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Re: [Bug-gnubg] improvement of cubeful equities in match play bearoffs

From: Joseph Heled
Subject: Re: [Bug-gnubg] improvement of cubeful equities in match play bearoffs
Date: Fri, 04 Apr 2003 19:46:25 +1200
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Joern Thyssen wrote:
On Fri, Apr 04, 2003 at 10:38:03AM +1200, Joseph Heled wrote

I thought eq(cfully live cube) would not be "easy".

In principle it is.

For match play it's explicitly calculated by the Cl2CfMatch-family of
functions. However, for money play Cl2CfMoney uses Janowski's formulae
directly, so there is not explicit calculation of the fully live cube
equity. My simple work-around is to call Cl2CfMoney with x=1 which
returns the exact fully live cube equity for all cube positions
(assuming the call to Cl2CfMoney is made with Jacoby and beavers off).

Anyway, have you staged a large nnumber of matches between the two strategies, to see that it really works?

No, not yet. The reason why I commited the code was that I'm most certain
that it's an improvement. The border line examples are a good proof. For
example, at -7,-7 with a centered cube gnubg's estimate of the equity in
3 roll vs 3 roll and 4 roll vs 4 roll will be more than 0.1 off.
With the new code it's less than 0.01.

Also, I don't want to play entire matches as they rarely end in
bearoffs. I would have to play an huge number of matches to get any
statistically significant result.

I'd rather take a sample of bearoff situations that can be
found in the two-sided bearoff database or so "close" that 2-ply will
pick it up.

That is what I had in mind (i.e. to start from bearoff positions). Sorry if I was not clear on that.

I don't think you want a rollout. What you want is to play and count number of wins (or actually the mwc). What I would do is play each position two times, with the same settings and same dice, only exchanging the players. This can reduce the variation by quite a lot.

I think you will need several 100K positions at least.


All these sample positions can be applied at a representative set of
match scores, cube values, and cube positions. The resulting equities
from both the old and the new code can be compared to cubeful rollouts.
The problem is which program to use for the rollouts? The new or the


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