LESSON 6: POT ODDS & PROBABILITIES

We made brief reference earlier to the concept of "pot odds", a term you'll often hear thrown around in cardrooms by wanna-be poker aficionados. Here's a little secret: the vast majority of these people have no idea what they're talking about. Shhh…don't inform them of their mistake – rather, learn about the proper use of pot odds here, and be content to watch your stack of chips steadily accumulate at the expense of those very same self-righteous opponents.

Generally

Pot odds refer to the relationship between the size of the bet you must call to see the next card to the size of the pot. We're about to get into some basic mathematics, but don't run screaming. It will be quick and painless, and you'll even get a wowipop at the end. This section is crucial to understanding when you should and should not be continuing with your drawing hands.Imagine we were to pose to you the following question: You hold



and the board is



A single opponent remains on the turn, and she bets $4. Should you call her bet to see the river and hopefully make your flush?

We hope you realized that there was an essential piece of information missing from this question, without which it was impossible to answer: the size of the current pot! If the pot were enormous (let's say $100 for this example), obviously you'd part with a measly $4 to see the river. But what if the pot size were only $8 after your opponent's bet? The answer is ‘no', you should fold. So where's the cut-off point at which you should be willing to call? Let's work it out mathematically:

There are 9 hearts remaining in the deck (you hold two, and there are two on the board) out of the 46 as-of-yet unseen cards. This means that your flush draw will come in on the river 9 out of 46 times, or approximately 20% of the time. This means that, roughly speaking, when 9 cards will give you the winning hand, you should only call the bet if it is less than 20% of the current pot size. Want the proof?

• Situation 1
  Let's say in the example above, you needed to call a $4 bet on the turn, and the pot (including that bet) was $8. $4 is more than 20% of the $8 pot so you should not call. What would happen if you did consistently make this call? Well, approximately 1 out of 5 times you would make your flush and win the $8 in the pot. The other 4 times, you would not make your flush, and lose the $4 you paid to call the bet. Therefore your expected value of calling this bet is:
  ($8 x 1) + (-$4 x 4) = negative $8
  
• Situation 2
  Same facts as above, but this time you need to call a $4 bet and the pot is $30). Since $4 is less than 20% of the $30 pot, you should call this bet. Mathematically speaking, the expected value of calling:
  ($30 x 1) + (-$4 x 4) = positive $14

Counting Outs

In the example above, we assumed that you had 9 cards (the remaining hearts in the deck) that would improve your hand to a winning flush. These are referred to as "outs". Take note of the following number of outs for other common hands:

• Open-ended straight draw – 8 outs to improve to a straight
• Gutshot straight draw – 4 outs to improve to straight
• Two pair – 4 outs to improve to a full house
• One pair – 5 outs to improve to two-pair or better

So the basic instructions for using pot odds are to first determine the number of outs you have to improve your hand, and then weigh the size of the bet you must call against the size of the current pot.

We provide for you here a simple chart showing the odds of improving your hand on the river based on your number of outs. Do we expect you to do all this math quickly in your head while seated at the table? Of course not! But as long as you spend the time now to understand the general theory involved, these decisions will come naturally and accurately with a little practice. Number of Outs - % of time you improve:

1 - 2% 2 - 4% 3 - 7% 4 - 9% 5 - 11%

6 - 13% 7 - 15% 8 - 17% 9 - 20% 10 - 22%

11 - 24% 12 - 26% 13 - 28% 14 - 30% 15 - 33%

16 - 35% 17 - 37% 18 - 39% 19 - 41% 20 - 43%

The idea of counting outs in multi-way pots can get complicated, and we would like to take this opportunity to refer you to Small Stakes Hold'Em by Ed Miller, which contains the best chapter on counting outs that we have ever seen in print.

Advanced Topic – Implied Odds

You sharper types might have noticed that we made an oversimplification in our discussion of pot odds above. Let's refresh your memory of Situation 1:

You needed to call a $4 bet on the turn, and the pot (including that bet) was $8. $4 is more than 20% of the $8 pot so we told you not to call. What would happen if you did consistently make this call? Well, approximately 1 out of 5 times you would make your flush and win the $8 in the pot. The other 4 times, you would not make your flush, and lose the $4 you paid to call the bet. Therefore your expected value of calling this bet is:
($8 x 1) + (-$4 x 4) = negative $8

Can you spot the simplification in the fact patter above? It's that the 1 out of 5 times you make your flush, you not only win the $8 currently in the pot, but you'll also likely make at least another $4 if you bet on the river with your winning hand (and potentially even another $8 if you're able to get in a check-raise!)

This concept is what's known as implied odds. They are essentially identical to pot odds, except they also factor in the additional money that you will extract from your opponents after you make your hand. Implied odds, although generally a little more complicated to calculate, are a better indicator of what your action should be, although we had to make sure that you understood the simpler concept of pot odds before hitting you with the more complicated permutation.

Therefore, even while a call may not seem to have a positive expected value given the current pot size, it may be nonetheless profitable once you factor in your expected winnings if you make the winning hand (especially if there are a lot of opponents remaining in the hand to pay you off). We refer you once again to Small Stakes Hold'Em, which also contains a great discussion of implied odds.

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