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After the Flop

Pot Odds and Expected Value

A simple introduction to the concept of pot odds and expected value, which determine how much you can pay to hit your draw in a cash game.

In cash games, you simply have to determine whether a call is "correct" in a mathematical sense. This means determining whether you would make money or lose money if you made the same decision in the same situation an infinite number of times. You compare what you would expect to win with what it will cost you to stay involved in a pot.

When your "expected value" is positive, you should stay in the hand.
This may sound complicated, but it need not necessarily be so. Calculating your expected value is a two-stage process, involving calculating your "pot odds", explained below, and then comparing that figure with the odds you have of hitting one of your outs.


Pot odds are defined as the ratio between the size of the pot and the bet facing you. For example, if there is $4 in the pot and your opponent bets $1, you are being asked to pay one-fifth of the pot in order to have a chance of winning it. 
A call of $1 to win $5 represents pot odds of 5:1.
If you are asked to pay $1 to win $10, you have odds of 10:1. If you need to find $3 to win $9, you have 3:1 and so on.

(Note: The size of the pot refers to the chips that are already in the pot, as well as all the bets made in the current betting round.)

Once you have determined the pot odds, you need to determine the odds of hitting your draw.


In the basics course we introduced the Rule of Two and Four, which offered an easy way of calculating your odds when holding a drawing hand on the flop.  
In that lesson, we calculated your odds of winning a hand in a percentage, but it can also be displayed as a ratio between winning and losing. A 20% winning probability can be translated as 4:1 odds - you will lose four in five times.
The precise mathematics behind this is not crucial at this stage. But the chart below shows a list of the most common draws you face in Texas Hold'em and the approximate chance you have of hitting them.
The first column ("Outs") shows the number of outs you have; the second column ("Odds flop to turn") shows the chance of hitting the draw on the next card; the next column ("Odds flop to river") shows the odds of hitting on turn or river, ie, on either of next two cards.

1 45:1 22:1 Smaller set vs Higher set
2 22:1 11:1 Higher pocket pair vs Smaller set
3 15:1 7:1 One overcard
4 11:1 5:1 Gutshot straight draw
5 8:1 4:1 Middle pair vs Higher pair
6 7:1 3:1 Two overcards
7 6:1 2,5:1 Gutshot straight draw plus overcard
8 5:1 2:1 Open-ended straight draw
9 4:1 2:1 Flushdraw
10 4:1 1,6:1 Gutshot plus two overcards
11 3:1 1,4:1 ---
12 3:1 1,2:1 Gutshot and Flush draw
13 2,5:1 1,1:1 ---
14 2,4:1 1:1 Straight draw plus two overcards
15 2:1 1:1 Flush draw plus two overcards


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