Math Question

If you have Ax (suited) what are the odds of you hitting the flush (for the entire hand..flop, turn, river)?

6.4% or 1 in 15 to make a flush by the river

50 unknowns, 11 cards in the deck we need.

a) The chance to flop the nut flush: 11/50*10/49*9/48=0.84%

b) The chance to flop the 4-flush: 11/50*10/49*39/48*3=10.9%

c) The chance to get one of our suit on the flop: 11/50*40/49*39/48*3= 43.8%

b1) The chance to hit the flush on the turn if we flopped a 4-flush: 9/47=19.1%.

b2) The chance to hit our flush on the river if we miss the turn. 9/46=19.6%

c1) The chance to score a runner runner flush: 10/47*9/46=4.16%


To conclude:

Flop the flush: 0.84%
Turn the flush: (.109)*(0.191)=2%
River the flush: (.109)*(0.809)*(0.196) + (0.438)*(0.0416)=1.7%+1.8%=3.5%

So the total is ~6.35% like greed said

If you are playing on Party against me, I think the number is more like 75% ish

And on prima, triple or more the chance to hit runner-runner flushes.