How to calculate pot odds and use them to decide a call

Pot odds are the price offered on a call. Divide the call by the pot you would be playing for after calling, and you have the minimum share of the time your hand needs to win.

What pot odds actually are

Every time someone bets into you, they are offering a price. You risk a fixed amount to win whatever is already in the middle. Pot odds turn that price into a single number you can compare against your chance of winning the hand.

That number is called the required equity, or the break-even percentage. Win more often than it, and calling makes money over many repetitions of the same spot. Win less often, and it loses money, however the individual hand happens to end.

Two things go into it and nothing else: what the call costs you, and how big the pot will be once you have called.

The cost of the call

The call is the amount you still have to put in to keep playing, not the total you have invested in the hand.

If you already put 3 BB in before the flop and now face a bet of 5 BB, the call is 5 BB. The 3 BB is gone. It is in the pot, it belongs to the pot, and it counts for the person deciding, in the sense that it makes the pot larger, but it is not part of your price.

This is the most common place people go wrong. Money already in the middle is not yours any more, and it never affects whether the next decision is profitable.

The pot you are playing for

The pot you would win is everything in the middle after your call goes in. So it is:

• whatever was there before the bet, plus
• the bet you are facing, plus
• your call.

Call that the final pot. It is the denominator.

The formula

required equity = call / final pot after calling

Multiply by 100 for a percentage. Then compare it with your estimate of how often the hand wins.

Some people prefer the ratio form: the pot before your call, expressed against the call. Both say the same thing. A ratio of 2.5 to 1 converts to 1 / (2.5 + 1), which is 28.6%.

Two worked examples

A flush draw where the price does not justify the call

Required equity is 4 / 14, which is 0.286, so 28.6%. In ratio form you are getting 10 to 4, which is 2.5 to 1, and that converts to the same 28.6%.

Now your side of it. You have four cards to a flush after the flop, so nine cards complete it. You can see five cards: your two and the three on the board. That leaves 47 unseen. The chance the next card is one of your nine is 9 / 47, which is 19.1%.

19.1% is below 28.6%, so the call does not pay on pot odds alone.

A straight draw where it does

Required equity is 400 / 3200, which is 12.5%. As a ratio you are getting 2800 to 400, or 7 to 1, and 1 / 8 is again 12.5%.

You hold an open-ended straight draw, so eight cards complete it. The chance the next card is one of them is 8 / 47, which is 17.0%.

17.0% clears 12.5%, so this call pays. Same draw quality as the flush example, near enough, and a completely different answer, because the price is different.

Outs are not pot odds

An out is a card that gives you the best hand. Counting outs is a separate skill from pricing a call, and the two only meet once the outs are converted into a probability.

To convert, divide the outs by the number of cards you cannot see. After the flop that is 47. After the turn it is 46.

The right-hand column carries a condition that gets forgotten constantly. You only get to see both remaining cards for one price when no further betting can happen, which in practice means someone is already all in. If there is another street of betting to come, the honest number is the left-hand column, because you will be asked to pay again on the turn.

The rule of four and two, and where it drifts

The shortcut is: outs times two for one card, outs times four for two cards.

For nine outs that gives 18% and 36%, against true values of 19.1% and 35.0%. Close enough at the table.

For fifteen outs it gives 60% against a true 54.1%. The shortcut drifts upward as the number of outs grows, so above about eight outs on two cards, take a few points off whatever it tells you.

What pot odds leave out

Implied odds

The formula uses the pot as it is now. If you complete your draw and the opponent is likely to pay you off on a later street, the real reward is larger than the current pot, and a call that fails the arithmetic can still be correct.

That is implied odds, and the honest description of it is an estimate. It depends on how deep the stacks are, on how well hidden your hand will be if it gets there, and on whether that particular opponent pays off. Treat it as a reason to call a little wider than the raw number, not as a licence to ignore the number.

The reverse exists too. If completing your draw still leaves you second best often enough, or if you will face another large bet you cannot call, the effective reward is smaller than the pot suggests.

They say nothing about what the opponent holds

Pot odds price the call. That is all they do. The other half of the comparison, your chance of winning, is an estimate you have to make, and it should be made against everything the opponent could hold in that spot rather than against one hand you have imagined for them.

If the flush card that completes your draw also completes a straight for part of their range, some of your nine outs are not outs. The formula will not warn you about that. It cannot see the cards.

What to take away

• The whole calculation is call / final pot after calling. Money you already put in does not enter it.
• Outs are not a percentage until you divide by unseen cards: 47 after the flop, 46 after the turn.
• The two-card figure only applies when no more betting can happen. On the flop with a turn and a river still to be bet, use the one-card number.
• Pot odds give you the price and nothing else. Implied odds, reverse implied odds and what the opponent could actually be holding all sit outside the formula and all change the decision.