1	10/8 6/5	eq: +0.893 (-0.107)
	Player: Opponent: 76.18% (G:3.03% B:0.06%) 23.82% (G:1.43% B:0.02%) Conf: ± 0.001 (+0.892…+0.894) Duration: 1.9 seconds
5.	2 ply	6/5 6/4	eq: +0.889 (-0.111)
	Player: Opponent: 74.90% (G:2.98% B:0.07%) 25.10% (G:3.13% B:0.04%)
1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.13

Position 13.20

1.	Rollout1	24/18 13/11	eq: -0.281
	Player: Opponent: 43.91% (G:7.68% B:0.35%) 56.09% (G:13.56% B:0.64%) Conf: ± 0.020 (-0.301…-0.261) Duration: 1 hour 06 minutes
2.	Rollout1	24/22 13/7	eq: -0.306 (-0.026)
	Player: Opponent: 42.86% (G:6.83% B:0.28%) 57.14% (G:12.20% B:0.45%) Conf: ± 0.018 (-0.324…-0.288) Duration: 58 minutes 32 seconds
3.	Rollout1	24/22 24/18	eq: -0.317 (-0.036)
	Player: Opponent: 42.83% (G:7.07% B:0.32%) 57.17% (G:13.23% B:0.51%) Conf: ± 0.021 (-0.338…-0.296) Duration: 1 hour 00 minute
4.	Rollout1	13/11 13/7	eq: -0.411 (-0.130)
	Player: Opponent: 40.29% (G:7.82% B:0.36%) 59.71% (G:14.03% B:0.68%) Conf: ± 0.019 (-0.430…-0.392) Duration: 59 minutes 14 seconds
1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.13

Position 13.25B

1.	Rollout1	20/16 10/4	eq: +1.421
	Player: Opponent: 88.52% (G:60.19% B:1.39%) 11.48% (G:2.48% B:0.23%) Conf: ± 0.009 (+1.412…+1.430) Duration: 7 minutes 36 seconds
2.	Rollout1	20/14 10/6	eq: +1.408 (-0.013)
	Player: Opponent: 88.36% (G:59.80% B:1.37%) 11.64% (G:2.46% B:0.23%) Conf: ± 0.008 (+1.400…+1.416) Duration: 6 minutes 46 seconds
3.	Rollout1	10/4 9/5	eq: +1.405 (-0.017)
	Player: Opponent: 87.65% (G:57.48% B:1.24%) 12.35% (G:1.98% B:0.11%) Conf: ± 0.008 (+1.397…+1.413) Duration: 5 minutes 19 seconds
4.	Rollout1	20/14 9/5	eq: +1.404 (-0.018)
	Player: Opponent: 88.21% (G:59.58% B:1.37%) 11.79% (G:2.55% B:0.23%) Conf: ± 0.008 (+1.396…+1.412) Duration: 4 minutes 19 seconds
5.	Rollout1	20/16 9/3	eq: +1.402 (-0.020)
	Player: Opponent: 88.25% (G:59.56% B:1.38%) 11.75% (G:2.62% B:0.24%) Conf: ± 0.009 (+1.393…+1.411) Duration: 4 minutes 51 seconds
1 2592 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.13

Position 14.16

1.	Rollout1	8/4 6/4	eq: +0.447
	Player: Opponent: 63.05% (G:9.98% B:0.60%) 36.95% (G:8.63% B:0.30%) Conf: ± 0.015 (+0.432…+0.462) Duration: 22 minutes 52 seconds
2.	Rollout1	14/8	eq: +0.305 (-0.142)
	Player: Opponent: 58.90% (G:8.41% B:0.44%) 41.10% (G:9.82% B:0.27%) Conf: ± 0.016 (+0.289…+0.321) Duration: 20 minutes 27 seconds
3.	Rollout1	7/1*	eq: +0.302 (-0.145)
	Player: Opponent: 59.80% (G:7.72% B:0.29%) 40.20% (G:10.83% B:0.34%) Conf: ± 0.017 (+0.285…+0.319) Duration: 25 minutes 49 seconds
1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.13

Position 16.9

Magriel only shows the 3, I placed a checker on the bar and made the other dice roll a 4 to arrive the position in Magriel.

