Hey everyone

Im trying to calculate the probability of a suited connector hitting a flush draw or better on the flop.

We got 67s

There a 3 ways we can get 2 cards of the same suit.

1. Hit, hit, miss
2. Miss, hit, hit
3. Hit, miss, hit

1. 11/50, 10/49=110/2450=4,5%
2. We miss, now we have 11/49 times 10/48=110/2352=4,7%
3. 11/50, we miss and now have to get it, 10/49=110/2450=4,5%

Which totals 13,7%, is this right?

All help is appreciated

Given two suited cards, hitting a flush draw or a flush on the flop has the following probability

Pr =( C(11,3) + C(11,2)*C(39,1))/C(50,3) = 11.8%

The first term in the numerator is hitting the flush wlth the flop having 3 of the remaining 11 flush cards. The second term is for a flush draw with 2 of the 11 flush cards falling and 1 of the 39 non-flush cards. The denominator is the number of possible flops given your hand.

C(N,r) is the number of combinations of r things out of N = N!/(r!*(N-r)!)

Thanks. I haven't used this formula before, or maybe I skipped school that day

Can this formula be used for all poker calculations, say you have 48, how would you use this formula to calculate the probability of flopping 567? First we have 12 outs, then we have 8 outs, and then 4. The denominator must still be C(50,3).

In general, the probability of an event is equal to the ratio of the number of outcomes favorable to the event to the total number of posssble outcomes. Combinations are outcomes.

For the 567 flop, there are four of each rank (=C(4,1)), so the total number of successful combinations is 4*4*4 = 64. Divide that by C(50,3) for the result.

Combinations are often the best approach because you don’t have to worry about order as you often do with other methods but their use is not always the easiest.

BTW, your use of outs is not correct. Outs represent the number of cards that can improve your hand on a single deal, such as having 9 outs with a four flush for a river card deal.

Thanks for your help, combinations definitely seems like the best approach.

Suited Connectors, Implied Odds and You