Match Equities

Forum Archive : Match Equities

ME at 1-away/2-away (crawford)

From:   Ian Shaw
Date:   30 April 2003
Subject:   Crawford 2-away is only worth 67.7%
Forum:   GammOnLine

I've completed 66,240 2-ply untruncated rollouts with GnuBg, half with
Leader winning the opening roll, and half with Trailer winning it. I
get a figure of 67.725% for Leader's Match Equity. The 95% Confidence
Interval is 0.047%, so we should be able to confidently say that 67.7%
is accurate to 1 decimal place.

Other METs quote:
71.25% (Zadeh)
70.0% (Woolsey&Heinrich, Ortega & Kleinman)
69.0% (Jacobs & Trice)
68.5% (Snowie 2)

My rollout value is lower than any of these, and lower than GnuBg's
own evaluations at 0, 1 and 2 ply, and lower than a 0-ply rollout (all
about 68.4%).

One feature I find strange about the rollouts is that Leader wins more
gammons than Trailer, no matter who gets the first move. This does not
show up in the evaluations, where the player with the first roll
always gets more gammons. The rollouts also show both sides getting
more gammons than the evaluations. I expected Trailer to get more
gammons, since he has the incentive to play for them. Maybe it is
easier for Leader to avoid gammons than for Trailer to achieve them.

I think I've adequately demonstrated on this forum that I'm no expert,
so I'd welcome other comments and opinions.

Here are the results in full. The overall MEQ for Leader is calculated
as Wins + ((Losses - Gammon Losses) / 2).


0-ply trials/side 7776

1st Roll   w      wg     wbg    l       lg     lbg   cubeless cubeful
Trailer  0.5232 0.1481 0.0126  0.4768 0.1887 0.0202  33.784%  33.784%
std err                                               0.290%   0.290%
Leader   0.5308 0.2192 0.0250  0.4692 0.1254 0.0099  69.939%  69.939%
std err                                               0.292%   0.292%
Leader's MEQ
Combined for Leader
         0.5038 0.2040 0.0226  0.4962 0.1368 0.0113  68.353%
    Combined Std Err 0.206% 95%CI 0.403%

2-ply trials/side 33120

1st Roll   w      wg     wbg     l      lg     lbg   cubeless cubeful
Trailer  0.5320 0.1527 0.0184  0.4680 0.1873 0.0259  34.236%  34.236%
std err                                               0.034%   0.034%
Leader   0.5208 0.2160 0.0323  0.4792 0.1271 0.0138  68.689%  68.689%
std err                                               0.034%   0.034%
Leader's MEQ
Combined for Leader
         0.4944 0.2017 0.0291  0.5056 0.1399 0.0161  67.725%
    Combined Std Err 0.024% 95%CI 0.047%

Ian Shaw  writes:

There was a bug. Gnubg variance reduction was not taking into account the
initial position setting. I guess the effect of this is to overcompensate
for the "bad" rolls of never getting a double on the first roll.

I'm not sure of the implication for my rollouts. Is the whole rollout
invalidated or just the reported standard error? I suspect the whole thing
is duff (groan). I'll redo my 0-ply ones initially and see what the effect

Excerpt from gnubg change log:

   Fri Jun 27 20:42:14 2003 Joern Thyssen
  * rollout.c (BasicCubefulRollout): fix bug in variance reduction
  when rolling out as initial position.
  (reported on GammOnline).

Neil Kazaross  writes:

Since this plays very fast it was easy to do 259200 rollouts with each
side on roll.

With the leader on roll he wins 51.39% of the games and 13.07% G's. With
the trailer on roll the trailer wins 48.61% games and 14.21% G's

Calculating that out results in the trailer winning 49.895% of all games
with 13.64% gammons and thus his ME is 31.7675%.

I'd estimate that the std dev of that ME is less than .1% and am running
a set of 648,000 overnight and will do 648,000 with the other side on
roll tomorrow.

Note that my rollouts have the side on roll winning substantially less
often than Ian's rollouts did. My 0-ply rollouts are also consistant with
my 0-ply rollouts using VR.

I cannot believe that using 2-ply play makes a big difference and believe
that we should take another look at the long 2 ply rollout.

The best way to do this is as a team with each member doing a few of the
15 possible opening rolls for each side using 2-ply world class w/VR.

Did you find the information in this article useful?          

Do you have any comments you'd like to add?     


Match Equities

Constructing a match equity table  (Walter Trice, Apr 2000) 
Does it matter which match equity table you use?  (Klaus Evers+, Nov 2005)  [GammOnLine forum]
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)  [GammOnLine forum] [Long message]
ME Table: Big Brother  (Peter Fankhauser, July 1996) 
ME Table: Dunstan  (Ian Dunstan+, Aug 2004)  [GammOnLine forum]
ME Table: Escoffery  (David Escoffery, Nov 1991) 
ME Table: Friedman  (Elliott C Winslow, Oct 1991) 
ME Table: Kazaross  (Neil Kazaross, Dec 2003)  [GammOnLine forum]
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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