Mec26: A ‘New’ Match Equity Table

Any player serious about reaching the upper echelons of backgammon knows that one requirement is to know the double and take points in match play especially as the number of points to finish shrinks. Naturally one will want to use the best data available, and different sources have published METs, or Match Equity Tables, over the years. The most popular to date is that of Kit Woolsey and Hal Heinrich, published in 1993 in Woolsey’s seminal work, How to Play Tournament Backgammon and available at GammOnLine. Others have appeared since then, such as the highly regarded one by Jake Jacobs and Walter Trice in their 1996 work, Can a Fish Taste Twice as Good?, and the Snowie 2.1 MET in the 1999 version of the program Snowie. How different are they? And is it worth the effort switching to another? The answer to that last question is entirely up to the reader.

Sometime about a month ago, there was a discussion among the GNU Backgammon developers on the default MET used in the program. The program allows the user to choose the match equity table of their choice, an option that is probably used very little, and by default uses the table by Zadeh published in 1977. This default choice seemed very poor so a discussion took place on which should be the new default. Joseph Heled, the developer of the neural nets, mentioned he used none of them, and instead used Mec26. No one knew what this was, so he explained that it was based on a small program published in 1996(!) by Claes Thornberg, and made freely available for download. News of it was published in the newsgroup rec.games.backgammon with a link to share with others. The reasons given were errors spotted with someone else’s match equity table work, and thus a program was written, to generate a new one using selected gammon values and winning chances. Having never seen it mentioned in either literature, or by expert players, I can only presume it went unnoticed or unheeded for the most part.

The table in question is the result of the program using values of 26% gammons, and 50% winning chances. The post-crawford values were done by Joseph Heled himself using GNUBG’s rollouts. Before going any further, the first question is whether it is verifiably better, and the answer is yes. It was tested against the Woolsey table and after 500,000 7-point matches, alternating the sides while retaining the same rolls so that each side got the same rolls once, the result was 50.06% against 49.94% for a total of 0.12% difference. This is despite the fact that differences of close to 2% can be seen between the two tables as shown below. It was also tested against the Jacobs/Trice table winning by a slightly lesser margin, and against the Snowie table as well. The very small overall effect on the score is explained by Heled, "the effect of MET is not that big since, again, many decisions are relative and will be right as long as the MET is consistent."

Still, it is worth mentioning that the table covers matches up to 25 points, extends to decimal points, and does bear some striking differences at some scores compared to Woolsey’s table. Far more than 0.12%. Comparing the Pre-Crawford 7-point match scores from the two tables, some of the more notable differences are:

	Woolsey	Mec26
1-away 2-away:	70%  /  30%	68.5%  /  31.5%
2-away 4-away:	68%  /  32%	66.4%  /  33.6%
2-away 6-away:	81%  /  19%	79.5%  /  20.5%
2-away 7-away:	85%  /  15%	83.5%  /  16.5%
3-away 4-away:	59%  /  41%	57.1%  /  42.9%
3-away 5-away:	66%  /  34%	64.6%  / 35.4%

And now of course for the table itself, but one last point. I am providing the table exactly twice below. The reason is simply that if you plan to print this out, the full table will easily go right off your screen, not to mention paper. The first table only covers 15 point matches, and should be easily printable, whereas the second includes the entire thing up to 25-away 25-away.