How to Use eXtreme Gammon to Understand Match Equity and Take Points
By Phil Simborg
First, some definitions. Match equity is the percentage of the time you will win the match from a given score, assuming that you and your opponent are equal players. For example, if you are playing a match to 5 and the score is tied, at any score, your match equity is 50%. Odds are, you will win half the time. But if you are losing the match, your odds of winning go down, and the reason it is important to know just what your odds are is that it will affect your cube decisions. By the way, if you are playing this game at a reasonably high level, you will also alter some of your checker play decisions based on the score as well.
For example, if you are losing 2-0 in a match to 5, the numbers we truly care about are NOT that you have zero and your opponent has 2, but rather that you need 5 points to win and he/she needs only 3. The way we express this is that you are 5-away and your opponent is 3-away. According to the latest analysis (by Rockwell and Kazaross) the leader at this score is a 58% favorite to win the match, and the trailer therefore has 42% match equity.
If you would like to know your match equity or winning
chances for any score, you can take a look at the table by clicking on Analyze,
and then Match Equity Table.
When you do this you will see the latest table, which looks like this:
Once you do this you will see the information below:
In the analysis shown, if you are red and you are 3-away, your take point is between 24.92% and 36.80%. The higher number is the take point if it is the last roll of the game or there is little or no opportunity for a redouble after you take the cube. The lower number is the number you can use more of the time, assuming that you will have the opportunity to redouble at the perfect time. Since the perfect time rarely happens, generally the number we use is slightly higher than the Live Cube number shown, or in this case, about 26% would be a practical number to use.
The “dead cube” take point is the result of using a formula that takes the match equity if you simply drop the cube and compares that to what you take the cube and lose (risk), and what you gain if you take the cube and win (reward). That formula is risk/risk+reward. In order to know your take point in a match, you need to know your match equities and use this formula, or you simply need to memorize the take points. It is not hard to memorize most of the take points for most of the scores that are commonly played, but you can always check yourself by looking at the above screen.
Now, the take points are assuming there are no gammons or backgammons, and many positions where there is a cube carry that additional risk. How much to value gammons and backgammons again depends on the score. The value is expressed in terms of how much a gammon is worth, or costs you, compared to winning or losing the game at a given score. Here again, you need to memorize or be able to calculate or estimate these values in order to make intelligent cube decisions.
And here again eXtreme Gammon can help you as a reference. When you go to analyze/cube information, you can click on the “gammon value” table below, and it will give you the values for both players at the given score shown.
For example, in the above position, if you click on Gammon Value you will see the screen below:
As you can see, any gammons that Red wins are worth .707, or 70.7% as much as winning a game. Blue’s gammon values are higher, because since he is 2-away from winning the match, a gammon with the cube in the center (at 1) wins the match.
If we click on the circle by the “2” we would see the gammon values if the cube is on 2. See below.
Now the value of Blue’s gammons have gone down to 0. Since Blue needs 2 points to win the match, and the cube is on 2, gammons and backgammons have no value to him at all.
Regardless of your level of play, it is critical to have an understanding of match equity, take points, and gammon values in order to play well, and fortunately, if you take the time to learn how to use it and read the numbers, eXtreme Gammon gives you the information you need to teach you these values and to remind you when you forget.
Note: Phil Simborg is a professional backgammon player and one of the leading backgammon teachers in the world. Phil and his teaching partners have a web site which provides a position of the day with an analysis and other interesting information at www.thebackgammonlearningcenter.com.