Very simple math question, but I need help

[fnord_too]

Easiest way to do this is to compute the chance you won't make the fh and subtract that from 1.

There is a 40/47 chance you miss on the turn followed by a 36/46 chance you miss on the river. So there is almost exactly a 2/3 chance you fail (~.666) so a 1/3 chance you succeed.

Your specific error is that you double count the times both the turn and river will give you a fh or better (say the final board is A2332 or A232A).