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11.5.3 Match Winning Chance

In match play we're generally not particular interested in the outcome of the individual games as much as the outcome of the entire match, so the interesting quantity for match play is match winning chance (MWC). As for the money equity the MWC can be calculated with and without the effect of the double cube. The MWCs are generally calculated with the use of a match equity table, which contains the chance of winning the match before a game starts, e.g., if the score is 0-0 in a 1pt match each player has 50% chance of winning the match before the game starts assuming they're of equal skill.

The cubeless MWC is calculated as: MWC(cubeless) = p(w) * MWC(w) + p(l) * MWC(l) + p(wg) * MWC(wg) + p(lg) * MWC(lg) + p(wbg) * MWC(wbg) * p(lbg) * MWC(lbg).

For example, if the w/g/bg distribution is 0 30 60 - 40 10 0 and the match score is 1-3 to 5 with the cube on 2 the cubeless MWC is:

MWC(cubeless)= 30% * 50% + 30% * 0% + 30% * 100% + 10% * 0% + 0% * 100% + 0% * 0% = 45%,

so the cubeless MWC is 45%.

Evaluating the cubeful MWC is more difficult, and as for the cubeful money equity it's possible to estimate cubeful MWCs from transformation on the w/g/bg distribution or directly calculate it from neural nets. GNU Backgammon uses the former approach, but the formula are currently not published.