And yeah, that’s how to finish the calculation off. Rolling three of a kind on the three rerolled dice is the catch that I had overlooked in doing the calculation.

And it really shakes my intuition that rolling three dice is so more likely to give three-of-a-kind than just rolling one die when you’re already two-thirds of the way to *two* three-of-a-kinds.

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]]>You’re a small bit off, but the spirit of your calculations is right.

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]]>Well, thanks. I do like sharing these since, at least, other bloggers seem to find reassurance that other people don’t have any idea how to catch or grow an readership.

]]>1 in 3 for rolling 1 die is right

There are 216 ordered triples with 3 dice

For rolling 3, first die 2 is 1/6, or 36/216

Second is (1/6)*(5/6), or 30/216

Third for 3 2s is 1/6 * 150/216, or 25/216

Add 5 ways to roll 3 of a kind without 2s (22111, etc)

96/216, or 4/9 beats 1/3, or 3/9

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]]>And Him Upstairs says something different so I shall go and rethink.

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]]>If you roll 3 dice to match the remaining pair, you have a 1/6 chance of rolling that number on one die, times 3 for the 3 dice, giving you 3/6 or 1/2 chance.

Which means my strategy changes right now

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