Odd circumstance probability (Flops)

[MrDannimal]

I was sweating a friend in a NL SNG at UB last night, and 14 of 16 boards came with a 3 or 4 flush. Does anyone know off hand the odds of that happening 14 times in 16 hands?

[BruceZ]

I was sweating a friend in a NL SNG at UB last night, and 14 of 16 boards came with a 3 or 4 flush. Does anyone know off hand the odds of that happening 14 times in 16 hands.

I'll include 5 flushes also, and I'll assume that all 16 boards go to 5 cards. I'm assuming by "board" you mean 5 cards, not just the flop, and that the flush cards are on the board, not in the player's hand. Let me know if you wanted something else.

First find the probability of getting 3 or more cards of the same suit on a single 5 card board.

4* [C(13,3)*C(39,2) +
C(13,4)*39 +
C(13,5) ] /C(52,5)
= 37.1%

Call that p. Then we can get the probability of 14,15, or 16 of these in 16 five card boards by the binomial distribution:

C(16,14)*p^14*(1-p)^2 + C(16,15)*p^15*(1-p) + p^16

or we can use the Excel function =1-binomdist(13,16,p,true)

= 1 in 20,759