Forum Archive :
Match Equities
ME at 1-away/2-away (crawford)
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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.
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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.
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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.
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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.
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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?
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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
- Constructing a match equity table (Walter Trice, Apr 2000)
- Does it matter which match equity table you use? (Klaus Evers+, Nov 2005)
- Does it matter which match equity table you use? (Achim Mueller+, Dec 2003)
- Does it matter which match equity table you use? (Chuck Bower+, Sept 2001)
- ME Table: Big Brother (Peter Fankhauser, July 1996)
- ME Table: Dunstan (Ian Dunstan+, Aug 2004)
- ME Table: Escoffery (David Escoffery, Nov 1991)
- ME Table: Friedman (Elliott C Winslow, Oct 1991)
- ME Table: Kazaross (Neil Kazaross, Dec 2003)
- 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)
- ME Table: Zorba (Robert-Jan Veldhuizen+, Dec 2003)
- ME at 1-away/2-away (crawford) (Fabrice Liardet+, Nov 2007)
- ME at 1-away/2-away (crawford) (Ian Shaw+, Apr 2003)
- 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)
- 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)
- 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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