Equity, outs and quick estimates

On this page

• Count clean outs and discount the ones that also help the opponent.
• Estimate equity from outs by multiplying by two or by four.
• Explain why the flop shortcut assumes you see two cards for one price.
• Use one-card equity when another bet is likely to come on the turn.
• Compare your estimate with the exact equity Rail computes.

Concepts used: Pot odds, Equity and equity realisation

Equity: your share if the cards ran out now

Your equity is the share of the pot your hand would win on average if every remaining card were dealt now, with no more betting. A tie counts as half a win.

Against a range it is the average over every combo your opponent could hold. Pot odds tell you how much equity a call needs; this lesson is about estimating how much you have, quickly and without a computer.

Counting outs

An out is an unseen card that should give you the best hand. Most draws come in a few standard shapes, and each has a count worth knowing:

• Flush draw: the suit has 13 cards and you can see 4 of them, two in your hand and two on the board. 13 − 4 = 9 outs.
• Open-ended straight draw: four cards complete it at each end. 4 × 2 = 8 outs.
• Gutshot: one rank, four cards. 4 outs.
• Two overcards: three of each rank are left. 3 × 2 = 6 outs, but only if pairing one really puts you ahead.

When you hold two draws at once, do not count a card twice. A flush draw with an open-ended straight draw has 9 flush cards and 8 straight cards, but two of the straight cards are of your suit and already counted.

Dirty outs

Some outs complete your draw and still lose. Before you count a card, ask what it does for the hands your opponent is likely to hold.

• A flush card that pairs the board can give a set a full house.
• A straight card that also puts a third or fourth card of one suit on the board can make someone else a flush.
• Overcard outs are worth little against two pair or a set, because pairing your card does not win.

Count such cards as half an out, or leave them out, depending on how likely the hand that beats you is. A rough discount is better than a precise count of the wrong thing.

From outs to equity: ×2 and ×4

On the flop you can see five cards, so 52 − 5 = 47 are unseen. With 9 outs the turn hits 9 / 47 of the time, about 19.1%. On the turn 46 cards are unseen, and the river hits 9 / 46, about 19.6%.

With both cards to come, it is easier to count the misses. You miss the turn with 38 of 47 cards and then the river with 37 of 46: 38 × 37 = 1,406 out of 47 × 46 = 2,162 runouts, about 0.65. So you hit about 35% of the time.

Nobody does that at the table. The shortcut: multiply your outs by 2 for each card to come. One card: 9 × 2 = 18%. Two cards: 9 × 4 = 36%. Both land within a point or two of the exact numbers, which is close enough to decide.

The ×4 rule runs high with big draws. With 15 outs it says 15 × 4 = 60%, but the exact miss chance is 32 × 31 = 992 out of 2,162, about 0.459, so you hit about 54%. Take a few points off when you have more than about 8 outs.

Does ×4 ignore the next bet?

Yes, and that is the point to remember. The ×4 number is your equity if you see the turn and the river for the price of one call. That only happens when someone is all in, or when you are sure the turn will check through.

Say the pot is 20 bb and your opponent bets 10 bb on the flop. The final pot is 20 + 10 + 10 = 40 bb, so a call needs 10 / 40 = 25%. With a flush draw, ×4 says 36%, a comfortable call. But if a second bet is coming on the turn when you miss, your call only buys one card, and ×2 says 18%: short of the price.

So use ×4 when no more money can go in, and ×2 when it can. The gap between them has to be paid for by what you win later when you hit. That is implied odds, the subject of the realisation and implied odds page.

Rules of thumb

• Flush draw 9 outs, open-ended 8, gutshot 4, two overcards up to 6.
• Outs × 2 per card to come: ×2 with one card left, ×4 with two.
• Use ×4 only when no more betting can happen; otherwise use ×2 and price the rest as implied odds.
• Discount outs that also improve the hands likely to beat you.

When they break

• ×4 overstates big draws: with more than about 8 outs, take a few points off.
• Outs assume you know what you are drawing against. Against a range, some of your outs are clean against one hand and dead against another.