Going for Gammons…It’s all About Risk/Reward By Phil Simborg
One of the toughest decisions we often have to make is just how much we should gamble to try to win a gammon. As you know, a gammon doubles the points you win, so if you can win a gammon, it’s like winning two games at once. The problem is, a lot of the time the play that is more likely to get you a gammon is risky and often results in losing more games. This conflicting interest is just one more reason why Backgammon is such a fascinating and complicated game.
There are two concepts that will help make the game less complicated and difficult, however, and I will give you the basics of those two in this article.
Everything in Backgammon boils down to odds, and as you know, odds is all math. Yes, there is a human factor…knowing how to read your opponent and take advantage of specific weaknesses of each opponent, but underlying every checker and cube decision is the odds, or the math, and even reading your opponent simply causes you to change those odds one way or another to adjust. The math of gammons vs. wins is actually quite simple.
For the sake of this article, let’s assume we are playing a money game, and in most money games the Jacoby Rule is in effect. (The Jacoby Rule states that you cannot win a gammon or backgammon unless the cube has been turned.) So we assume that the cube is on 2 (if the cube is on 4 or 8 or more, the exact same principles and ratios apply).
If you win the game on 2, you win 2 points. If you lose the game, you lose 2 points. If you win a gammon, you win 4 points. If you win a backgammon, you win 6 points. (Because gammons are relatively rare, and the math gets more confusing, I will only discuss gammon vs. winning odds in this article.)
Now here is the interesting part that most people either don’t realize or they tend to forget. If the cube is on 2 and you win 2 points, you have a net gain of 2 points. But if you lose the game and lose 2 points, you have a net loss of 4 points!
Now that concept baffles a lot of people, so let’s do the math. Let’s pretend you are playing for $1 a point. The cube is on 2, and you are winning, and if you go on to win the game you will end up with $2.00. But if you lose the game, not only do you not get that $2 your opponent would have paid you, but you have to reach in your pocket and give him $2. So you actually have $4 less than you would have had if you had won the game.
Let’s put it another way. Suppose you came to the table with $10 in your pocket. If you win the game, you would have $12 in your pocket, but if you lose the game, you would have only $8 in your pocket. So the point is, if you turn a game from a win to a loss, and the cube is at 2, you have $4 less than you would have had.
Now let’s look at what happens if you turn a winning game into a gammon. Instead of winning $2, you win $4. So your net gain by winning a gammon is $2 (2 more points at $1 a point).
The bottom line is that winning a gammon is only half as important as winning the game, and so in technical terms, we say that the value of a gammon is worth .5 in a money game. In layman’s terms, we say that you need to win twice as many gammons as you might lose in order for it to be right to make a play that increases your gammon chances.
This is a very important principle, and even if you do not carefully calculate the math over the board and you just make rough estimates, as most of us do, you need to know the basic risk/reward of going for gammons.
I said there were two basic concepts that will help you, and here is the second:
I have been playing Backgammon for over 50 years, and every day I see positions that are completely unfamiliar to me! I am sure that some of the time it is just because there are so many positions it is impossible to remember them all, but it’s also because there truly are millions of possible positions that can evolve on the board. With that in mind, it is not possible to simply memorize every position and the right answer, so the ONLY way to really learn to play Backgammon correctly is to learn the basic concepts and ideas and make your best guesses and calculations to apply those concepts when you are playing.
I have given you the basic math above, but how to apply them over the board is just as important as knowing the math, and that takes practice, but it also takes knowing how to do the math and how to apply it over the board. The best way to learn this is by taking the time to go through a few specific examples and then, because we have the benefit of very excellent computer programs today, we can check our math and our decisions using those computers. Once you learn how to do this using a couple of examples I will give you in this article, it will help you apply it over the board in other positions that will come up for you.
Let’s take a look at Illustration 1 below. Black has to play 22, and he has two choices: he can move the two checkers off his 4 point to his 2 point and then take 2 checkers off, or he can take 4 checkers off. If you move the checkers off your 4 point, there is no chance that you will leave a blot and get hit, so you will certainly win this game 100 percent of the time. But if you do that, you only get 2 checkers off instead of 4, and White is a lot more likely to get off the gammon.
If you take 4 checkers off, you will certainly win more gammons, but you might lose more games. So the question is, how many more gammons will you win by taking the extra 2 checkers off, and how many more games will you lose if you do that?
