Calculating Card Odds and Pot Odds in Poker
David Sklansky, I'm not really great at calculating odds. But I do understand the concepts of card odds and pot odds, at least on a general basis, and I understand what these numbers mean when I play. I can even boil what you need to know down to one quick sentence:
Play draws that are hard to hit only when the pot is large and there are lots of players in it.
That about sums it up, but here's some explanation if you're interested:
Card Odds
When you want to calculate "card odds", you're calculating what the odds are that you won't hit your hand. (Odds are always stated in those terms, really, even when you're talking about other games. They're always based on the odds that your desired outcome won't happen.)
The odds of catching pocket aces in a Texas holdem game are 220 to 1. This means that you'll have pocket aces on average only once every 221 hands.
Pot Odds
When you want to calculate "pot odds", you're calculating what kind of payoff you'll receive if you win the pot versus what you're having to bet. If you have a pot with $2000 in it, and you have to call a $20 bet in order to play, your pot odds are 2000 to 20, or 100 to 1. (1 betting unit could win you 100 betting units.)
Odds are just fractions stated in reverse, basically.
Positive and Negative Expectation
You have a positive expectation when the payoff on a bet is higher than even money.
You have a negative expectation when the payoff on a bet is lower than even money.
To calculate this, you need to understand the odds of winning your bet versus the odds that the payoff is offering you.
A roulette example: A single number bet in roulette pays off at 35 to 1. The odds of hitting a single number in roulette are 37 to 1. Since the odds of winning are lower than the odds your bet is offering, you're making a negative expectation bet, which means you're going to lose money in the long run playing roulette.
How it works in poker: The card odds are more or less your chances of hitting your hand and winning. The pot odds are the payoff if you win. If the card odds are lower than the pot odds, you're making a negative expectation bet. If the card odds are higher than the pot odds, then you're making a positive expectation bet.
Winning players make positive expectation bets.
A Quick Example - Drawing to a Flush
Suppose you have AK of hearts as your starting hand. The flop come 5h - 9h - 2s. You have 4 cards to the nut flush on the flop.
The odds of hitting your flush are based on the 9 hearts left in the deck versus the other 47 cards in the deck. In other words, the odds are 47 to 9, but you can simplify that and say that the odds are about 5 to 1 that you'll hit your hand.
If it costs you $1 to play in a pot that has $10 in it, then you're getting pot odds of 10 to 1 on your bet. Since you have a 5 to 1 chance of hitting your hand, you have a positive expectation bet.
Why Card Odds and Pot Odds Are Only Part of the Picture
Poker is a game of incomplete information. You don't know what cards your opponents are holding. This makes betting strictly on a card odds versus pot odds basis a problematic way of playing.
Some bets might have a positive expectation even if you don't have the appropriate pot odds to justify the bet. This is because the other player or players might fold in the face of your bet or raise, and in that case, you'll win the pot. So this amount has to be added to your expectation.
In a semi-bluff situation, you might be making a profitable bet or raise with a calling hand even if you don't have the pot odds to warrant it because of the additional expectation added by your opponents' chances of folding.
More
There's a lot more involved in calculating odds than just this. You have to be able to calculate outs, know when to discount outs, and read your opponents and calculate how that affects your odds too. But this article was meant to be an introduction to the concepts, so I won't get into all of that here. But I'll add additional articles about those concepts in the future.
More detailed poker odds and pot odds can be found at this calculating poker odds page on TightPoker.
If you liked this article, you'll probably also be interested in the following:
David Sklansky's All-In Tournament System - Information about the all in or fold system that Sklansky outlines in his Tournament Poker for Advanced Players book.
Phil Hellmuth's No Limit Starting Hands Suggestions - Which hands to play preflop, and how to play them, and a little bit of information about why. For beginners to no limit holdem.
Texas Holdem Starting Hands - An article I wrote about Texas holdem starting hands. Again, for beginners, this one is more focused on limit holdem.
Beginners should also be sure to check out the article about poker hand rankings too.
This page was last updated on January 5, 2006.
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