Draw odds

Set mining odds: how often you flop a set

You call with a small pair, hoping to flop three of a kind. Most of the time you miss and fold. The math is about whether the times you hit pay for all the times you do not.

How often a pair flops a set

You hold 66. You can see 2 cards, so 50 are unseen.

  • There are 19600 different flops.
  • 2304 of them have at least one six. That is 11.8%.
  • The other 17296 miss. For each hit, you miss about 7.5 times.

The rank does not matter. Twos and queens flop a set exactly as often.

What the call has to win

Say you call 5 before the flop and fold every time you miss. To break even, each time you hit you need to win about 7.5 times your call. That is 37.5 on a 5 call, from money that comes after the flop.

That number is the floor, not the target. It assumes your set always wins, and it does not. It assumes he will pay you, and he may fold. So the smaller the stacks behind, the worse the call. This is what implied odds means in practice.

When you miss the flop

You
No six. Two outs left.

Two sixes are left. Two outs.

Cards to comeExact
Flop to turn, one card4.3%
Turn to river, one card4.3%
Flop to river, both cards8.4%

By the price alone, two outs cover a bet of about 5% of the pot. Almost any real bet is too big. That is the other half of set mining: when you miss, you let it go.

Other draws

Off the Felt has levels for pocket pairs and made hands, where the right answer is often fold.

Get Off the Felt, free on iPhone

Free. No account, no ads, no in-app purchases. iPhone only.