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Optimal non-contact bearoff distribution

Posted By: Taper_Mike
Date: Wednesday, 14 January 2015, at 11:01 p.m.

In Response To: Optimal non-contact bearoff distribution (Timothy Chow)

Money Game
Blue on roll. Cube action?


If we ignore the opponent’s checkers, and work only at reducing our own EPC, then there is usually an optimal move in any non-contact position. It may not lead to an ideal position, but it will lead to a position that has a lower EPC than any available alternative. On average, you cannot do better than to choose this play.

It is not correct, therefore, to aim at the 7-5-3 position. What is right is to select the play that gives you the lowest EPC obtainable given your current position and roll. If you follow this strategy, it is frequently possible, in two or three moves, to a turn a non-ideal position into an ideal one. If a certain roll, such as the 61 above, takes you away from ideal position, it is often possible to get back on track on the next roll.

When you factor in the opponent’s position, things get a little trickier. Tim Chow has pointed out in the past that rather than choose plays that have the lowest EPC, you may wish to choose a play that is close, but which has a higher (or lower) variance, depending on your circumstance. In practice, however, I have found that simply minimizing EPC handles most positions.

In table below, I present all legal moves you can play with a 61 in the position above. For each, I give the expected number of rolls remaining. You can multiply "Rolls Remaining" by 8-and-1/6 to arrive at EPC.



X to play 6-1.
No. Move Rolls Remaining Difference (%)
1. 9/3, 5/4 10.5468 --
2. 9/3, 8/7 10.5471 -0.00277246%
3. 8/2, 5/4 10.5531 -0.059586%
4. 9/3, 6/5 10.5544 -0.0727098%
5. 9/2 10.5574 -0.100437%
6. 9/3, 4/3 10.5641 -0.16438%
7. 8/2, 6/5 10.567 -0.19145%
8. 8/2, 4/3 10.5676 -0.197322%
9. 8/1 10.5718 -0.237108%

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