Man versus machine

Not surprisingly, I was playing some backgammon against the computer today. What was surprising, to me at least, was the following position came up that got marked as “doubtful” by GnuBG:


Now, I didn’t even think about this one, clearly the right move is 11/7,10/7 and making the 6 prime. But GnuBG said no, 10/6, 9/6 is better. Huh?

GnuBG says 10/6, 9/6 has equity +0.788, 11/7, 10/7 has equity +0.715; a difference of -0.073 and so a blunder! Extreme gammon rates it similarly, 10/6, 9/6 gets +0.797 while 11/7, 10/7 gets +0.736, a difference of -0.061 and again a blunder!

It gets worse for me. After the next exchange of rolls, I was at the following position:


D’uh – clearly 9/2 is the right move. But no, GnuBG says 7/2, 5/2!!! 9/2 has +0.728 equity, versus +0.792 for 7/2, 5/2, a difference of -0.064 and so another blunder! Extreme gammon agrees again.

The key here is the cube. With the cube in the middle, the moves I actually made are the correct moves. But the cube has already been offered and taken, and that makes a difference. I no longer have the option to double red out after a rough roll, I have to take what I get – and if I get something bad red has the redouble.

As it happens, what I got was a 5-6 on the first roll bearing in against the men still on my one point, forcing me to leave two blots. Red rolled a 5, putting me on the bar, I danced, and then got redoubled out. So it really could have worked out better for me. But the main thing was these back-to-back positions where the difference in correct play depends so much on the cube position.

This table shows the winning chances for each move for the first position, per GnuBG:

Win W g W bg Lose L g L bg
11/7, 10/7 0.811 0.129 0.005 0.189 0.005 0.000
10/6, 9/6 0.835 0.146 0.005 0.165 0.005 0.000

And this is the equity, depending on who owns the cube:

Equity Cube in Middle Equity, Red’s cube Equity, Black’s cube
11/7, 10/7 +1.000 +0.715 +1.000
10/6, 9/6 +0.934 +0.788 +0.978
Difference +0.066 -0.073 +0.022

Very similar charts for the second position:

Win W g W bg Lose L g L bg
9/2 0.824 0.115 0.004 0.176 0.005 0.000
7/4, 7/3 0.833 0.145 0.006 0.167 0.005 0.000
Equity Cube in Middle Equity, Red’s cube Equity, Black’s cube
9/2 +1.000 +0.728 +1.000
7/4, 7/3 +0.925 +0.781 +0.970
Difference +0.075 -0.053 +0.030

I find it also interesting that the drop in equity for leaving an indirect shot is a lot lower when black owns the cube in both positions as well. I think either of these would make a good “quiz” question for Phil Simborg. Having them back to back like that in a game definitely made me stop and think about the value of owning the cube!