Recall that in Backgammon, you roll a pair of fair dice, and you move pieces acc

Question

Recall that in Backgammon, you roll a pair of fair dice, and you move pieces accordingly to an available spot (or out of the board). Suppose that the game is about to finish and your oppoonent has one piece left one squre away from the end, so if she makes it to the next turn (i.e. if you would be unable to go get out), she will win. Also recall that if you roll a double, then you get to move four times (e.g. a double 3 is the same as 3, 3, 3, 3). For 1 a b 6, if right now you have a two pieces left, one a squares from the end and the other b squares from the end, what is your chance of winning?

Explanation / Answer

We can get doubles in the following ways when we role a pair of fair die

1 1

2 2

3 3

4 4

5 5

6 6

A total of 6 ways

The total number of ways the pair of die can fall is 6*6=36 ways

So the probability of winning =6/36=1/6

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