There are "52 choose 3" = 22,100 flops, if we ignore any hole cards, as if we are railing.Originally Posted by Lucothefish
Monotone: 4c1 * 13c3 / 52c3 = 1144 / 22100 ~ 5.18%
Two tone: (4c1 * 13c2 * 3c1 * 13c1) = 12168 / 22100 ~ 55.06%
Rainbow: 4c3 * ( 13c1 )^3 = 8788 / 22100 ~ 39.76%
If we take into account all of Hero's possible hole cards, pairs, unsuited, and suited, these probabilities are exactly the same. But it's a bunch more complicated to do the math.
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