1.	Rollout1	Bar/21 13/10	eq: -0.178
	Player: Opponent: 45.45% (G:10.68% B:0.51%) 54.55% (G:13.25% B:0.62%) Conf: ± 0.022 (-0.200…-0.156) Duration: 52 minutes 54 seconds
2.	Rollout1	Bar/21 8/5*	eq: -0.272 (-0.094)
	Player: Opponent: 45.20% (G:12.42% B:0.67%) 54.80% (G:20.24% B:1.41%) Conf: ± 0.028 (-0.300…-0.244) Duration: 1 hour 03 minutes
1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.13

Position 17.8

1.	Rollout1	13/10	eq: -0.606
	Player: Opponent: 33.70% (G:7.81% B:0.28%) 66.30% (G:15.57% B:0.80%) Conf: ± 0.018 (-0.624…-0.588) Duration: 26 minutes 41 seconds
2.	Rollout1	24/23 13/11	eq: -0.690 (-0.084)
	Player: Opponent: 31.83% (G:6.83% B:0.27%) 68.17% (G:16.65% B:0.72%) Conf: ± 0.022 (-0.712…-0.668) Duration: 44 minutes 54 seconds
3.	Rollout1	24/23 8/6	eq: -0.720 (-0.114)
	Player: Opponent: 31.03% (G:6.22% B:0.19%) 68.97% (G:13.85% B:0.58%) Conf: ± 0.024 (-0.744…-0.696) Duration: 29 minutes 22 seconds
4.	Rollout1	8/5	eq: -0.731 (-0.125)
	Player: Opponent: 31.70% (G:6.66% B:0.22%) 68.30% (G:18.70% B:0.95%) Conf: ± 0.025 (-0.756…-0.706) Duration: 47 minutes 01 second
5.	Rollout2	13/11 8/7	eq: -0.740 (-0.134)
	Player: Opponent: 32.52% (G:7.07% B:0.26%) 67.48% (G:21.43% B:1.20%) Conf: ± 0.018 (-0.758…-0.722) Duration: 1 hour 34 minutes
1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply 2 2592 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.13

Position 18.3

1.	Rollout1	Bar/24 11/6	eq: -0.810
	Player: Opponent: 29.52% (G:7.39% B:0.21%) 70.48% (G:16.60% B:1.15%) Conf: ± 0.022 (-0.832…-0.788) Duration: 34 minutes 54 seconds
2.	Rollout1	Bar/24 23/18	eq: -0.891 (-0.082)
	Player: Opponent: 30.66% (G:9.52% B:0.51%) 69.34% (G:25.53% B:2.58%) Conf: ± 0.025 (-0.916…-0.866) Duration: 38 minutes 47 seconds
3.	XG Roller+	Bar/24 13/8	eq: -1.000 (-0.190)
	Player: Opponent: 27.86% (G:6.81% B:0.17%) 72.14% (G:22.82% B:2.47%)
4.	XG Roller+	Bar/24 6/1	eq: -1.000 (-0.190)
	Player: Opponent: 26.02% (G:4.99% B:0.09%) 73.98% (G:21.62% B:1.53%)
1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.13

Title Change

 

You may have noticed I have changed the title of this blog, I have also changed the “What is this Blog About” page.  I am still struggling with finding time to write much here, and I have certainly lost the original theme of the blog. Hopefully what I do post will still be of benefit, but all I can say right now is the blog is “about Backgammon.”

Opening 21

Yes, I know, I am not being consistent at all with what I am posting here based on the stated theme, but part of me is still trying to get a handle on the best way to learn this game, so I am going all over the place. For those few readers I have hopefully you will understand and bear with me, otherwise by blog becomes simply a place for me to try to organize my own study which is okay as well.

Opening Roll Source Material

Most of the information I am using for my study of opening rolls is coming from the opening information at http://www.bgonline.org/., these are often referred to as “Stick’s” rollouts because bgonline is maintained by Stick Rice. Timothy Chow, who comments here frequently, has published a very handy summary of 2nd roll information which can be found at http://www-math.mit.edu/~tchow/2ndmove.shtml. You will also find on Timothy’s page links to information on nactation, a link to a similar summary of opening moves using standard notation, and a link to the opening information on Tom Keith’s Backgammon Galore site. I will not bother to duplicate those links here at the moment.

