On Tue, 3 Jan 2017, Ian Shaw wrote:
The 1-sided database gives the most efficient bearoff by minimising the
average rolls required.
The "using normal distribution" 1-sided database that Isambard mentions in
other posts does only this, but the regular one has the distributions of
rolls needed to bear off (it knows that 0004 bears off in 1 roll 3 times
out of 36 and 011011 only once) and should get your example below right.
The 2-sided database plays the cube perfectly (in money games) while using
the 1-sided one may lead to errors there. I think a misplay by the 1-sided
database would involve a forthcoming double (but I have no example to
offer).
Sometimes, this isn't the best play. When the opponent is close to the
end, it may necessary to increase the probability to bear off in fewer
rolls than your opponent, at the expense of increasing the average rolls
required.
For example, consider when you have 2 on the four point, 1 on the five
and 1 on the six, and roll 21. If your opponent has the same position as
you, then the best play is 4/3 4/2 to bear off in the fewest rolls, on
average. If your opponent has all 4 on the one point, then 6/4 5/4 is
the best play, so that 66, 55 and 44 all win for you on the next roll.
It doesn't help you at all to optimize your chance of bearing off in 2,
3, 4, 5, or 6 rolls, because you'll never get the chance.
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