Pot odds, solved.

Learn how to price a call with worked examples, interactive calculators, a reference chart and six practice questions.

The whole thing, in one line
Required equity = cost to call pot before bet + matched bet + call
Here, pot means the pot before the opponent bets. Use only matched money you can win, and include your call in the final pot. The basic formula excludes rake and future betting.
Read me first

How this page works.

Three minutes here will save you twenty later. Every section answers one question and ships with a working tool — read top to bottom, or jump straight to the calculator.

Step 01
Learn the idea

One fraction. Required equity = cost / final pot. Everything below builds on this.

Step 02
Use the tools

Drop in real numbers. Calculators show what the answer looks like in practice.

Step 03
Test yourself

Six worked spots at the end. Get five right and you're ahead of the room.

A 60-second example

The whole idea, in one hand.

Click through the five steps below before touching a calculator. If this clicks, the rest of the page is just permutations.

  1. 01 The spot

    On the turn, villain bets $50 into a $100 pot. You have nine clean flush outs and no other way to win. What price are you getting?

  2. 02 The pot if you call

    If you call, the final pot will be $100 + $50 + $50 = $200. Your $50 call is included.

  3. 03 Required equity

    You risk $50 for a share of the $200 final pot. Break-even equity is $50 / $200 = 25%, before rake.

  4. 04 Your draw probability

    With nine clean outs and 46 unseen cards on the turn, the chance of hitting the river is 9 / 46 ≈ 19.6%. That is below 25%.

  5. 05 The decision

    The call loses money on direct pot odds alone. Extra money won when you hit can change the result, but only if the payoff is realistic and your outs are clean.

The Intuition

Every call is a tiny bet.

When villain bets $50 into a $100 pot, you're not deciding "is my hand good?" — you're being offered a tiny side bet at 3-to-1 odds. Your hand only has to win 25% of the time to break even. Pot odds is the framework for evaluating that side bet against your hand's equity.

Core idea

If there is no further betting and no rake, a call has positive expected value when your equity exceeds the call price divided by the final pot. Other spots also require future-cost and payoff estimates.

TL;DR

Pot odds give the break-even price. Compare that with equity against the betting range, while accounting for the assumptions behind both numbers.

The Calculator

Plug in real numbers.

Pre-set the most common bet sizes — 1/3 pot, 1/2 pot, 2/3 pot, pot, overbet — and see the required equity emerge live.

Calculator

The pot odds calculator

Foundational

Required equity is the cost to call divided by the final pot, including your call. Enter the pot before the bet and the matched bet you face. This heads-up model excludes rake and future betting.

Pot before bet
$100
Bet to call
$50
Required equity
25.0%

Required equity = call / (pot before bet + matched bet + call) = 50 / (100 + 50 + 50) = 25.0%.

The Other Half

Counting outs.

Outs estimate your chance of improving. Whether those cards win depends on the board and the opposing hand or range.

Calculator

Outs to draw probability

Core skill

These examples assume clean outs. Flop-to-river figures assume you see both cards; turn-to-river figures use 46 unseen cards. Draw probability is not the same as equity against every opponent.

DrawOutsHit by river (turn)Hit by river (flop)
Flush draw 4-to-a-flush 9 19.6% 35.0%
Open-ended straight 8 cards complete it 8 17.4% 31.5%
Gutshot inside straight 4 8.7% 16.5%
Double gutshot two inside straights 8 17.4% 31.5%
Flush + pair 9 flush + 5 trips/2pr 14 30.4% 51.2%
Flush + OESD the monster combo 15 32.6% 54.1%
Two overcards 6 cards pair an overcard; not always winners 6 13.0% 24.1%
Set → boat/quads 7 flop outs; 10 on an unpaired turn 10 21.7% 33.4%
OESD + pair huge equity hand 13 28.3% 48.1%
Flush + gutshot very strong combo 12 26.1% 45.0%
Two pair → boat 4 outs after a blank turn 4 8.7% 16.7%
Pair → trips tight draw 2 4.3% 8.4%
The Future Money

Implied odds.

Extra money won after improving can make a call profitable. The amount depends on effective stacks, the opponent and whether your improved hand wins.