Don’t feel bad if you cannot come up with those answers. I have shown problems like this to some of the best players in the world, and even they are not able to come up with definitive numbers, but they are able to “estimate” fairly well. The point is, all you have to do is decide if the additional gammons are more than twice as many as the losses.
Illustration 1
The key in every situation is to try to project what is likely to happen on the next few rolls. In Illustration 1, the answer if pretty obvious to good players, and that’s because the risk of losing is extremely small. In order for Black to lose after taking 4 checkers off, White must NOT roll a 6 on the next roll, because if he rolls a 6 he must leave. He must also leave if he rolls 55…so 12 out of 36 games there is no chance of leaving a shot. Now, let’s say White does not roll a 6 or 55. That means that with any other roll if White decides to stay and wait for the shot, he must break one or more points in his inner board.
Let’s say White does that. Black only leaves a shot if he rolls a 1, but not 11, and that’s only 10 out of 36 rolls. And then, if Black does leave a shot, White hits it only if he rolls a 1, and that’s 11 out of 36 rolls. AND THEN, even if all that happened, White is still a long way from winning this game, as Black can easily come in and get around and win.
The fact is, according to the bots (computer programs, I now use only ExtremeGammon by the way), if Black takes 4 checkers off he is going to win this game about 99.9 percent of the time. If he plays safe, he wins 100 percent of the time, so by taking the “riskier” play he is only risking one tenth of one percent!
Now, how many more gammons does he win? Again we look to the bots for the answer, and it tells us that if we take 4 checkers off we win gammons about 22 percent of the time, and if we make the “safer” play we win gammons about 8 percent of the time. So in this situation, the decision is simple: pick up an extra 2 points 14 percent of the time or lose the 4 points (when you turn a win to a loss) one tenth of one percent of the time. It would be foolish to play safe, or just take 2 checkers off in this position.
Now let’s take a look at Illustration No. 2.
This is very similar, but Black has to play 33. Again, he can move his back checkers forward and take 2 off and be guaranteed not to leave a shot, or he can take 4 off. There are some big differences between this position and the first one, however. Before I list those differences and how they affect the decision, see if you can come up with them for yourself, and then read on.
I hope you were able to readily see the big differences between this position and the first one: a) in this position Black has no checkers off, and in the first position Black had 5 off, so the gammon chances are far less; b) in this position, White has a better board, so a hit would cause more losses; c) in this position, White is not forced to run if he rolls a 6, so he is more likely to get a shot.
In this situation, the right play is to play safe, and that is because by playing safe you virtually ensure a win every time, and if you make the riskier play and take 4 off, you still don’t win many gammons. In fact, the bots tell us this: if you make the safe play you win 99.7 percent of the time and you win a gammon only 1/10^{th} of 1 percent of the time…almost never. If you take off 4 checkers your gammon wins go up to 1.4 percent but your wins go down to 96 percent. So you lose 3.7 percent more often and win gammons only 1.3 percent more. Again, applying our basic math, if you lose 3.7 percent more, you would have to win gammons twice as much, or 7.4 percent more to be worth going for the gammon.
Now take a look at Illustration No. 3 below.
This position is the same a 2 except that Black has 5 checkers off and White has a worse board. Clearly you have less risk of losing this game by taking 4 checkers off, and clearly you will win more gammons here by taking them off. Again, experts can estimate these numbers very well, but most of us must just make our best guesses. Hopefully, now you know the basis for making your guess: will you win twice as many gammons as you will lose as a result of your play? In the situation in Illustration 3, I hope you would conclude that the answer is yes, and that you would take 4 off.
Again I go to the bots for the definitive answers (they are not always 100 percent right, but in situations like this it is very close). The bots tell us that by taking 4 off we win gammons about 16 percent of the time and win the game about 100 percent of the time. If we take two checkers off and move our other two off the 5 point, we only win gammons about 8 percent of the time, but we are still favored to win the game 100 percent of the time! So in this situation, taking 4 off doubles our gammon chances and doesn’t even cost us a single win! It’s a true nobrainer.
All of the above examples and principles apply to “money game” situations and they also apply to many match play situations. Match play gets a lot more complicated because at certain scores winning a gammon is extremely important, and at other scores it doesn’t matter at all, or matters very little. In money games the value of the gammon is always .5, but in match play it could be as low as 0 and as high as 1.06, so you have to learn when those gammons are really important and when they are not.
In this article I have given you some simple, and extreme examples, but in real life the decisions you will have to make will be far more complex, but hopefully you now have the basic principles to apply, and hopefully, this will make you a better player.

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