Outs & Pot Odds

Outs

Put simply, outs are the number of cards that are still to be played which could help your hand. In other words, outs are the number of cards that you WANT. Obviously, the higher the number of outs there are, the better your chances of getting them. Pretty much the only thing you need to be able to do in order to understand this most basic set of odds is: divide the number of outs (numerator) by the number of unseen cards in any given game (denominator). When you have the result, shift the decimal point two places forward and you have your odds in the form of a percentage.

There are, however, a few very minor complications. The first of these is that your denominator will either be 50, 47 or 46, depending on the stage of the game. Here you need to remember the word flop, which means the first three cards that are turned over in a game of Texas Hold ’Em. Since Texas Hold ’Em starts with a 50-card deck (minus the two cards you are given, which are called your pocket cards), the pre-flop denominator in calculating your odds will be 50. The post-flop denominator, then, will be 47, once you subtract the cards that have been revealed in the flop. And the denominator changes again to 46 after the turn, or the fourth card that’s revealed. Let’s look at some examples to help clarify this idea.

Example #1:
Question: You’ve got two queens to start, which is quite a nice hand of course, but the flop doesn’t produce another. What are your odds of getting a queen on the turn?

Answer: Your numerator will be 2, since there are two more queens in the deck. Your denominator will be 47, since the flop revealed three cards out of the original 50. Divide 2 by 47, move the decimal place two spots forward, and you’ve got a 4.3% chance of getting that queen on the turn.

Example #2:
Question: What are your odds of getting a queen on the river, or the last card that’s revealed (after the turn)?
Answer: Since the queen didn’t show up on the turn, there are still two in the deck somewhere. That means your numerator will remain 2. The denominator, however, will change to 46, since there’s one less card to be played, after the turn. Divide 2 by 46 and your odds still hover around 4.3%.

Example #3:
Question: What are your odds of getting the third queen on the turn, and the fourth queen on the river?
Answer: Multiply the odds of getting a queen on the turn by the odds of getting the last queen on the river. As we established in Example #1, you’ve got about a 4.3% chance of getting a queen on the turn. Convert that back to 0.043. Now figure out the chances of getting the final queen on the river. The numerator changes to 1, since there’s only one queen left, and the denominator remains 46, as in Example #2, since we’re up to the river. Your odds are about 2.2%. Now convert that to 0.022, and then multiply it by 0.043. Your final answer is 0.0009, or about 0.09% after you move the decimal point two spaces forward. These are not very good odds.

Note: It’s crucial to convert your odds back to their original, non-percentage form when you multiply them. If you keep them as a percentage, your final answer for Example #3 would be about 9.5%, which is clearly a LOT different from 0.09%.

Pot Odds

You’ll see pot odds mentioned on every poker resource you look at for advice. You can’t avoid them. Pot odds are invaluable to success at poker, and that’s why we’ve included this crucial section.

Once you hit the flop, you should use pot odds to determine your next action. By the time the flop is dealt, you’ll be in one of two categories: you’ll either be winning (with a “made hand”), or you’ll want to improve your hand (“drawing,” or going for better cards). If you have a made hand, you should bet and raise. Don’t worry about pot odds yet. You’ll want to win the pot now because more cards can only help your opposition. An example of a made hand would be an ace and a king, with the board showing a king, jack and 4.

If you don’t have a made hand, you’ll be drawing. This is when pot odds start to matter a lot: when it’s time to decide whether to call or fold.

First, you must count the number of outs you have. Outs, if you remember, are cards that will make your hand the best hand. For example, if you have a king and a jack, and the board shows a queen, 10 and 7, your outs are four aces and four 9’s. That’s eight outs total!

Calculate your % chance of hitting an out by taking the number of outs multiplied by 2, and then add 2. Once you’ve got this number (in our example, that number is 18%), multiply it by the value of the pot to see the value of the maximum bet that you can call. Imagine that the pot in our example was $200. Eighteen percent of $200 is $36, so you should call any bet that’s less than or equal to $36.

Once again, the formula for calculating pot odds is:
(# of outs) x (2) + (2) = APPROXIMATE % OF HITTING.

Then… (Pot total) x (Percentage of hitting an out) = YOUR BETTING LIMIT.

And please, please, PLEASE remember to convert your percentage to a decimal before multiplying it with the total of the pot. Your math teacher would never forgive you, and your betting limit would be dangerously high! In the meantime, let’s look at an extended example of pot odds from a real poker situation:

Example #1
You’re playing at a table with $5 and $10 limits, respectively, and the pot is $200. After the turn, the board—the cards that are face up on the table—shows 2, 5, 9 and queen.

Imagine that you’ve got a pocket hand of jack and 10. That means that all you need from the river is an 8 or a king, and you’ll be able to complete a straight. Your opponent bets $10. You’re deciding whether or not to call your opponent’s bet. This is where your pot odds become important. First, however, you’ll want to calculate your chances of just winning the bet.

Bearing in mind how to calculate your outs, we’ll put 8 in the numerator position, since there are four 8’s and four kings that haven’t been revealed yet. The denominator, meanwhile, will be 46, since we’ve already finished the turn and the board has four cards. Dividing 8 by 46 gives you about a 17.4% chance of completing the straight and winning the bet.

Now let’s think about that pot of $200. Since your opponent is betting $10, and you stand to win as much as $200, that’s a potential profit of 20 times the bet; or, looking at it from an odds perspective, the bet is 1/20th of the pot. If you compare your 17.4% chance of winning the bet with the big difference between the bet and the pot (the bet is only 5% of the pot), your pot odds tell you that it might be a good idea to go for it.

This example demonstrates that pot odds are just a comparison between risk and profit. Nothing is risk-free, as all gamblers know, but pot odds are an important way of gauging when is a good time to take that risk. It’s crucial to have that kind of perspective in Texas Hold ’Em Poker, in particular.