[gaming_mouse]

There are nCr(52,5)= 2598960 possible flops.

After n hands, we will have nCr(n,2) "attempts" at having two identical flops. Let nCr(n,2) = x.

Then, for a very close approximation to the solution, we need to solve:

1 - (2598959/2598960)^x = .5
(2598959/2598960)^x = .5
x*log(2598959/2598960) = log(.5)
x= log(.5)/log(2598959/2598960)
x= 1801461.44989

Returning to the definition of x, we solve for n:

(n^2 - n) = 3602922.89978
n^2 - n -3602922.89978 = 0

The positive solution is 949.56

At 30 hands/hr, that means you'll see the same flop about once every 31 hours.

gm

EDIT: woops. i made an arithemetic error calculating the logs the first time. Adjustments are above.