These charts are very handy, but I am finding that to get a grasp on the material I need more than that, so I am attempting to group and offer some reasoning for the plays in an attempt to more easily learn what to do rather than rely on brute force memorization. I am also trying to get more comfortable with using nactation, so I am using it mixed with traditional notation and simple descriptive text (eg, make the 20pt) below.

Opening 21

There are basically two options for playing the opening 21, slotting (21$, 13/11 6/5) and splitting (21S, 13/11 24/23).

My tendency has been to play 21S except at gammon-go scores where I tended to the slot. The rollouts indicate that 21$ is a slightly better play than 21S. One thing I did find surprising is that according to Stick’s rollouts 21$ is best even at gammon save scores, Keith’s rollouts differ from this but those are cubeless rollouts. However the difference in slot and split at GS in Stick’s rollout is very small, probably not statistically significant.

I have started playing 21$ instead of 21S as my typical 21 opening. I am still struggling with this in a couple of respects, one is mentally dealing with getting hit, especially after a roll of 64 where you end up with two checkers on the bar. More difficult for me at this point is playing my second roll when I am unable to cover the slotted checker. This is an area I need to work on.

Replies to 21$

Hit the slotted checker if possible except with 11.  This is pretty easy to remember as it seems quite logical. The only question that remains is what do with the rest of the roll, of course with 31 you don’t have a rest of the roll after hitting.

11: Is the one exception to the hit the slot if you can rule. The best play with 11 is to make your 5 and 7 points. (nactation: N). Hitting here is around a 0.03 error. Without doing a lot of work to try and understand this one it seems that the value of making the 3 prime and having a good shot at a quick 4 prime must outweigh the value of hitting. Still this seems like a less than obvious best play to me.

22: This one can gives me pause OTB as it is very tempting to make the 20pt – given all we hear about the value of doing that, but the best option here (based on Keith’s data and bot evaluations) is to hit the slot and make the 4 point. (nactation: e)

41: Play 24/23 with the second checker, the two other options of slotting the 5 or 7 pts leave too many return shots. (nactation: U)

42: Play the second checker down to the 11 pt, it gives you a builder and can only be hit with 65. (nactation: S)

43: Stick’s rollouts (which for 2nd rolls do not have any at score information) gives a very slight edge to playing 24/21 with the second checker, Keith’s are the same except at GG Keith’s play is down (13/10). This makes sense as you need to contain checkers for the gammon and getting the extra builder down improves you chances of doing this. (U, except at GG S)

44: Pretty easy, make the 20 pt and the 9pt. (B)

54: A very slight edge goes to bringing a checker down to the 8pt (S), running the checker out after the hit ( R) is not far behind although I find it surprising that R is not better at least at GS scores)

64: Easy, run your checker to the 14pt hitting both blots in the process. (K)

Split Against The Slot.  At first blush splitting when you cannot hit the slotted checker may not seem the best thing to do since you are giving your opponent two blots to shoot out and the slot gives them more ways to hit. However, some of the hitting plays that present themselves after these splits are not necessarily all that good for your opponent as they either bury checkers, force them off their 5pt, and/or leave good return shots.

32, 51, 52: S

21: Timothy’s chart gives both S and $ as options here, recent extensive 4ply XG rollouts by Neil Kazaross posted on the BGonline forum make it pretty clear that the $ is best, but the difference is still only 0.005 http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=59007

62: Has 3 viable options S (24/18 13/11), Z (13/7 24/22) and N (13/7, 6/4). Running out with a back checker (R) and bringing two down from the midpoint (D) have also gotten consideration. Based on recent rollout data S is best with Z being close and N not totally out of the question. http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=58683

63: Running a checker out (R) is the best play here rather than splitting, and the reverse split (24/22 13/7, Z) is slightly better than the normal split. None of the plays are huge errors (S being about –0.015 worse than R)

Rather Obvious Plays. 53, 55 both make your 3 pt, 65 always runs a checker on the 2nd roll except for against 61P where you can’t, and 66 is forced 61 make your bar point.

And Finally.  33: Make your 5 pt and the 22pt. This play is harder to remember than it seems because in many cases the 2nd 33 is not used to make the 5 pt even though that might seem like the logical play at first glance. My instinct with this play is to make my 5 and 3 pt because having two home board points seems like such a good idea. But that is behind the best play and the more typical 33 second roll play of making the 22 and the 10 (B).

