Wraps: how an Omaha straight draw can have 20 outs

In Hold'em a straight draw tops out at eight outs: an open-ended draw, or two gutshots at once. Omaha has no such ceiling. A hand with four connected hole cards can have up to 20 outs on the flop, more than a flush draw (9). The reason is the same exactly-two-hole-cards rule that causes so many misreads: you choose which two of your four cards play, and you can choose differently for each card that arrives.

A wrap, counted card by card

Take the hole cards T-9-6-5 (T is the ten) and a flop of 8-7-2. You have no straight yet: the 8 and 7 on the board need a third board card from a straight, and you may only use two of your own. Now count every rank that would give you one.

Six ranks, and 4 + 3 + 3 + 3 + 3 + 4 = 20 cards. The 4 and the jack have four copies each because you hold none of them. The 5, 6, 9 and ten have three each, because you hold one of each.

Each row uses exactly two hole cards and three board cards, so the count obeys the rule. The only thing that changes from row to row is which two hole cards you pick. In Hold'em, T-9 on that same flop would have only the 6 and the jack, which is 8 outs. The extra 6-5 in your hand adds four more ranks.

How the outs scale

Go through every four-card hand with four different ranks against every flop of three further different ranks, count the cards that give a straight, and leave out hands that already have one. The possible out counts are 0, 4, 8, 9, 12, 13, 16, 17 and 20, and 20 is the maximum. One hand in each size is below.

The 13-out hand, 9-8-6-5 on 7-4-2, looks much like the 20-out one but has only four ranks that work: the 3 (four cards) and the 5, 6 and 8 (three each).

What 20 outs is worth

You can see seven cards: four in your hand and three on the flop. That leaves 45 unseen cards, so on the turn the chance of hitting one of 20 outs is 20 ÷ 45 = 44.4%. To catch one by the river, take the chance of missing both cards from one:

1 − (25 ÷ 45 × 24 ÷ 44) = 1 − 600 ÷ 1,980 = 69.7%.

Dealing out every turn and river pair from the 45 cards confirms it: 690 of the 990 give a straight, the same 69.7%. Here is how the sizes compare on the turn alone:

Set that against a price. If someone bets the size of the pot on the turn and you call, you risk one unit to win two, so you need to win at least 1 ÷ 3 = 33.3% of the time. The 20-out hand clears that with room to spare, and the 13-out hand does not, at 28.9%. How a pot-sized bet is worked out is covered in a separate post; the point here is that two similar-looking draws can be priced very differently.

Where the count overstates the draw

Twenty outs is the number of cards that give you a straight. It is not the number that win. Three things take it down:

1. Someone has a better straight. If the turn is the ten, your hand is 6-7-8-9-T. An opponent holding J-9 has 7-8-9-T-J, the jack-high straight, and beats you.
2. The board pairs or has three of a suit. A turn that pairs the board lets a player with a pair in hand make a full house, and three suited board cards let anyone with two of the suit make a flush. Both beat a straight.
3. You are counting against hands you cannot see. The 45 unseen cards include your opponents' hole cards. If they hold some of your outs, there are fewer than 20 left in the deck. That is why the percentages are a guide and not a promise.

A habit worth building

Count wraps by rank, not by "this card or that card". List the ranks that complete a straight, note how many copies of each you hold, and add: four per rank you do not hold, three for each you hold once. Then check each against the exactly-two rule: a straight only counts if two of your cards and three board cards make it.

Omaha Poker shows your outs grouped by what they make in its live hand insight, alongside your win chance and the pot odds on a call. Compare its count with your own on the next wrap you flop.