Understanding Match Equity in Backgammon

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When you are playing a backgammon match to a given number of points, the doubling cube decisions can be quite complicated. Whether or not you should double or take really boils down to two factors: the position of the checkers on the board, and the score of the match.

There are some backgammon positions that are clearly a double and a drop at one score, but not even a double at another score.
For example, take a look at Position 1 below.

Match Equity

Black is on roll and losing by 0-3 in a match to 5. He clearly should double here, and at this score, white should pass. But if Black was winning 3-0, he certainly should not double, and if he did, white should not only take the cube, but he should redouble on the next roll.

So here we have an example where the same position at different scores has very different strategies. When looking at the position on the board, you have to consider your winning and losing chances as well as your odds of winning or losing gammons and backgammons, AND THEN you must adjust your thinking depending on the score. For example, if you only need 1 point to win the match, you would NEVER double, but if your opponent needs only 1 point to win the match and you need more than one, you would ALWAYS double as soon as you can. (The exception is the Crawford Rule which does not allow you to double the first game your opponent is 1 away from winning the match.)

Over the years, with the help of backgammon computers, the experts have developed match odds at various scores and put them into a Match Equity Table. It is based on the idea that at a given score each player has certain odds of winning the match when compared to his opponent’s score. Of course, this always assumes both players are of equal skill. For example, if you are playing a 5 point match and you just begin, the score is 0-0 and you each have a 50% chance of winning the match. So your match equity at the beginning of the game is 50%.

Now the game starts and a few rolls later your opponent has gained an advantage on the board and he doubles you. It is important to know what your odds are if you simply drop the cube and are now losing 0-1 in the match to 5, or if you take and lose 2 points. Knowing the comparative difference in your odds helps you decide if the position is worth taking the chance to accept the cube or if you should just drop. Obviously, if your opponent is barely winning the game it is an easy take, and if he’s way ahead, it is an easy drop. But most games are not so clear. Often you get the cube when it’s somewhere in between your opponent being a little ahead or way ahead. Knowing the match equity helps you make that decision.

The experts have determined that if you are losing 0-1 in a match to 5, your odds of winning the match are 42%, and of course, your opponent’s odds have gone up to 58%. They have also determined that if you are losing 0-2 in a match to 5, your odds have gone down to 34%, and of course, your opponent’s odds are now 66%.

What that means is that if you are given the cube at 0-0 and you drop, you go from 50% to 42%, but if you take and lose 2 points you go from 50% to 34%. So assuming you don’t get gammoned, by taking the cube and losing you have cost yourself 8%…that’s the difference between having 42% or 34%. Ah, but if you take and win, you become a 66% favorite to win the match instead of your opponent. So the difference between dropping the cube and going to 42% and taking and winning and going to 66% is a whopping 24% difference. What that tells us is that if there are not serious gammon risks, and you have some reasonable chances to win the game (over 21% in fact), you gain a lot more by taking the cube than dropping at this score.

Remember, however, that if you take the cube, depending on the situation on the board, you will win some of the time, so unless there are strong gammon risks against you, if you have reasonable winning chances you really are not giving up too much of your match equity (only 8%) by taking the cube at this score. At any given score, you have to weigh the risks of taking or dropping the cube and what affect it has on your match winning chances if you win or lose the game or if you win or lose gammons or backgammons.

Trying to figure out all of these backgammon odds over the board can get very complicated, but here again, the experts have given us some help to make it easier. Over the years, they have devised a “Match Equity Table” that simply lists all of the winning and losing odds at various match scores. VIRTUALLY EVERY TOP PLAYER IN THE WORLD KNOWS THIS TABLE BY HEART.

The reason why every top player has taken the time to study and memorize the Match Equity Table is because it truly is useful when you are playing a match. Above I gave you an example of the equity difference consideration in whether or not to take a cube, but the exact same considerations must be made in the decision of whether or not to give the cube. It is just as important to know how much you have to gain or lose if your opponent takes or drops a cube, and you must weigh those considerations in making your determination to give the cube.
Below is the Match Equity Table for matches of 5 points or less. Please take a good look at this and I will tell you how to read it and use it.

Match Equity Table

The table is used to determine the odds of each player winning or losing a match when they are a certain number of points away from winning. It doesn’t matter if it is a 5 point match or a 21 point match, this table can be used whenever both players are within 5 points of winning.

Let us say, for example, that the score is 0-0 in a 5 point match. That means that both players need 5 points to win. So if you go up to the 5 on the top column, and you scroll down to the 5 from the across column, you will see 50. That means that both players have a 50% chance of winning.

Now let’s say that you have 1 point and your opponent has 3 points in a match to 5. What that means is you need to win 4 points to win the match, and your opponent needs 2. So you go to the 4 across the top, and you go down to where the 4 intersects the 2, and you will see the number in the box is 68. That means that at the beginning of the game, your opponent has a 68% chance of winning the match. You, of course, have a 32% chance of winning, and you can find that number by going to the 2 across the top and scrolling down to the 4.

Sound confusing? It is at first, but if you do it a few times and if you look at the numbers enough times, eventually you will have them memorized. Keep in mind that you only have to memorize the match equity number for the leader in the match as the other player’s odds is simply the difference between that and 100 percent.

When I first learned about the Match Equity Table, I carried a copy with me in my pocket to every backgammon tournament and studied it before every match until I had it memorized. It is something EVERY MATCH AND TOURNAMENT PLAYER should know.

Once you master this, the next step is to learn about the cost and value of winning and losing gammons and learning how to apply that as well at various match scores.

Did I make this seem to you that backgammon is perhaps more complicated and complex than you thought? I hope so, because truly, it is! Backgammon is a game of skill, and until you learn that and believe it, you will always believe that you win or lose simply because of luck. Yes, the dice often have a lot to do with whether we win or lose, but your odds increase greatly when you learn the tools and strategies that greatly reduce the luck factor. Learning the Match Equity Table is an extremely important tool for match play. Once you learn it and apply it, you will win more often and you will find that you have “better luck” as a result.