Replies to 21S

Play Like First Roll.  Many of the replies to 21S are played liked the first roll—or at least like of the main options for the first roll. These are:

31P, 51S, 61P, 32S, 42P, 52S, 54S, 62S, 63S (or 63R), 65R

Other Non-doubles

21: Playing 24/21 (21U) has a very slight edge over 21S, but both are viable plays.

41K: Hit both blots in your home board.

43:

53P or 53S: 53P gets an extremely small edge, but splitting is very close which is why I put it here rather than in the play like first roll group.

64H: Hit the checker on the 15 with 24/15

Doubles

11e (6/5(2),24/22) – Against the slot 11 is played as N, but with the split playing N gives shots with 6s and 7s, so this requires a safer play

22N, make the 4 and 11 points.

33B, make the 21 and 10 points.

44B, make the 20 and 9 points.

33 and 44 are both difficult for me to keep in mind because I have to fight the desire to make the 5 point with them. Of course with 44 this is moving two from the 13, with 33 you still have 2 3s to play. While making the 5pt with a 33 on the second roll is right at times, making it with a 2nd roll 44 is almost never right. 

55A, Hit on the 1 and make the 3, giving you a good start on a blitz.

66B Same thing for 66 on all 2nd rolls except after 61P, where you can’t, B with a 66 makes both bar points.

Things to Remember – Handy Rules and Guides

One of the things that I am struggling with is remembering all of the rules of thumbs, guidelines, etc. that I am coming across as I attempt to improve my game. So I decided to create a post that will expand as I collect more information, and hopefully find that it is helpful to me and others. Some of the items have been discussed in other places, but this is sort of a “cheat sheet” for trying to keep things in a handy reference. (And yes, I know, I am not posting much here as I seem to always be behind on my backgammon study)

Safe/Bold Criteria

Trice discusses this and I think I dealt with it in an earlier post, It is a guide for deciding whether to play safe or take more risk to gain a positional advantage.

The follow description of safe/bold criteria is taken from http://www.bkgm.com/articles/Townsend/BasicsOfBackgammon1.html

Here are some additional criteria for bold vs. safe play and how to interpret them:

1. Home board points. Relative strength in home board points allows for more aggressive play.
2. Anchors. One anchor vs. none allows for more aggressive play, this extends to:
   • Multiple anchors vs. single anchor.
   • A higher anchor vs. a lower anchor.
3. Blots in your home board discourage aggressive play (if you hit, they may hit you as they re-enter). Conversely enemy blots in his home board invite an exchange of hits.
4. More back men allow for more aggressive play, while counterintuitive, this is based on sound logic:
   • More than one man back can combine to form an anchor.
   • A single man back can only escape or be attacked.
   • A hit with only one man back may critically reduce your racing lead.

Other factors to be evaluated include outer board blocking points (especially points that block the escape of an enemy back man with 5’s or 6’s), blots exposed (the side with more exposed blots will wish to clean them up rather than expose more in many cases), and racing lead (lead discourages bold play).

The Last Two Checkers

Trice gives a chart of the number of the rolls that bears off one or two checkers at the end of game. Trice discourages memorization of the chart and supports learning to calculate the rolls. I find that – at least in online play—taking the time to calculate the rolls is a bit of an issue and my memory is not what it used to be.  While you have to know the number of rolls for doubling decisions there is a handy rule for determining how to place you checkers when playing. This will usually be where you have born off the 13th checker with half the roll and then must decided how to play the other half of the roll, for example if the have checkers on the 5 and 3 with a 1 to play should you move a checker from the 5 to the 4 or from the 3 to the 2.  To determine the best play use 3, 2, 4, 1, 5, 0 as a guide to determine how far apart to place you checkers, 3 apart being the best if possible, followed by 2 apart and so on. [Note: In a comment on this article Timothy Chow points out that an easier way to remember this is to place your two checkers as close to 2.7 pips apart as possible.]

So in the above example moving 3/2 is better than moving 5/4 because it places the checkers 3 apart rather than 1 apart.

For a nice chart of 1 and 2 checker positions and rolls to bear off see http://www.bkgm.com/articles/Koca/CuringYourShortBearoffBlues.html.

