Poker school · lesson 4 of 7

The maths of a call

Pot odds, equity and outs, how to turn one into another, and a worked flush-draw example from the price to the decision. 5 min read.

The price: pot odds and the equity you need

Facing a bet, you are buying a share of the pot. Do you win often enough to pay for it? Compare the equity you need, which comes from the price, with the equity you have.

Pot odds compare what you can win with what the call costs. Say the pot is 20 bb and villain bets 10 bb. There are now 30 bb in the middle and it costs you 10 to call: pot odds of 30 to 10, or 3 to 1.

The equity you need turns that into a percentage: divide the call by the pot after you call. Here that is 10 ÷ 40 = 25%. Win more than a quarter of the time and the call makes money over time. Odds of 3 to 1 and 25% are the same thing said two ways.

The price of a call

25% needed

Your call10 bbTheir bet10 bbPot before the bet20 bb

The pot is 20 bb and villain bets 10 bb. You call 10 bb to win a pot of 40 bb: pot odds of 3.0 : 1, and your call is 25% of the pot, the equity you need. Try it with your own numbers

Prices worth remembering

A third of the pot20%Half the pot25%Two-thirds of the pot28.6%The pot33.3%Twice the pot40%

The equity you need to call, by the size of the bet. Bars run from 0 to 100%. Try it with your own numbers

Tip: Rake comes out of the pot you win, so it raises the price a little. If 2 bb of a 40 bb pot is raked, you win 38 bb and need 10 ÷ 38 = 26.3%.

Your side: equity and outs

Equity is your share of the pot if all the cards were dealt with no more betting. With a draw you are usually behind, and want to know how often you will catch up.

So count your outs: the unseen cards that give you the best hand. A flush draw has 9, an open-ended straight draw 8 and a gutshot 4. Only count cards that really win: a flush card that also pairs the board can give villain a full house, and that is a dirty out.

On the flop there are 47 cards you can’t see; on the turn, 46. So 9 outs on the flop arrive on the turn 9 times in 47, which is 19.1%.

The rule of 2 and 4

At the table a quick estimate does the job. Multiply your outs by 2 for the chance on the next card, or by 4 for the chance by the river from the flop, when you are sure to see both cards.

The rule against the exact figures, from the flop

4 outs: rule 8% and 16%; exact 8.5% and 16.5%.
8 outs: rule 16% and 32%; exact 17.0% and 31.5%.
9 outs: rule 18% and 36%; exact 19.1% and 35.0%.
15 outs: rule 30% and 60%; exact 31.9% and 54.1%.

The rule of 4 against the exact chance by the river

Rule of 4: outs × 4Exact chance

1 out4% / 4.3%

2 outs8% / 8.4%

3 outs12% / 12.5%

4 outs16% / 16.5%

5 outs20% / 20.4%

6 outs24% / 24.1%

7 outs28% / 27.8%

8 outs32% / 31.5%

9 outs36% / 35.0%

10 outs40% / 38.4%

11 outs44% / 41.7%

12 outs48% / 45.0%

13 outs52% / 48.1%

14 outs56% / 51.2%

15 outs60% / 54.1%

16 outs64% / 57.0%

17 outs68% / 59.8%

18 outs72% / 62.4%

19 outs76% / 65.0%

20 outs80% / 67.5%

From the flop, with nothing more to be bet. Close for small draws, high for big ones: with 15 outs the rule says 60%, the exact chance is 54.1%. The draws the lesson quotes are in bold. The axis runs from 0 to 100%. Count the outs for your own draw

It is close for small draws and runs high for big ones. Only use the 4 when nobody can bet on the turn, for example when someone is all-in.

A worked example

A flush draw facing a half-pot bet

You hold 6 of hearts, 5 of hearts on king of hearts, 9 of hearts, 2 of clubs. The pot is 10 bb, villain bets 5 bb, and you both have plenty behind.
The price: call 5 to make the pot 20. Pot odds of 3 to 1; equity needed 5 ÷ 20 = 25%.
Your outs: the 9 unseen hearts.
The next card: 9 ÷ 47 = 19.1%. The rule of 2 says 18%.
By the river: 35.0% for the flush. The rule of 4 says 36%.
Against king of spades, queen of diamonds, PokerIQ’s exact equity by the river is 38.9%: two pair, trips and straights add a little to the flush.

Your outs on the deck

Your cards6♥5♥

BoardK♥9♥2♣

Out (9)Seen: your cards and the boardUnseen, no helpDirty out (none in this hand)

♠AKQJ1098765432♥AKQJ1098765432♦AKQJ1098765432♣AKQJ1098765432

9 outs of 47 unseen: 19.1% on the next card, 35.0% by the river. Against none of them is dirty. Count outs for your own hand

Equity needed against equity held

Equity needed (the price)25%

Flush on the next card19.1%

Below the price

Flush by the river35.0%

Above the price

By the river against , exact38.9%

Above the price

The dashed line is the price, 25%. The flush on the next card falls short of it; by the river, and against the real hand, the draw clears it, but only if nothing more can be bet. Check an equity yourself

If villain’s 5 bb were all-in, nothing more could be bet, and 38.9% is well above 25%: call. But villain has chips left and will often bet the turn. Then you are only sure of the next card, and 19.1% falls short of 25%.

That gap is where implied odds come in. To make the call pay, you must win more on later streets when you hit: 5 ÷ (9 ÷ 47) − 20, about 6.1 bb more. With deep stacks against top pair, that is realistic. With only a few big blinds behind, it isn’t, and the call loses.

