How to calculate how many outs you have in poker

Figuring out how many cards will improve your hand

Odds and Info
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After you've gotten your initial cards dealt to you in a poker hand, you usually need to draw or hit certain cards to make your hand a winner. Outs are the all the possible cards you could get that would improve your hand.

Most commonly, you'll be talking about how many outs you have after the flop in Texas Hold'em.
For example, if you have the Ace and Jack of Diamonds in the hole and the flop is Queen of Diamonds, Ten of Clubs, and Three of Diamonds, you have a lot of outs.

First, any Diamond that shows up on the turn or river will give you a flush. Since there are 4 diamonds already showing and 9 left in the deck, that's nine outs. Additionally, any King will give you an Ace-high straight. Since you've already counted the King of Diamonds when you counted diamonds, just count the three remaining Kings, so that's already a total of 12 cards in the deck that will likely give you the winning hand, or 12 outs.

Some common scenarios in Texas Hold'em:

If after the flop you have:

Four cards to a flush you have 9 outs.
Four cards to an open-ended straight (i.e. 3-4-5-6) you have 8 outs.
Four cards to a inside straight (i.e. 3-4-6-7) you have 4 outs.
If you need to pair one of your hole cards, you have 3 outs.

Using Your Outs

Knowing how many outs you have doesn't help you much if you don't know what it means. The more outs you have, the more likely it is that you'll hit your hand.

But how likely? There are a few ways of figuring it out.

Outs as Odds

This is the easiest and most useful because when you're done figuring it out, you can transfer it directly into a pot odds calculation. I'll explain.

To state your chances of winning as odds you figure out how many outs you have and how many unknown cards are out.

Take the above example. You know the two cards in your hand and the three cards on the board. That leaves 47 cards unknown out of a 52 card deck. You have 12 outs. So 12 cards that are left help you and 35 do not. Therefore your odds of hitting your hand on the next card is 35 to 12 against. You can simplify that to just under 3-1 against by dividing the both numbers by the lower number.

That means you need 3-1 pot odds or better to profitably continue in the hand.

Outs as Percentages

To get a percentage, divide your outs by the unknown cards left. As above, 12/47 = .255 or 25.5%. Which, you will note, is just under 3 - 1.

With Two Cards to Come

With more than one card to come, the math gets more complex. But don't worry, there's a quick and dirty way to figure it out. If you're at the turn and want to know how good your chances are to hit your hand by the river, simply multiply your outs by four. That will be your approximate percentage chance of hitting your hand when drawing two cards.