N-Roll Positions

N-Roll positions where the number of rolls to bear off without a double can be readily determined. This would be situations where there are checkers only the ace and deuce point, N being the number of checkers on the points divided by 2 and rounded up. For N roll positions the player on roll has the following chances of winning the game (rounded, cubeless):

2 – 86%

3 – 79%

4 – 75%

5 – 72%

Some positions that are not true N-roll positions will be very close, for example if you have 1 checker on the 3pt, 2 on the 2 pt, and 3 on the ace point you do not have a true N-roll position, but unless you roll 2-1 three times in a roll it is not going to matter.

Race Formulas

When there is not longer contact there are a variety of formulas that can be used as a guide to determine if you should double. None is perfect, but most are better than just guess. The two I use are:

Walter Trice’s Method which he discusses in Boot Camp:  I have rearranged it some to make it more formulaic, but this is the same logic:

If leaders pip count is > 62 Trice Number= leader count/10 + 1 round up

If leaders pip count < 62 Trice Number = (leader count-5)/7 round down

Count Difference = Trailer Count – Leader Count

If Count Difference < Trice Number  — Take

If Count Difference +3 > Trice Number – Double

If Count Difference + 2 > Trice Number – Redouble

Trice applies this formula to low wastage positions. In positions with higher wastage Trice applies the above to an adjusted pip count. In Boot Camp he uses the Ward count to make adjustments to pip counts but applies the decision criteria above.

Keith Count – Is the adjusted pip count method I use. The Keith Count works as follows:

Start with the raw pip count

add 2 for each checker more than 1 on the ace point

add 1 for each checker more than 1 on the 2 point

add 1 for each checker more than 3 on the 3 point

add 1 for each gap on the 4, 5 and 6

For player on roll add 1/7 of pip count (round down)

Once the above is calculated for each side

Keith Number = Adjusted Count for Player on Roll – Adjusted count for opponent

If Keith Number < 4 double

If Keith Number < 3 Redouble

If Keith Number > 2 Take

For an excellent discussion of the Keith Count as well as other formulas and race theory in general see http://www.bkgm.com/articles/CubeHandlingInRaces/

Bearing Off with Opponent on Bar But With Checkers Off

This type of position arises from a backgame, ace point game, or similar situation. You managed to hit your opponent and send them to the bar after they started bearing off. Now you are bearing off with the opponent on the bar and need to decided whether to bear off two checkers leaving a blot in your home board or to move to avoid the risk. Bill Robertie gives the following guidance for these situations:

The first metric we want to calculate is the crossover count. A crossover is simply a move of a checker from one quadrant to another, or from the bar to the opponent’s inner board, or from the inner board to the bearoff.

Next we employ the following rule of thumb:
>If you trail by two or less in the crossover count, play safe. You’re doing well enough in the race that there’s no need to take additional risks.
>If you trail by five or more in the crossover count, take two checkers off and leave a blot. You’re a big underdog in the race, and you need the extra checker speed.
>If you trail by three or four, you’re in a grey area.

In the grey area, decisions depend very much on the exact arrangement and count of checkers in the inner board. You next want to look at all of the following considerations and see if they point toward one play or another.
(1) If you trail by three crossovers, tend to play safe. If you trail by four, tend to bear off.
(2) If White has a blot in his board, tend to bear off. If no blot, tend to play safe.
(3) If taking two checkers off brings you to an even number of checkers, tend to bear off, otherwise tend to play safe.
(4) If you have a speed board, tend to play safe, otherwise tend to bear off. A speed board is one where Black’s home board spares are heavily concentrated on the one and two points, which implies that small doubles are more likely to bear off four checkers through the bearoff. With a slower board, where the checkers are spread evenly across points, small doubles often won’t save a roll.

The above is taken from a problem solution on the Backgammon Forum at 2+2 Poker Server. http://forumserver.twoplustwo.com/138/backgammon/problem-week-39-solution-651194/

Game Winning Chances When You Have One Checker on the Bar and Checkers Off

This is another bearoff situation where you have borne off several checkers and end up with one checker closed out on the bar. The following assumes that Red has a fast board (all checkers on the lower points) and white has the idea bear off position with a closed board and the spares on the 6, 5, and 4 pts. Then the cubeless winning percentages are:

% to win in reference positions
N off	1	2	3	4	5	6	7	8	9	10	11	12
Red	4.5	7	11	15	22	30	39.5	51	58	69	76.5	84
White	95.5	93	89	84	78	70	60.5	49	42	31	23.5	16
d		2.5	4	4.5	7	8	9.5	11.5	7	11	7.5	7.5

The last line shows the difference for red (the player on the bar) by having one more checker off than is in the top column.

