Calculating Odds and Outs; Part II: Pot odds

by ~ May 12th, 2008. Filed under: Instructional posts.

* Modified June 15th, 2010 *

Well, we’ve figured out how to count chances or “outs”. Now let’s see what to do with that information.

“Odds” in poker refers to a lot of different types of aspects. Unfortunately for the beginner, any one of these aspects could be the subject of discussion and could be referred to as just “odds”, with the assumption that everyone knows what type of odds is being discussed.


Outs and Odds

Flip a coin. The chances of it coming up heads is 50%, the chances of tails is 50%. These are even odds, or 1 to 1. 50% + 50% = 100%, or all the possible outcomes.

Roll a die. It has six sides. On average, every six times you roll the die, five times you will not get the number one, and one time you will get the number one. Roll it 318 times, on average 53 times it comes up with a one, 265 times it doesn’t. The chances of rolling a one is 5 against, to 1 for, so 5 to 1 odds.

Let’s go back the some examples from the “outs” post.

You hold A8, the flop comes K65.

To make the flush on the turn, there are 13 – 4 spades = 9 spades left, or 9 outs. There are 52 total cards less 5 known cards = 47 remaining unseen cards. If you take the unseen 47 cards, you have 9 chances to get a spade and 47 – 9 = 38 times you will not get a spade. Your odds are 38 to 9. Divide 38 by 9 and you get 4.2 to 1 odds of hitting the flush on the turn.

What about trying to just hit an Ace? 47 unseen cards, 3 remaining Aces, 47 less 3 = 44 non-Aces. 44 to 3 odds, or 14.7 to 1.

To hit the flush or an Ace, there are 9 flush outs plus 3 Ace outs for a total of 12 outs, so 47 less 12 = 35 or 35 to 12 odds, or 2.9 to 1 odds.

The next example was an open ended straight draw, where you hold 98 and the flop is A76. This time you’re looking for any 10 or 5, so eight cards in total. 47 unseen cards less 8 straight-filling cards = 39. Divide 39 into 8 and you get 4.9 to 1 odds of hitting the straight on the turn.

Obviously, this is easy to calculate in advance for any number of potential outs that you may have.


Okay, now there’s two routes to go. Either look at what these odds tell you, or, look at how the odds change for the river and how the turn and river cards together can be evaluated. I think it’s less confusing to look at what the odds tell you first.


Pot Odds

Say the blinds are 5/10, you just called with your A8, the small blind folds and the big blind checks. There’s now $25 in the pot. The flop comes K65 and the big blind bets $10, making the pot $35 total. In order to call, you have to pay $10 to have a chance to win that $35. That’s $35 to $10, or 3.5 to 1 odds. (Note that you do not include the $10 to call in the winnings because you could have just kept the $10 by folding each time. You are investing $10 with the hopes of winning the $35 pot available to you.) Because these odds are being calculated relative to the pot, these are called “pot odds”.

Say you think that you need the flush to win. If you look at the chart above, when you have 9 flush outs you have 4.2 to 1 odds against making your flush on the turn. You are getting 3.5 to 1 pot odds. To make your call worthwhile in the long run, you need better pot odds than your cards are giving you.

There are a number of ways of proving this, but let’s try this method.

In order to get to a common whole number I’m going to use 1,820 repetitions of the same situation. Run this scenario 1,820 times, and at 4.2 to 1 odds the flush hits once every 5.2 times so 350 times. In 1,820 repetitions you paid $10 at total of 1,820 times for a cost of $18,200, and in 350 instances you won the $35 pot. 350 multiplied by $35 = $12,250, plus 350 times your $10 that you get back when you win, so $12,250 + $3,500 = $15,750 total winnings. In other words, after running the scenario 1,820 times, you lose $2,450 or an average loss of $1.35 each time, so fold rather than call.

Now let’s assume that your opponent has likely paired the King. In this case any of the three remaining Aces are outs for you as well. You have a total of 12 outs, 12 outs gives you 2.9 odds, the pot odds are 3.5 to 1, pot odds are greater than the odds the cards are giving you, so call as in the long run you will come out ahead.

Quick check using repetitions. 1,365 repetitions, you win 350 times. $10 x 1,365 = $13,650 cost. $35 per win times 350 wins = $12,250 plus $10 recovered 350 times, so $12,250 plus $3,500 for a total of $15,750 and net of plus $2,100 or $1.54 average. So, now it pays to call.

These calculations are just proofs. The thing to remember is that if you are getting better pot odds than the odds that the cards are offering to you, call. If not, probably fold, though we will cover some aspects later that may make it worthwhile to continue in the hand.

If someone says “you gave me pot odds to call”, this is what they are referring to. If you have the best hand and you bet too small, someone who may be still drawing for their hand has the correct odds to call. That’s why minimum betting at the flop or turn is so bad. The only people it scares away are the ones who have absolutely no hand and no draws, and even then it only works if no one is aggressive enough to raise you off the hand with a substantial re-raise.


Simple? Ah, but we haven’t looked at the river odds, or the turn and the river cards combined yet. 🙂


The rest of the series:


Compendium of instructional posts:

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