Arthur J. O'Dwyer wrote:
>
> On Sun, 4 Sep 2005 videoguy505@[EMAIL PROTECTED]
wrote:
>>[...]
>> My question is, is there an optimal strategy for this game...
>> especially regarding when to save a 5? I know that a later turn is
>> obviously better, since you know the score to beat.
>
> No, that can't be right. Wouldn't you just try to score as high as
> possible all the time, no matter when your turn was? I know I would. :)
That's a slightly different goal. The strategy that
maximizes your expected score may not be the same as the
strategy that maximizes your likelihood of exceeding a
specified score. For example, suppose an earlier player has
already achieved a perfect score of 24, so your only hope
of sharing in the pot is to match that score. A strategy
that aims to maximize your expected score might tell you
to be content if you roll 1-2-5-6-6-6 for a total of 23,
but if you follow that strategy in this situation you are
guaranteed to lose.
It seems to me the goal of the Kth player should be to
maximize the likelihood that his score exceeds the maximum
of the K-1 preceding scores and the expected maximum of
the N-(K-1) scores that will follow. Since the score that
K actually achieves can influence the expected scores of
the later players (by "raising the bar"), the calculation
seems quite complicated. Perhaps it could be attacked by
starting with the Nth player and computing his expected scores
when he aims to exceed each of the possible preceding maxima,
then work back to the (N-1)st player, and so on.
--
Eric Sosman
esosman@[EMAIL PROTECTED]
|