Expected value

Expected value puts the comparison in big blinds. For a call with no more betting, it is your equity times the pot you would win, minus the call. Calling 10 bb into a 40 bb pot with 30% equity is worth 0.30 × 40 − 10 = +2 bb. With 20% it is −2 bb. Over many hands, both add up.

In PokerIQ

The Analyser’s Odds and value panel shows the pot odds, the equity needed after rake, and your equity by the river with its certainty badge. With a draw and betting to come, it shows the next-card chance, whether the direct odds are enough, and if not, how much more you would need to win later.

Rule R4 then decides. A draw calls on direct odds, or on implied odds when the extra it needs is within your style’s limit: 15% of your stack behind after calling for Tight, 25% for Balanced, 40% for Aggressive. In the example, Balanced calls with at least about 24.4 bb behind after calling.

Hand and outs counts the cards that put you ahead of villain, with any dirty ones shown apart. The free Pot odds and Outs calculators do the same sums.

Terms in this lesson

Pot odds Equity needed Odds and percentages Rake Equity Outs Clean and dirty outs Flush draw Open-ended straight draw Gutshot Rule of 2 and 4 Direct odds Implied odds Expected value All-in Top pair Certainty badges Rules R1 to R12 Style

The maths of a call

Pot odds, equity and outs, how to turn one into another, and a worked flush-draw example from the price to the decision. 5 min read.

The price: pot odds and the equity you need

Facing a bet, you are buying a share of the pot. Do you win often enough to pay for it? Compare the equity you need, which comes from the price, with the equity you have.

The price of a call

25% needed

Your call10 bbTheir bet10 bbPot before the bet20 bb

The pot is 20 bb and villain bets 10 bb. You call 10 bb to win a pot of 40 bb: pot odds of 3.0 : 1, and your call is 25% of the pot, the equity you need. Try it with your own numbers

Prices worth remembering

A third of the pot20%Half the pot25%Two-thirds of the pot28.6%The pot33.3%Twice the pot40%

The equity you need to call, by the size of the bet. Bars run from 0 to 100%. Try it with your own numbers

Tip: Rake comes out of the pot you win, so it raises the price a little. If 2 bb of a 40 bb pot is raked, you win 38 bb and need 10 ÷ 38 = 26.3%.

Your side: equity and outs

Equity is your share of the pot if all the cards were dealt with no more betting. With a draw you are usually behind, and want to know how often you will catch up.

On the flop there are 47 cards you can’t see; on the turn, 46. So 9 outs on the flop arrive on the turn 9 times in 47, which is 19.1%.

The rule of 2 and 4

At the table a quick estimate does the job. Multiply your outs by 2 for the chance on the next card, or by 4 for the chance by the river from the flop, when you are sure to see both cards.

The rule against the exact figures, from the flop

4 outs: rule 8% and 16%; exact 8.5% and 16.5%.
8 outs: rule 16% and 32%; exact 17.0% and 31.5%.
9 outs: rule 18% and 36%; exact 19.1% and 35.0%.
15 outs: rule 30% and 60%; exact 31.9% and 54.1%.

The rule of 4 against the exact chance by the river

Rule of 4: outs × 4Exact chance

1 out4% / 4.3%

2 outs8% / 8.4%

3 outs12% / 12.5%

4 outs16% / 16.5%

5 outs20% / 20.4%

6 outs24% / 24.1%

7 outs28% / 27.8%

8 outs32% / 31.5%

9 outs36% / 35.0%

10 outs40% / 38.4%

11 outs44% / 41.7%

12 outs48% / 45.0%

13 outs52% / 48.1%

14 outs56% / 51.2%

15 outs60% / 54.1%

16 outs64% / 57.0%

17 outs68% / 59.8%

18 outs72% / 62.4%

19 outs76% / 65.0%

20 outs80% / 67.5%

It is close for small draws and runs high for big ones. Only use the 4 when nobody can bet on the turn, for example when someone is all-in.

A worked example

A flush draw facing a half-pot bet

You hold 6 of hearts, 5 of hearts on king of hearts, 9 of hearts, 2 of clubs. The pot is 10 bb, villain bets 5 bb, and you both have plenty behind.
The price: call 5 to make the pot 20. Pot odds of 3 to 1; equity needed 5 ÷ 20 = 25%.
Your outs: the 9 unseen hearts.
The next card: 9 ÷ 47 = 19.1%. The rule of 2 says 18%.
By the river: 35.0% for the flush. The rule of 4 says 36%.
Against king of spades, queen of diamonds, PokerIQ’s exact equity by the river is 38.9%: two pair, trips and straights add a little to the flush.

Your outs on the deck

Your cards6♥5♥

BoardK♥9♥2♣

Out (9)Seen: your cards and the boardUnseen, no helpDirty out (none in this hand)

♠AKQJ1098765432♥AKQJ1098765432♦AKQJ1098765432♣AKQJ1098765432

9 outs of 47 unseen: 19.1% on the next card, 35.0% by the river. Against none of them is dirty. Count outs for your own hand

Equity needed against equity held

Equity needed (the price)25%

Flush on the next card19.1%

Below the price

Flush by the river35.0%

Above the price

By the river against , exact38.9%

Above the price

Expected value

In PokerIQ

Hand and outs counts the cards that put you ahead of villain, with any dirty ones shown apart. The free Pot odds and Outs calculators do the same sums.