Match Equities

Forum Archive : Match Equities

 
ME at 1-away/2-away (crawford)

From:   Fabrice Liardet
Date:   19 November 2007
Subject:   GG vs GS
Forum:   GammOnLine

If one players plays gammon-go and the opponent gammon-save (e.g. the
gammon values are 1 for GG and .for GS), will it result in more or less
gammons?  In comparison to the standard gammon value of .5 for both
players, of course.

David Rockwell  writes:

This is a very interesting question. My very limited number of rollouts on
the subject indicate that there are more gammons. I do not have a lot of
confidence in this yet. If anyone has done serious work with this, I'd be
very interested in seeing the results.

Here's my speculative reasoning to explain this result. Throughout most of
the game, GG will vary some plays trying to increase gammon wins and GS
will vary some plays trying to decrease gammon losses. These variations
will roughly offset so that there is no increase or decrease in gammons
(yet).

However, if GG gets an effective attack or closeout - GG will vary some
plays trying to increase gammon wins, but GS will not have a choice of
moves. This will increase the number of gammon wins for GG.

If this is true, it has implications for the use of cubeless rollouts to
determine the best play at GG or GS, even after adjusting for the price of
gammons.

Fabrice Liardet  writes:

Yes, common sense seems to shout that there will be more gammons, and your
reasoning does a lot better in explaining why than I had thought of. Now if
you look at the opening moves, it sounds reasonable to say that the most
likely outcome is that GS will split immediately and will succeed in making
an advanced anchor, after which the gammon rate is drastically lower. It is
not obvious to me that GG will blitz him often enough to compensate.

David Rockwell  writes:

Your comment raises the right question -- Which is more significant, the
trailer's efforts to increase gammons or the leader's efforts to decrease
gammons? It isn't clear.

The primary reason this is important is to know how well we can trust
opening roll rollouts at CL for use at GG and GS after adjusting for the
price of gammons. Tom Keith's fine site uses this approach to take
advantage of existing data. But he adds the caution than score based
rollouts may produce different results. There may be similar DMP issues as
well, but I suspect DMP is a lesser concern.

Raccoon  writes:

According to Tom Keith's 46,656-trial cubeless money game rollouts:

0-ply gammon rate = 26.59%, or 13.295% per player
2-ply gammon rate = 27.62%, or 13.81% per player

Are you wanting to know whether the Trailer at 1-away 2-away Crawford wins
more or less than 13.295% (or 13.81%) gammons?  And whether Trailer at 1-
away 2-away Crawford wins more or less than 50% of games?

Raccoon  writes:

GNU Backgammon rollout at the score 2-away 1-away Crawford, version .1

Full Cubeful Prune, G11 MET, .Ply Play

      Leader       Leader         Trailer  Trailer Wins   Leader's
Roll  Plays        Wins (SD)      Wins     Gammon (SD)    ME (%)    Trials
----  -----------  -------------  ------   -------------  ------    ------
3-1   8/5 6/5      .5483 (.0026)  .4517    .1110 (.0019)  71.865     1296
4-2   8/4 6/4      .5358 (.0061)  .4642    .1226 (.0018)  70.659     1296
6-1   13/7 8/7     .5314 (.0024)  .4686    .1244 (.0021)  70.353     1296
6-5   24/13        .5340 (.0014)  .4660    .1321 (.0012)  70.096     3888
4-3   24/20 13/10  .5019 (.0029)  .4981    .1262 (.0020)  68.782     1296
5-3   8/3 6/3      .5115 (.0060)  .4885    .1367 (.0019)  68.741     1296
6-2   24/18 13/11  .5080 (.0059)  .4920    .1349 (.0021)  68.656     1296
3-2   24/21 13/11  .5030 (.0026)  .4970    .1308 (.0020)  68.609     1296
6-4   24/14        .5114 (.0024)  .4886    .1399 (.0020)  68.579     1296
6-3   24/15        .5081 (.0010)  .4919    .1377 (.0008)  68.523     7776
5-4   24/15        .5081 (.0010)  .4919    .1377 (.0008)  68.523     7776
5-2   13/8 24/22   .5053 (.0026)  .4947    .1365 (.0020)  68.442     1296
2-1   13/11 24/23  .4994 (.0007)  .5006    .1308 (.0006)  68.433    14000
5-1   13/8 24/23   .4982 (.0023)  .5018    .1328 (.0020)  68.270     1296
4-1   13/9 24/23   .4950 (.0024)  .5050    .1312 (.0021)  68.192     1296
----  -----------  -------------  ------   -------------  ------    ------
                   .51329         .48671   .13102         69.115

