It’s Good to be Greedy (99.86% of the Time)

In backgammon a greedy bearoff play refers to taking off as many checkers as possible with the current roll. In the position above it is only possible to bear off one checker so the greedy play is 6/off. It is not uncommon, however, to see players move 6/5, 2/1 in this type of position. The thought behind this is to smooth out the position so that a 5 will not miss the next time it is rolled.

So which play is correct 6/off or 6/5, 2/1? More importantly how does one decide when the greedy play is correct and when to fill gaps and smooth out the position? In the winter 2020 edition of the USBGF’s Prime Time Backgammon mathematician and backgammon player Art Benjamin explores this question in his regular Math Overboard column.

Rather than analyzing all of the possible bearoff positions and rolls with a backgammon bot (a very difficult task given the number of possible position/roll combinations) Dr. Benjamin and his team created a mathematical model that allowed direct calculation of the optimal move for all possible noncontact bearoff positions and rolls.

The results of this analysis showed that making the greedy play is almost always correct. Specifically, of the 1,139,523 possible combinations of positions and rolls there are only 1669 (about 0.14%) where the greedy play is not the best play. Most of the positions where it is a significant error to make the greedy play are positions with 13 to 15 checkers remaining, large stacks on the 1,3 and/or 5 points and no or only 1 check on each of the 2, 4, and 6 points. These positions are not very common, you might play for years and never encounter one of them!

What does this mean for everyday play? When bearing off without contact just take as many checkers off as possible every time and don’t give it a second thought. You will make the correct play 99.86% of the time!

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