Gammons- It’s all About Risk & Reward- Part 2

Let’s take a look at Illustration 1 below. Black has to play 2-2, 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.

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 5-5…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 5-5. 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 1-1, 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 Snowie the backgammon bot, 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 Snowie 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 3-3. 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 insure a win every time, and if you make the riskier play and take 4 off, you still don’t win many gammons. In fact, Snowie tells 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 Snowie for the definitive answers (Snowie is not always 100 percent right, but in situations like this it is very close). Snowie tells 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 no-brainer.

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.