🎣 Draws and outs: wraps, clean outs and the "×4" rule trap

Wraps: straight draws with four cards

Outs are cards that improve your hand to a strong one (in tasks — to a straight or better). After the flop there are 45 unknown cards in the deck.

In Hold'em an open-ended straight draw is 8 outs. In Omaha four cards combine into "wraps": straight draws with 13, 17 or even 20 outs.

Example: you hold 9♠8♠6♦5♥, the flop is 7♣4♥K♦. Any three, five, six or eight gives you a straight, minus the cards already seen — 13 outs. And J♠10♦7♣6♥ on 9♣8♦2♥ is 20 outs: any queen, jack, ten, seven, six or five.

The ×2 and ×4 rule — and where it lies

Quick estimate: outs × 2 ≈ your chance to improve on the next card (in %), outs × 4 ≈ your chance by the river.

For small draws the rule is accurate: 9 outs × 4 = 36%, the exact answer is 36.4%. But for big wraps it overstates a lot:
— 13 outs: rule — 52%, exact — 49.9%;
— 16 outs: rule — 64%, exact — 59%;
— 20 outs: rule — 80%, exact — 69.7%.

The reason: the rule doesn't account for the fact that you can't improve twice. On big draws calculate more precisely or memorize these numbers.

Clean and dirty outs

Not every out improves you to the best hand. Against a set, any card that pairs the board gives your opponent a full house — those outs are "dirty".

That's why some draws are favorites against a set and others aren't:
— the 20-out wrap J♠10♦7♣6♥ on 9♣8♦2♥ against a set of nines 9♠9♥A♦K♣ — 54.4%. The draw is the favorite;
— the nut flush draw A♥10♥6♣5♦ on K♥8♥3♣ against top set K♦K♠7♣2♦ — 29.6%. Only 9 outs, and even a made flush loses if the board pairs: the set will have a full house;
— a wrap with the nut flush draw A♥J♥10♦7♣ on 9♥8♥2♣ against a set 9♠9♦K♣Q♠ — 53%.

And here's the reverse case: a flopped nut straight J♣10♦4♠2♣ on 9♣8♦7♥ against a set of nines 9♠9♦3♣2♦ — 59.8% for the straight. The set, with its outs to a full house and quads, wins 40% of hands.

Draws to a non-nut hand are a trap

The most expensive mistake with a draw is making your hand and losing. On a 9♥8♥7♣ board, six-five in your hand gives a nine-high straight — the "low end". It loses to anyone with ten-six or jack-ten, and those hands are common on this board.

Same with flushes: a flush draw without the ace in a multiway pot often leads to a flush that pays off a higher one.

The rule: count only the outs that give you the nuts or near-nuts. The rest — at a big discount.

Practice: 10 flops — count the outs.