QuickenBrain

Choose a die after two rolls

Build the distribution of sums before choosing a counter to an opponent.

Count sums, not just faces

Use A = [2, 2, 4, 4, 9, 9], B = [1, 1, 6, 6, 8, 8] and C = [3, 3, 5, 5, 7, 7]. Roll your chosen die twice and add; the opponent does the same. Each sum comes from 36 ordered face pairs. For A, sum 6 occurs in 2 + 4 and 4 + 2, each in four ways, giving eight ways.

A + A448648811813418
A’s sums have different multiplicities; they are not equally likely.

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First lesson in this subject: Count equally likely outcomes

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