Match Equities

 Which match equity table is best?

 From: Martin Krainer Address: martin.krainer@aon.at Date: 14 October 2003 Subject: Question to different MET's Forum: rec.games.backgammon Google: 3f8bc29b\$0\$24880\$91cee783@newsreader01.highway.telekom.at

```I know that Kit's MET is very popular, but there are some other
interesting ones like from Jacobs, Kazaross, Zadeh and so on.
Well, I know they differ not very much in the most cases, but for example
in 1away, 2away there are differences up to 1,5-3% (many have 68,5 there,
and Kit has 70). That could make a big difference in an analyze.
What causes these differences? (just the estimated chances for gammons?)
What MET do you prefer?

Regards
Martin
```

 Douglas Zare  writes: ```It can make a big difference relative to the value of one point in the match. However, this only happens when you hit certain decisions at certain scores. Most of the time, your decisions should not depend on which MET you use, and when they do, it is rare that the difference will decide the match. Several empirical tests by Joseph Heled have found that modern tables only outperform the Woolsey-Heinrich table by roughly 50.1-49.9 in 7 point matches, or about 1 elo point. Nevertheless, all common match equity tables agree that gammons are more valuable at 5-away 5-away and 4-away 5-away than for money. Particularly if you use a bot to analyze match play, you need to understand what the bot's match equity table says about the match score, or else you will get noisy feedback from the bot. > What causes these differences? (just the estimated chances for > gammons?) What MET do you prefer? In constructing match equity tables, some people use more or less complicated mathematical models. The mathematical models do not provide enough complexity, sometimes ignoring imperfect cube efficiency, sometimes ignoring the possibility of becoming too good to double, and sometimes assuming that the checker play is the same as for money play. Sometimes the mathematical models produce silly results like a lower equity for the trailer at 2-away 4-away than at Crawford 2-away. However, these errors may cancel. That the model was too simple doesn't mean the MET is wrong. Some people used empirical evidence to construct match equity tables. There was not enough data collected to give accurate estimates for many scores. I believe the Woolsey-Heinrich table used results of over a thousand matches just for the 5x5 table, and the uncertainties were in cases greater than a percent. There wasn't enough data to give an accurate, consistent match equity table for longer matches. Further, much of the evidence collected for the Woolsey-Heinrich table was collected from people who might have been viewed as experts at the time, but whose play was far below what we expect of experts today, particularly with regards to match play. Also, I believe Kit Woolsey stated that he smoothed out the entries to make them easier to remember, but I think later analysis shows the 3-away 4-away entry in the W-H MET is wrong, and there should _not_ be a smooth progression of 2-away 3-away, 3-away 4-away, 4-away 5-away, and 5-away 6-away. To me, it is important that a match equity table give values in tenths of a percent, rather than just to the nearest percent. It is not that I usually judge positions within tenths of a percent, but roundoff errors in the entries get magnified when you use the entries to compute take points and gammon prices. An error of 0.5% may get magnified to 4%, worth about 2 pips in the race and 0.200 after D/T, at some match scores. This is far more important for longer matches and lopsided match scores than for scores within the 5-point match. The gammon rate assumed in the creation of a MET is important. A higher gammon rate tends to favor the trailer, with some exceptions such as 4-away 5-away and a decision at 2-away 3-away. A table based on a higher gammon rate will tend to have lower gammon prices for the trailer (e.g., post-Crawford), since the trailer will have less urgency to win a gammon now if a later gammon is likely. I think the 26% gammon rate assumed by modern tables such as Snowie's table is much more accurate than the ~21% assumed for the W-H table. The W-H table has all of these faults: A bad entry at 3-away 4-away, only 2 digits of precision, an assumed gammon rate of 20%. However, it was not convincingly beaten in tests, appearing only 1 elo point worse, which is impressive to no one. Since the more modern tables disagree with each other far less than they disagree with the W-H table, I think it is not of practical value to look for improvements on the modern METs. It is far more important to start using some MET than to switch to a better one. So, I start my backgammon students off with the W-H MET, albeit with the 3-away 4-away entry crossed out. Douglas Zare ```

 Martin Krainer  writes: ```Hello Douglas, Thanks much for this great answer. Very interesting was, that you said that the 26% gammon rate is more accurate than 20 or 21%. Why dont we know already exactly about the gammon chances? Arent the PC's already fast enough, that we could say: Its nearly for sure a number between 25 and 27 %? ```

 Douglas Zare  writes: ```There are a couple of issues. First, we can determine the gammon rate for any particular bot and setting, but they don't have to agree with each other. Gregg Cattanach posted a rollout on Gammonline suggesting that the gammon rate for Snowie 4 2-ply standard is about 27.2%+-0.3%. This would not be the same for other bots, though. Snowie 4 has a style that leads more backgames and to fewer blitzes than Snowie 3. Jellyfish, on the other hand, avoids backgames even more, but it bears off too aggressively after closing a checker out. These style differences may make a large difference in the gammon rate without making a large difference in the playing strength. Second, the gammon rate in money play may not be the same rate in match play, so it might not be the right thing to use when making a match equity table. For example, I think it is clear to play very aggressively for the gammon trailing Crawford 2-away. The leader doesn't need to trade any wins for gammons, and can concentrate on winning and saving the gammon. Does the net effect of the trailer's altered strategy and the leader's altered strategy favor one side or the other? This is not something to guess a priori. Some rollouts suggest that the trailer wins slightly less than 50%, but so many more gammons that the trailer wins more than 32% of the matches, which is what you would get if you assumed no alteration, but a 28% gammon rate. I'm not sure what happens at other scores, but I am very suspicious of the assumption that the bg/g/w distribution from money play carries over to match play. Here is an example: Snowie's MET says the trailer wins 25.22% from Crawford 3-away. This appears to come from ignoring the value of the free drop, and assuming that the trailer wins a backgammon 0.9% of the time. The free drop is certainly worth something, and so many METs say the equity should be less than 25%. However, at Crawford 3-away, gammons are so unimportant that the checker play is close to that at DMP, when one more frequently plays backgames and ace point games, which lead to many more backgammons. At Crawford 3-away, the backgammons are worth something, and they should not happen only 0.9% of the time, even though the leader need not risk a backgammon to save the gammon. I think the net effect is larger than the value of the free drop. So, in conclusion, we don't really know how many gammons ought to be won in money play, but if we did, it would not necessarily let us improve our match equity tables. Douglas Zare ```

### 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)