Calculator

Implied odds — the missing variable

Advanced

This turn model counts the current pot plus an estimated extra payoff when a clean out hits. Enter matched bets you can cover and the effective stack remaining after your call.

Extra payoff needed on a hit = call / hit probability − final pot after calling.
Worked example. On the turn, nine clean outs have a 9/46 ≈ 19.6% chance of hitting. Facing a $50 bet into $100, the final pot after calling is $200. The break-even extra payoff is $50 / (9/46) − $200 = $55.56 from the opponent when you hit. This assumes every hit wins, every miss loses without another bet, and no rake. More than that payoff is needed for positive expected value.

Defending

Minimum Defense Frequency.

MDF is a range-level benchmark from a simplified heads-up river model. It is different from the equity needed to call.

Theory

Minimum Defense Frequency

Advanced

Minimum Defense Frequency is the share of your range that continues by calling or raising to make a zero-equity bluff break even in a simple river model. It is not a mandatory defense rate against every opponent.

Bet sizeDefend ≥ (MDF)Bluff success needed (α)
⅓ pot 75.0% 25.0%
½ pot 66.7% 33.3%
⅔ pot 60.0% 40.0%
Pot 50.0% 50.0%
1.5× 40.0% 60.0%

MDF is a benchmark for a simplified river model. Against a half-pot bet it is 66.7%. It describes total defense, including calls and raises; opponents who bluff too little can justify folding more.

The Aggressor's Math

Bluff:value ratios.

In a simple polarized river model, the balanced bluff share makes a pure bluff-catcher indifferent to calling. Larger bets allow a larger bluff share.

Theory

Bluff:value ratios on the river

Advanced

Assume value hands always beat the bluff-catcher and bluffs always lose when called. The figures below are the bluff share of the betting range in that simplified river model.

Bet sizeBluff %Value %Value : Bluff
⅓ pot 20.0% 80.0% 4.00 : 1
½ pot 25.0% 75.0% 3.00 : 1
⅔ pot 28.6% 71.4% 2.50 : 1
Pot 33.3% 66.7% 2.00 : 1
1.5× pot 37.5% 62.5% 1.67 : 1
2× pot 40.0% 60.0% 1.50 : 1

Bet size changes the balanced bluff share. In this simple polarized river model, a half-pot bet has 25% bluffs and a 2× pot bet has 40%. These are fractions of the betting range, not instructions to bluff that often in every situation.

Reference

The numbers, on one page.

Compare matched heads-up bets with the equity required to call and the pot odds offered. All pot sizes are before the bet; rake and future betting are excluded.

Reference

The cheatsheet to print

Reference

Required equity = call / (pot before bet + matched bet + call). Pot odds compare the money available before your call with the cost of calling.

¼ pot
16.7%
5 : 1 odds

A $25 bet into $100 gives you $125 to win for a $25 call.

⅓ pot
20%
4 : 1 odds

A $30 bet into $90 gives you $120 to win for a $30 call.

½ pot
25%
3 : 1 odds

A $50 bet into $100 gives you $150 to win for a $50 call.

⅔ pot
28.6%
2.5 : 1 odds

A $60 bet into $90 gives you $150 to win for a $60 call.

Pot
33.3%
2 : 1 odds

A $100 bet into $100 gives you $200 to win for a $100 call.

1.5× pot
37.5%
1.67 : 1 odds

A $150 bet into $100 gives you $250 to win for a $150 call.

2× pot
40%
1.5 : 1 odds

A $200 bet into $100 gives you $300 to win for a $200 call.

3× pot
42.9%
1.33 : 1 odds

A $300 bet into $100 gives you $400 to win for a $300 call.

What Goes Wrong

The eight common leaks.

Knowing the math is half the battle. Here's the half nobody talks about — the ways smart players still bleed money even after they understand pot odds.

Leak 01
Counting outs that are not clean

A card that improves your hand can also give an opponent a better hand. Count only winning outcomes; there is no universal 50% discount.

Leak 02
Assuming a future payoff

Implied odds depend on extra money an opponent will actually pay when you hit. Deep stacks make that possible, not guaranteed.