This table can be used not only to aid in doubling decision but in  making decisions about the best way to play certain rolls that force you to leave a blot in the bearoff. It is taken from an article by François Tardieu in which he discusses using this information to make these types of decisions. The complete article can be found at http://www.gammonlife.com/writers/07tardieuart1.htm.

I See Said the Blind Man

 

Despite my best intentions of posting regularly and working through 501 Essential Problems along with Boot Camp my blog is going largely unattended. I am playing a lot of online tourneys, but not spending the in study and analysis I should be. And writing things for a blog as opposed to notes for myself takes more time. But I wanted to post a position that I was just looking at from the analysis of one of my matches. Maybe it is overly simple, but it took be quite a while to see what would have lead me to the right answer so maybe someone else will find it of interest.

My thought process when I played 20/17 with the three was to reduce the chances of getting hit.  Playing 20/17 as opposed to the correct play of 8/5 with the 3 leaves 9 shots as opposed to 11 shots.

When I first looked at this error in the analysis I was left scratching my head about what I would have seen during the match that would have lead me to the correct the play. My play actually gives a fractionally high winning percentage, but is a blunder based on equity due to the extra gammons (and backgammons) picked up with the correct play. 

I was about to give up on ever being able to see this in the course of a match, when suddenly the answer hit my, and it is remarkable simple. While leaving the blot on the 5 gives black 2 more shots at hitting it, it also gives white potentially 3 more shots at picking up the blot next turn if black is unable to move it.  The moral of the story for me is to not only think defensively, but think about how to give yourself the best chance of picking up the blot. 

	is Player 2 score: 1 pip: 100 11 point match pip: 119 score: 0 is Player 1
XGID=-b–CCBCA—-B–a–cabbbbA:0:0:1:53:0:1:0:11:10
to play 53

1.	Rollout1	Bar/20* 8/5	eq: +1.051
	Player: Opponent: 80.01% (G:26.77% B:2.06%) 19.99% (G:4.55% B:0.06%) Conf: ± 0.012 (+1.039…+1.063) Duration: 8 minutes 32 seconds
2.	Rollout1	Bar/20* 20/17	eq: +0.925 (-0.126)
	Player: Opponent: 80.52% (G:25.51% B:1.77%) 19.48% (G:7.29% B:0.12%) Conf: ± 0.011 (+0.914…+0.936) Duration: 11 minutes 25 seconds
1 1296 Games rolled with Variance Reduction. Dice Seed: 25 Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.11, MET: eXtremeGammon

Problem 64 From 501 (Part 3)

 

Continuing our discussion from Part 2, lets say that red got their worst roll of 42 and played it as best as possible, followed by blue fanning we arrive at the following position.

Pip counts: Blue 132, Red 72
Position ID: m20BwFDuzRkCAA Match ID: QQkAAAAAAAAA

Now looking at the temperature map we see:

There are several rolls here that force red to leave a shot, which is getting to the bottom the issue. Of course we could continue with all the other possibilities for a complete analysis, but we have enough to see why the 8/4 move is coming out ahead.

Problem 64 From 501 (Part 2)

In Part 1 of this post I noted that the play given in 501 of 13/12* 7/3 is actually not the best play. For easy reference the position is:

---

Red to play 14

Pip counts: Blue 121, Red 83
Position ID: m22BgEG2cxsEAA Match ID: QYkQAAAAAAAA

The better play as noted in Part 1 is 13/12* 8/4, but the real question is why is this play better?

Certainly having an extra spare on the 4 point as opposed to the 3 point does not seem to gain much in this position as you would normally prefer to diversify the spares.

Perhaps the best question to ask here is what loses the game for red, and that answer is pretty easy, blue must get a hit. Not only must blue get a hit, but that hit needs to come pretty quickly because blue does not have the timing to play out an extended backgame or ace point game. Their board is going to crunch soon, assuming they get the two checkers off the bar.

So red needs to make sure that blue does not get a quick shot. With either of the two plays under consideration there is not chance of blue hitting the red blot on either the 7 or 8 the next time around. So the answer must lie deeper.

