Backgammon Match Equities

Match Equities

Neil's numbers

From:   Kit Woolsey
Address:   kwoolsey@netcom.com
Date:   9 October 1994
Subject:   Re: Equity/Action Table
Forum:   rec.games.backgammon
Google:   kwoolseyCxEFrs.6J3@netcom.com

Come on, Durf. Match equities aren't all that complicated, and they really are important if you are to maximize your chances to win matches. First of all, it might surprise you to know that I have never been able to memorize my own table -- my memory isn't too good either. Fortunately there are formulas around which help those of us with poor memories. The best one I know was developed by Neil Kazaross -- called Neil's numbers. It is as follows: 3 4 5 6 7 8 9 10 11 12 13 14 15 10 9 8 7 6 5 4 The numbers on top represent the number of points the trailer has to go. The numbers on bottom represent what each point the leader is leading is worth over 50%. If there isn't a whole number there, interpolate. For example, suppose you are ahead 3-0 in a 7 point match. The trailer has 7 points to go, so each point of lead is worth 6 1/2 points over 50% to you -- thus your equity is about 69 1/2% (my table says 70%). That's all there is to it! The above table is easy even for us dumbbells to remember -- after the trivial start all you need to remember is "8 is 6, 11 is 5, 15 is 4" and you're done. Also, the calculations involved are pretty simple to do in your head quickly. Neil's numbers are incredibly accurate if the leader has 3 or more points to go, but tend to break down when the leader has 2 or 1 points to go. Thus it is best to memorize that part of my equity table (even I was able to do that), and you're all set. As far as using the table to make cube decisions, it isn't as complicated as people make it to be. For example, suppose you are ahead 2-0 in a 7 point match, and a 4-cube comes sailing your way. If you pass, it is 2-2 for 50% equity. If you take and are right (i.e. you win) you will be ahead 6-0 for 91% equity. If you take and are wrong (i.e. you lose) you will be behind 4-2 for 34% equity. Thus you are risking 16% to gain 41%, so you are getting 41 to 16 odds on your take (somewhere between 2 to 1 and 3 to 1), so you can act accordingly. As for estimating your chances of winning a given position, maybe there are players who can actually go through the calculations which Robertie describes. I'm not one of them! When I am presented with a cube decision, I make an old fashioned seat of the pants estimate of my winning chances, based on my experience and intuition. I then compare this estimate with the odds I am getting on my take (calculated as I described above), and that is what I base my decision on. Crude, and my estimate of my winning chances in a position might be way off, but at least once I have made that estimate I know what to do with it. If you don't know how to use match equities you might be able to make a very accurate estimate of your winning chances and still not be able to make a sensible cube decision. If anybody is interested in learning more about match equities and tournament play I could immodestly recommend a certain book, but that might be construed as *shudder* advertising, so maybe I shouldn't do that. Kit

Paul Money writes:

The book which Kit modestly fails to mention is "How To Play Tournament Backgammon", author K. Woolsey. It is essential reading for anyone who aspires to handle the cube with confidence in match situations. I cannot recommend it too highly. This is an unsolicited testimonial!

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