Given: My hand is any pair
How do I calculate the probability of making a four of a kind by the (flop, turn, &) river?
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Sign up to join this communityGiven: My hand is any pair
How do I calculate the probability of making a four of a kind by the (flop, turn, &) river?
Without taking into account the fact that the very act of seeing the flop with one or several other player(s) influence the distribution of the flop (*), here's one way how you could compute these odds:
I may have miscalculated something here or there but this answer should give you the basic idea.
Looking at just combination and only matching your pocket pair
Quads on the board is possible
flop
combin(2,2) * combin(48,1) / combin(50,3) = 0.245%
turn
combin(2,2) * combin(48,2) / combin(50,4) = 0.490%
river
combin(2,2) * combin(48,3) / combin(50,5) = 0.816%
It surprises me the chances double going from the flop to the turn but that is what these numbers say. You do double the number of free cards.
You are typically playing pocket pair for the set and quads is gravy (sometimes gravy you need).