There are several possible scenarios on blues next roll, these are:

16 Rolls get 1 checker off the bar (split evenly between coming in on the 1 and 5)

16 Rolls dance

4 Rolls get both checkers in 2 rolls bring checkers to the 1 and 5 point, 1 roll makes the 1 and one stacks the 5. (yes technically these are blues 24 and 20 points, but we are looking at this from red’s perspective).

Let’s look at the case were blue brings in one checker on the ace point.

After red plays 13/12* 7/3 and blue plays bar/24 we have the following position:

---

Red on roll

Pip counts: Blue 132, Red 78
Position ID: m20BwFB25xoCAA Match ID: QQkAAAAAAAAA

There are a lot of good rolls for red in this position, 66, 62, 63, 65, 52, 53, and 32 all make the ace and put blues checker back on the bar. Of course that was the whole reason for playing 7/3 was to maximize the rolls that made the ace point.

But since we are trying to figure out why this is the weaker of the two plays we are considering we need to look not only for the good rolls for red but also for the not so good rolls. Seeing the bad rolls in this case is not so easy, at least for me. To help out with the analysis I used the temperature map feature on gnubg, so here are the equities and best moves based on a 2ply evaluation. (I used 2ply because both 3ply and 4ply give 7/3 as best while 2ply gives 8/4 as best in a basic evaluation)  for red on this roll.

 

Now let’s compare this to the temperature map after moving 13/12* 8/4 and blue moving bar/24.

This is beginning to give us some hints as to why 8/4 is better than 7/3. Now we have to use a little caution here as the gnubg evaluation is not necessarily correct, but this is a good tool to help us see what might be going on.

Note that after 8/4 the worst roll for red is 31, and playing this correctly gives red an equity of +1.011. But after 7/3 31, 42, and 43 are all worse for red than the worse roll after 8/4.  There are also 3 rolls for red after 8/4 that are better than the best roll for red after 7/3.  Of course we are not looking at the whole picture here, just the case where blue enters one checker on their 24, but we are beginning to see a way to attack this analysis in detail. In part 3 of this post we will look at little more closely at why some of these rolls are worse after 7/3.

Problem 64 From 501 (Part 1)

This is the first problem I am going to tackle out of 501, and part of my goal in doing so is to attempt to delve into a more detailed analysis of a position to see how much I can learn. The position may be getting more analysis then it deserves, but it is the learning process that I am interested here more so than the position itself. I have picked this position because it is the first one I encountered (skipping chapter 1) where the answer in the book seems to be incorrect.

---

Red to play 14

 

Pip counts: Blue 121, Red 83
Position ID: m22BgEG2cxsEAA Match ID: QYkQAAAAAAAA

After making a fairly quick first pass through 501 I am now working through the positions in much more detail. I was proud of myself when I came up with the same play as Robertie for this position, that play is 13/12* 7/3.

My reasoning for this play was that it maximizes builders for the ace point. This is the same reasoning that Robertie gives, noting that making the ace point will increase the gammon chances.

So far so good, unit I start analyzing the position in GNUBG and then what do I find?

#		Ply	Move	Equity
	1	R	13/12* 8/4	+1.238
			0.908 0.458 0.007 – 0.092 0.003 0.000 +1.278 +1.238 0.001 0.001 0.000 – 0.001 0.000 0.000 0.002 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 870065397 and quasi-random dice
			Play: world class 2-ply cubeful prune [world class]
			keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
			Skip pruning for 1-ply moves.
			Cube: 2-ply cubeful prune [world class]
•	2	R	13/12* 7/3	+1.228 ( -0.010)
			0.902 0.464 0.007 – 0.098 0.004 0.000 +1.271 +1.228 0.001 0.001 0.000 – 0.001 0.000 0.000 0.002 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 870065397 and quasi-random dice
			Play: world class 2-ply cubeful prune [world class]
			keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
			Skip pruning for 1-ply moves.
			Cube: 2-ply cubeful prune [world class]

Close, but 13/12* 8/4 is just a bit better, the extra gammons from 13/12* 7/3 don’t quite make up for the extra losses, but what is going here? Why is the 7/3 worse?  Answering these questions is where the real learning lies, and that is the subject of Part 2.