      Trailer      Leader         Trailer  Trailer Wins   Leader's
Roll  Plays        Wins  (SD)     Wins     Gammon (SD)    ME (%)    Trials
----  -----------  -------------  ------   -------------  ------    ------
6-3   24/18 13/10  .4954 (.0024)  .5046    .1217 (.0021)  68.686     1296
6-2   13/5         .5058 (.0011)  .4942    .1394 (.0009)  68.321     7776
5-1   13/8 24/23   .5019 (.0028)  .4981    .1369 (.0022)  68.246     1296
5-2   13/8 13/11   .4980 (.0024)  .5020    .1359 (.0022)  68.108     1296
6-5   24/13        .4719 (.0013)  .5281    .1122 (.0010)  67.987     3888
4-1   13/9 6/5     .5028 (.0033)  .4972    .1448 (.0022)  67.900     1296
3-2   13/10 13/11  .5043 (.0025)  .4957    .1469 (.0021)  67.872     1296
6-4   8/2 6/2      .5005 (.0016)  .4995    .1449 (.0015)  67.782     1296
4-3   13/9 13/10   .5019 (.0025)  .4981    .1486 (.0021)  67.663     1296
5-4   13/9 13/8    .4984 (.0018)  .5016    .1452 (.0019)  67.657     2592
2-1   13/11 6/5    .4932 (.0029)  .5068    .1426 (.0021)  67.532     1296
5-3   8/3 6/3      .4828 (.0020)  .5172    .1585 (.0023)  66.218     1296
6-1   13/7 8/7     .4633 (.0023)  .5367    .1523 (.0020)  65.548     1296
4-2   8/4 6/4      .4651 (.0026)  .5349    .1681 (.0024)  64.849     1296
3-1   8/5 6/5      .4488 (.0025)  .5512    .1746 (.0024)  63.710     1296
----  -----------  -------------  ------   -------------  ------    ------
                   .48894         .51106   .14484         67.185

                   -------------  ------   -------------  ------
Total:             .50115         .49885   .13793         68.150


I'll run each rollout out to 46,656 trials 0-ply, and then start on 2-ply.
 
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Match Equities

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ME Table: Kazaross-XG2  (neilkaz, Aug 2011) 
ME Table: Rockwell-Kazaross  (Chuck Bower+, June 2010) 
ME Table: Snowie  (Chase, Apr 2002) 
ME Table: Snowie  (Harald Retter, Aug 1998) 
ME Table: Woolsey  (Raccoon, Apr 2006) 
ME Table: Woolsey  (Kit Woolsey, May 1994) 
ME Table: Woolsey  (William R. Tallmadge, Jan 1994) 
ME Table: Zadeh  (Jørn Thyssen, Mar 2004)  [GammOnLine forum]
ME Table: Zorba  (Robert-Jan Veldhuizen+, Dec 2003) 
ME at 1-away/2-away (crawford)  (Fabrice Liardet+, Nov 2007)  [GammOnLine forum]
ME at 1-away/2-away (crawford)  (Ian Shaw+, Apr 2003)  [GammOnLine forum]
Match equities--an alternate view  (Durf Freund, Oct 1994) 
Neil's new numbers  (neilkaz, Aug 2011) 
Neil's numbers  (Kit Woolsey+, Oct 1994) 
On calculating match equity tables  (Neil Kazaross, July 2004)  [GammOnLine forum]
Turner formula  (Gregg Cattanach, Feb 2003) 
Turner formula  (Stephen Turner, June 1994) 
Using a match equity table  (Michael J. Zehr, June 1992) 
Value of free drop  (Neil Kazaross, Oct 2002)  [GammOnLine forum]
Which match equity table is best?  (Martin Krainer+, Oct 2003) 
Which match equity table is best?  (Ian Shaw+, Dec 2001) 
Why use a match equity table?  (Kit Woolsey, Feb 1999) 
Worth memorizing?  (Alef Rosenbaum+, Feb 2003) 

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