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Pot Odds

Math is an important part of poker strategy.  When people talk about poker math or "the odds" as it relates to poker, they are usually talking about pot odds.  Pot odds refers to the price the pot is giving a player facing a bet.  It represents their potential reward for making the investment of calling the bet.  

Pot Odds Basics

Whenever a player is facing a bet, they are getting a price to call.  

For example, say there is $100 in a heads up pot and Player 1 bets $50.  It is $50 for Player 2 to call and he has the potential to win the $100 pot plus player 1's $50 bet for a total of $150.  

To find his pot odds, simply divide the amount he can win by the amount he must call.  

Pot Odds Formula with Example

Pot Odds=(Pot Amount+Bet amount)/(Bet Amount)

In this case, (100+50)/50=3.  Thus he is getting 3:1 on his call, or in other words, his pot odds are 3:1.

So how often does Player 2 have to win to make calling correct?  To convert pot odds to percentages, take 1 divided by the pot odds plus 1.

Percentage=1/(pot odds+1)

So in this example the calculation would be 1/(3+1)=1/4=0.25=25%.  Thus, Player 2 would need to win at least 25% of the time to justify calling Player 1's bet.

See if US players have basic pot odds down pat at Americas Cardroom.

Pot Odds of Drawing

In a $1/2 NLHE hand the board reads K♥8♥2♠3♣.  Player 1 goes all-in for $20 into an $80 pot holding A♦K♦.  Player 2 is holding 9♥T♥ for a flush draw.  What are his pot odds and should he call?

His pot odds are (80+20)/20=5, or 5:1.  

He has a flush draw, which gives him 9 outs from the remaining 44 cards.  That leaves 35 cards that do not give Player 2 the flush, making his pot odds 35/9=~4, or about 4:1.  Thus, Player 2 needs to be getting at least 4:1 to call for his flush draw.  Since the pot is laying him 5:1, he has a call.  

To check that this is right, lets play the hand 44 times.  35 times Player 2 calls and loses $20 for a total of $700.  9 times he calls and wins $100 ($80 pot plus $20 bet) for a total of $900.  Net profit is $200, or about $4.55 per hand.  

Now what if instead of being all-in, Player 1 had $200 more behind?  In this case Player 2 can expect to win more when he makes his flush and Player 1 calls an additional bet on the river.  This is called implied odds.  In these situations, players may call a bet getting insufficient pot odds because they have reason to expect they will make enough additional money on the river to justify their call.  

When drawing to questionable hands, it also may happen that a player makes his hand only to see it is second best, losing additional money in the process.  This is called reverse implied odds.  Savvy players try to avoid these situations by folding questionable draws, such as straight draws on boards where a flush is possible.  

Pot Odds of Calling Chart

Shown below is a chart of calling common bet sizes in No Limit Hold'em, correlating pot odds, and the percentage of the time required to win in order to call.  

No-Limit Holdem Pot Odds Chart

Bet Size

Pot Odds

Equity Required

Full Pot

2:1

33.3%

3/4 Pot

2.33:1

30.0%

2/3 Pot

2.5:1

28.6%

Half Pot

3:1

25.0%

1/3 Pot

4:1

20.0%

1/4 Pot

5:1

16.7%

Pot Odds of Bluffing

Everyone loves bluffs, and they involve pot odds as well.  When someone makes a bluff where they can only win when their opponent folds, they are getting a price from the pot just like drawing hands do.  

Pot Odds Bluffing Example Infographic

Lets say Player 1 bets the river with complete air.  The pot is $100 and he bets $80.  He stands to win $100 when his opponent folds, but will lose $80 when he is called.  The pot odds equation is the same; take the amount he can win and divide it by the amount he might lose:

Pot Odds=100/80=1.2

He is getting 1.2:1 on his bluff, meaning it must succeed 1/(1+1.2)=0.4545= 45.5% of the time to be positive expected value.  

To confirm, lets say his opponent will fold 60% of the time in this case.  So 60% of the time he wins $100, and 40% of the time he loses $80.  His EV is (.6)(100)+(.4)(-80)= $28.  Since 60>45.5, his EV is positive.

If we flip it to folding only 40% of the time, his EV becomes (.4)(100)+(.6)(-80)= -$8.  Since 40<45.5, his EV is negative.

Pot Odds of Bluffing Chart

Next is a bluffing chart, which shows the bet size of the bluff, pot odds, and how often it must succeed in order to be profitable.  Notice that the pot odds for bluffs are worse than calling a bet because when calling a bet, the other player's bet increases pot odds by exactly 1. 

No-Limit Holdem Bluffing Chart

Bet Size

Pot Odds

Success % Required

Full Pot

1:1

50.0%

3/4 Pot

1.33:1

42.9%

2/3 Pot

1.5:1

40.0%

Half Pot

2:1

33.3%

1/3 Pot

3:1

25.0%

1/4 Pot

4:1

20.0%

The methods used in these examples can be used to calculate pot odds for any poker scenario; draws, bluffing, hero-calling, and more.  Just remember to divide the amount that can be won by the amount that might be lost.  Then compare the calculated pot odds to the chances of winning in the given scenario. For an alternative take on pot odds see the rule of 4 and 2.

Pots odds, bet sizing and +EV bluffs are everything at Bovada Poker's anonymous tables.