Outs & drawing odds

An out is any unseen card that improves your hand into the likely winner. A flush draw has nine of them (nine cards of your suit remain), an open-ended straight draw eight, a gutshot four. Counting outs turns "I have a draw" into a number you can put straight into the pot-odds topic's machinery: once you know the chance the draw arrives, you know whether the price in front of you is a good one.

The count converts to equity by pure deck arithmetic. After the flop, 47 cards are unseen (52 minus your two and the board's three); after the turn, 46. One card to come, a draw with o outs hits exactly o / 46 of the time. Two cards to come, it hits 1 − C(47−o, 2) / C(47, 2) — the complement of missing twice. The famous shortcuts approximate those exact numbers: rule of 2 (multiply outs by 2 for one card) and rule of 4 (by 4 for two). They're slightly high, and the gap grows with the out count — the widget shows both numbers side by side so you can see where the shortcut bends.

Try it: from outs to equity

Set a draw size and a street. The exact percentage comes from the combinatorics above; the shortcut sits beside it so the approximation error is always visible.

Exact chance of hitting
35.0%
Rule of 4 shortcut
36%

1 − C(38,2) / C(47,2) = 35.0% — the shortcut lands 1.0 points high at this out count.

The classic draws, worked exactly: the flush draw's nine outs arrive by the river about 35% of the time, the gutshot's four about 16%. Compare those against what a bet asks of you. Calling needs breakeven equity of c / (p + c) — the pot-odds formula — and every common bet size translates to a minimum viable out count when exactly one card is left to come:

Bet to callBreakeven equityOuts needed (one card to come)
25% pot17%8
33% pot20%10
50% pot25%12
75% pot30%14
100% pot33%16

Read that table as a filter, not a rulebook. It prices a draw with nothing else going for it — no fold equity, no future betting, no showdown value. Real draws carry extra ways to win (the Implied odds topic prices the future-street money; semi-bluff raises add folds on top), which is why hands like the open-ended-plus-flush-combo in the check-raise topic play aggressively rather than meekly calling.