Position Analysis in a Chouette Money Game

Today’s position analysis is a particularly fun one, because it happened to me in an actual money game recently. I was Black and having a wonderful time, on my way to gammoning my opponents (it was a chouette, a backgammon variant where one player plays against several others on the other side), and they were holding a 4-cube. I was about to win this month’s rent, when I rolled a terrible roll. 

Take a look at Position 1 and see if you can figure out what that terrible roll was.  

Well, I rolled a 5-2 (a 6-2 would have done the same thing), and what resulted was what you see in Position 2. 

Of course, there was a lot of noise, cheering, and celebration from my opponents, and they immediately give me back the doubling cubes at 8. 

If you said you would drop the cube, join the club—most people who look at this situation, and others like it, will quickly drop this cube. But the truth is, not only is this a take, IT’S NOT EVEN A DOUBLE! 

Now, when I say it’s not even a double, I mean that “technically” speaking, and according to the math, it is wrong to double. But when you have a real situation over the board where there is a strong chance that your opponent might make an emotional decision, or one made out of fear, and might drop, it is often right to double anyway. 

In this situation, I took quite a bit of time to make a decision and did my best to think through all the variables over the board, and I calmly took the cube.   

First, I will give you my thoughts. I know that as Black I cannot get gammoned, no matter how bad things get, because I already have checkers off. And I know that if White does not hit me immediately, he stands a very excellent chance of getting gammoned.  

I realized that out of the 36 possible rolls, 27 hit me right away, which means that 9 don’t. So 25 percent of the time I don’t get hit on the first roll, and most of those my opponent will get gammoned, so it didn’t take me long to realize it’s a sure, clear take. 

I then realized that even if my opponent does hit me on the first roll, that doesn’t necessarily mean I lose…in fact, according to Snowie (a computer software program) I still win about 10 percent of those games after one checker gets hit. (If two checkers get hit those odds go down to 5 percent, but 5 percent is still something worth considering.) 

When you put this into Snowie you find out that in fact, it was not a double at all and a clear take. See Position 2 for the numbers. What the numbers Position 3 show is that White wins a total of 70 percent of the time, but none of White’s wins are gammons. Black wins 30 percent of the time but most of those (22 percent) are gammons, or double wins. 

So here is how this boils down statistically. If I were to play this game 100 times and drop the 4 cube every time, I would lose a total of 400 points over the 100 games. But if I take, I would lose at 8 a total of 70 times, and that’s 560 points, but I would win 8 points 8 times, and that is 64 points I win back, but I also win gammons, or 16 points, 22 times, and that’s 352 points. So if we add the 352 to 64, that’s 416 points we win back, and if we subtract that from the 560 points we lost, that’s a net loss of 144. So If I drop the cube every time in 100 games I lose 400 points, but if I take the cube I lose 144, so I have saved 256 points (or $256 if I was playing for $1 a point) by taking.

Of course I’m not going to play this game 100 times, but the point is that the odds apply equally even if I play it one time, and if I make every decision on every cube based on the odds, the 100 times certainly does come into play and is very meaningful…as much as I play backgammon, I probably makes thousands of cube decisions a week (every time you do not turn the cube you are, in effect, making a cube decision).

Bottom line, it’s all math, and for me, the best way to learn and understand the math is to do just what I’ve done in this article. First, make estimates over the board, and then run it through Snowie to see if I was right or wrong, study the numbers, and do my best to remember them when this, or similar situations, come up in the future. 

Position 3