Leak 03
Skipping the river price

Compare the call price with your equity against the betting range. If your hand only beats bluffs, estimate the bluff share rather than assuming every large bet is value.

Leak 04
Treating MDF as a mandatory call rate

MDF is a simplified range-level benchmark. Against a player who bluffs too little, folding more can be correct.

Leak 05
Overbluffing opponents who call too often

Reduce bluffs against opponents who rarely fold. The adjustment depends on their actual calling range and the price of the bluff.

Leak 06
Ignoring effective stacks

You cannot win unmatched chips. Cap the call and any projected payoff at the chips the players can actually contest.

Leak 07
Ignoring reverse implied odds

Improving to a second-best hand can cost additional bets. A draw is less valuable when hitting it can still leave you behind.

Leak 08
Treating tournament chips like cash

Chip-EV pot odds do not include payout effects. ICM can change the equity needed for a tournament call, depending on stacks and payouts.

Test Yourself

Six spots. How many can you solve?

Six practice questions covering call prices, clean outs, defense frequencies and effective stacks.

  1. 1. On the turn, villain bets $50 into $100. You have nine clean flush outs, no other way to win and no future payoff. Is calling profitable on direct pot odds?

    Pot before bet: $100 Bet: $50 Clean outs: 9
    Answer No — about 19.6% is below the required 25%

    A call needs 50 / (100 + 50 + 50) = 25% equity. Nine clean outs among 46 unseen cards give 9 / 46 ≈ 19.6%. With no additional ways to win or later payoff, the call has negative expected value.

  2. 2. Villain bets ⅔ pot on the river. What is the minimum equity you need to call, before rake?

    Bet size: ⅔ pot Street: River
    Answer 28.6%

    For a $60 bet into $90, the final pot after your $60 call is $210. Required equity is 60 / 210 ≈ 28.6%. MDF is a different number: 90 / (90 + 60) = 60% of the defending range.

  3. 3. On the flop, villain makes a pot-sized all-in bet. You have a bare gutshot with four clean outs and no other way to win. Does calling meet the direct pot-odds threshold?

    Clean outs: 4 Bet: Pot-sized all-in Cards to come: 2
    Answer No — about 16.5% is below the required 33.3%

    A pot-sized bet needs 1 / (1 + 1 + 1) = 33.3% equity. With four fixed clean outs and both cards guaranteed, the chance of hitting is 1 − (43/47 × 42/46) ≈ 16.5%. The all-in condition removes any later payoff.

  4. 4. In the simple heads-up river model, what MDF corresponds to a half-pot bet?

    Bet size: ½ pot Model: Zero-equity bluffs; no future betting
    Answer 66.7%

    MDF = pot / (pot + bet) = 1 / 1.5 ≈ 66.7%. Defending this often makes a zero-equity bluff break even. It is a range-level benchmark, not a requirement to call a particular hand or an underbluffing opponent.

  5. 5. In the simple polarized river model, what fraction of a pot-sized betting range consists of bluffs at equilibrium?

    Bet size: Pot Model: Value always wins; bluffs always lose when called
    Answer 33.3%

    The bluff share is bet / (pot + 2 × bet) = 1 / 3 ≈ 33.3%. That is two value hands per bluff and makes a pure bluff-catcher indifferent to calling.

  6. 6. Heads-up on the river, the pot is $400 before villain shoves $400. You have only $80 left. What equity do you need to call?

    Pot before shove: $400 Your effective call: $80 Uncalled excess returned: $320
    Answer 14.3%

    You can call only $80. Of the $400 shove, $80 is matched and the other $320 returns to villain. The pot you can win after calling is $400 + $80 + $80 = $560. Required equity is $80 / $560 ≈ 14.3%, before rake.

Three numbers. That’s it.

Pot odds is one fraction with three inputs. Once you have it, every interactive on this page is just an extension of the same idea.

01

Required equity

Call / (pot before bet + matched bet + call). Include only money you can win; this direct-price calculation excludes rake.

02

Your equity

Nine fixed clean outs hit about 35.0% from flop to river if you see both cards, or 19.6% from turn to river. Actual equity also depends on the opposing range.

03

Compare

Compare equity with the direct-price threshold, then account for later costs, realistic payoffs and tournament payout effects where relevant.