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Average number of rolls to enter x checkers from the bar

Posted By: Havard Raddum
Date: Tuesday, 15 March 2011, at 8:44 a.m.

In Response To: Average number of rolls to enter x checkers from the bar (Bob Koca)

Good thing you checked my home work, professor. You're right, I made the mistake of only entering two on doubles. I have redone the exercise, and also for entering on y-point boards, 0 <= y <= 5. This time I have been careful to distinguish between: a) entering doubles, b) rolls that enter exactly two, c) rolls that enter exactly one, and d) dancing numbers.

Expected number of rolls to enter x checkers against y-point board:

Expected number of rolls 5-point board 4-point board 3-point board 2-point board 1-point board 0-point board
1 checker 3.273 1.800 1.333 1.125 1.029 1.000
2 checkers 6.248 3.240 2.222 1.688 1.322 1.000
3 checkers 8.953 4.572 3.111 2.391 1.994 1.833
4 checkers 11.411 5.782 3.901 2.953 2.354 1.833
5 checkers 13.944 7.063 4.774 3.639 2.988 2.694

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