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Count your outs, multiply by four on the flop and two on the turn. It is the best shortcut in poker and it has two failure modes, one of which costs money every session.
You are being asked to call c into a pot that already
holds p. Calling wins p + c when it is good
and loses c when it is not, so it breaks even when you
are good c / (p + 2c) of the time.
A $20 call into a $60 pot needs 20 / 100, so 20%. That is the number to compare your equity against, and everything below is about getting the equity right.
After the flop you have seen five cards, so 47 are unseen. Two of them
are coming. The chance that none of your k outs
arrives is the chance both cards come from the other
47 - k, and everything else is the chance you hit.
| Outs | By the river | Rule of 4 | River only | Rule of 2 |
|---|---|---|---|---|
| 2 | 8.4% | 8% | 4.3% | 4% |
| 4 (gutshot) | 16.5% | 16% | 8.7% | 8% |
| 6 | 24.1% | 24% | 13.0% | 12% |
| 8 (open-ended) | 31.5% | 32% | 17.4% | 16% |
| 9 (flush draw) | 35.0% | 36% | 19.6% | 18% |
| 12 | 45.0% | 48% | 26.1% | 24% |
| 15 | 54.1% | 60% | 32.6% | 30% |
| 21 | 69.9% | 84% | 45.7% | 42% |
Exact, by counting: 1 - C(47-k, 2) / C(47, 2) with two cards to come, and k / 46 with one.
Through nine outs the rule is within a point, which is closer than your read is. Past twelve it drifts, and at fifteen outs it claims 60% against a real 54.1%, an overstatement of about 6 points. The reason is simple double counting: multiplying by four counts the runouts where you hit twice, once for each card.
The rule of 4 answers "how often do I get there by the river". You only get to use that answer if no further bet stands between you and the river, which in practice means one of you is all-in.
Facing a flop bet with more money behind, the card you are about to see is the turn, and only the turn. The right number is the river only column, and the flush draw everyone calls a 36% shot is a 19.6% shot for the price in front of you. Using the by-the-river number for a call that only buys one card is the single most expensive habit this shortcut creates.
Implied odds are the honest counter-argument, and they are real: the money you win on the turn when you hit can more than cover the gap. But implied odds are an estimate of somebody else's future behavior, and the two-card equity is an estimate of nothing. Do not let one quietly stand in for the other.
The arithmetic above is exact, and the input to it usually is not. Two ways the count goes wrong more often than the multiplication does:
Drills that make the count automatic: real spots, an answer marked against a hand evaluator rather than a table somebody typed up, and the exact equity shown next to what you said. The early levels and the whole glossary are free. The point is to stop needing the shortcut.