Recall the question from the last section. Each of the two players rolls a die, and the winner is determined by the sum of the faces:

If this game is played many times, which player do you think will win more often, and why?

To analyze this problem effectively, we need a clear enumeration of all possible outcomes. Let's examine one scheme that is based on a familiar idea: an addition table.

Start with a two-dimensional table:

		Red Die
	Blue Die + 1 2 3 4 5 6 1             2             3             4             5             6

Each possible outcome for the sum of the two dice can be enumerated in this table. For example, if the outcome were (1,1), here is how you would record it:

		Red Die
	Blue Die + 1 2 3 4 5 6 1 1 + 1           2             3             4             5             6

This is how you would record the outcome (2,4):

		Red Die
	Blue Die + 1 2 3 4 5 6 1             2       2 + 4     3             4             5             6

This is how you would record the outcome (4,2):

		Red Die
	Blue Die + 1 2 3 4 5 6 1             2             3             4   4 + 2         5             6

Note that the outcome (4,2) is different from the outcome (2,4).

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