You don't need to be a mathematician to play well, but you do need to know how often you hit your draw and how much it costs to try. With those two numbers you know whether a call wins or loses money in the long run.
Before the flop
| Situation | Probability | Frequency |
|---|---|---|
| You're dealt a pair | 5.9% | 1 in 17 |
| You're dealt a specific pair (AA, for example) | 0.45% | 1 in 221 |
| You're dealt two suited cards | 23.5% | 1 in 4 |
| You're dealt QQ+ or AK | 2.6% | 1 in 39 |
| With a pair, you flop three of a kind or better | 11.8% | 1 in 9 |
| With a pair, you make three of a kind or better by the river | 19.2% | 1 in 5 |
| With two unpaired cards, you pair one of them on the flop | 32.4% | 1 in 3 |
| With two suited cards, you flop a flush | 0.84% | 1 in 119 |
| With two suited cards, you flop a flush draw | 10.9% | 1 in 9 |
| With two suited cards, you make a flush by the river | 6.4% | 1 in 16 |
With a pocket pair you flop a set a bit less than once in eight. That's the basis of set mining: calling with small pairs only pays off if, when you hit, you can win much more than you paid.
Outs: the cards that give you the hand
Outs are the cards left in the deck that give you the best hand. With a flush draw you have 9 (there are 9 cards of your suit left); with an open-ended straight draw, 8 (four at each end).
From the flop there are 47 unseen cards; from the turn, 46. The exact probability of hitting is:
| Draw | Outs | Turn Turn or river | On the turn | Flop to river | Rule of 2 and 4 |
|---|---|---|---|---|---|
| Flush draw + open-ended straight draw | 15 | 31.9% | 54.1% | 30% / 60% | |
| Flush draw | 9 | 19.1% | 35% | 18% / 36% | |
| Open-ended straight draw (OESD) | 8 | 17% | 31.5% | 16% / 32% | |
| Two overcards | 6 | 12.8% | 24.1% | 12% / 24% | |
| Two pair → full house | 4 | 8.5% | 16.5% | 8% / 16% | |
| Inside straight draw (gutshot) | 4 | 8.5% | 16.5% | 8% / 16% | |
| Pair → three of a kind | 2 | 4.3% | 8.4% | 4% / 8% |
The rule of 2 and 4
To work it out in your head: multiply your outs by 2 for the probability of hitting on the next card, and by 4 from the flop if you're going to see both the turn and the river. With 9 outs: 18% and 36%, very close to the exact 19.1% and 35%.
The rule overshoots with lots of outs: with 15 (flush draw plus open-ended straight draw) it gives 60% and the real figure is 54.1%. And count only clean outs: if a card of your suit pairs the board and gives your opponent a full house, it isn't an out.
Pot odds: how much equity you need to call
Pot odds compare what you call with what you can win. The minimum equity for a call not to lose money is:
what you call ÷ (final pot if you call)
If the pot is 100 and your opponent bets 50, you call 50 for a final pot of 200: you need to win 25% of the time. By bet size:
| Opponent's bet | Minimum equity to call |
|---|---|
| Quarter pot | 16.7% |
| Third of the pot | 20% |
| Half pot | 25% |
| Two-thirds pot | 28.6% |
| Three-quarters pot | 30% |
| Pot | 33.3% |
| Two pots (overbet) | 40% |
Compare it with your outs: with a flush draw on the turn (19.6%), calling a half-pot bet (25%) loses money unless you expect to win more when you hit. That extra profit is your implied odds, and it's what makes some calls profitable that pot odds alone don't justify.
The app's "Odds and probabilities" page has these tables at hand and a pot odds calculator.