Pot Odds Made Easy

Because some players have difficulty with the concept of pot odds and others stumble over the practical task of calculating them in the heat of battle, it's time to demystify and sweep out whatever confusion still surrounds this subject while simplifying the arithmetic. In fact, no arithmetic is needed at all. Instead, a handy chart is included here that ought to prove helpful to new and experienced players alike.

Figuring pot odds is a necessary part of any poker player's game. Without it, we don't have any way of knowing whether the odds against making our hand are offset by this fundamental relationship: How much will it cost to keep playing this hand and how much money am I likely to win if I catch the card I need? By understanding the relationship between the odds against making our hand and the money we figure to win if we get lucky, we can play skillful high-percentage poker instead of treating the game like some form of gambling.

These calculations involve comparing the total number of unknown cards with the number of cards that will complete your hand – the "outs" – and then doing a bit of division.

For example, whenever you hold four cards to a nut flush on the turn in a hold'em game, there are 46 unknown cards (52 minus your two cards and the four on the board). Of those 46 cards, 37 won't help you, but the other nine cards are the same suit as your flush draw, and any one of them will give you the nut flush.

The odds are 37-to-9, or 4.1-to-1, against making your draw. Percentage poker players will call a bet in this situation only if the pot is four times the size of the bet. In a $20-$40 game, the pot would need to contain at least $160 – or else you'd have to be able to count on winning at least a total of $160 from future calls (this is called "implied odds," and is a guesstimate of sorts) – to satisfy this requirement.

If you're the kind of player who's fond of inside straights and other long-shot draws, consider this: You have only four outs on the turn. That's not much when you consider that 42 of the remaining cards won't help you at all, and the chances of completing your hand are less than 9 percent. If you'd prefer expressing that figure in odds, here's the bad news: The odds against completing your inside-straight draw are 10.5-to-1, and you'd need a pot that's more than 10 times the cost of your call in order to make it worthwhile.

If you had two pair and knew for a fact that your opponent had a flush, you'd be in the same kettle of fish, since only one of four cards will elevate two pair to a full house. When can you play hands like this? On two occasions. The first occurs when you hit the multistate Powerball lottery, win $90 million or so, and $20-$40 hold'em now becomes the equivalent of playing for matchsticks. The other occasion is in a game with complete maniacs, whose collective motto is: "All bets called, all the time." You would need to win more than 10 times the amount of your call to justify this kind of draw. But if you figure to win a $450 pot by calling a $40 bet with an inside-straight draw, go ahead. Go for it.

A chart is provided here that makes it easy to learn the odds against all of the common draws you're likely to come up against in a hold'em game. If you memorize it, you won't have to waste even a fraction of a second doing arithmetic at the poker table. Personally, I find it tough concentrating on the cards in play and my opponents while trying to do calculations at the poker table. Fortunately, there are simplified methods that enable you to approximate the percentage of time you'll make your hand.

An easy method involves multiplying your outs by two, then adding two to that sum. The result is a rough percentage of the chance that you'll make your hand. Let's suppose you have a flush draw on the turn. You have nine outs. Nine times 2 equals 18, and 18 plus 2 equals 20. That's pretty close to the 19.6 percent chance you'd come up with if you worked out the answer mathematically.

If you have only four outs, our quick proximate measure (4 outs x 2 + 2 = 10) is very close to the actual figure of 10.5. If you have 15 outs, our quick measure yields a figure of 32, while the mathematically precise figure is 32.6 percent.

The strategic implications of this are simple: If you have a 10 percent chance of winning, the cost of your call should not be more than 10 percent of the pot's total. With a 32 percent chance, you can call a bet of up to one-third the size of the pot.

While the "outs times 2 plus 2" method is an easy calculation to make at the poker table, it's even easier to commit the chart to memory. That way, you never have to figure a thing. Just tap into your memory bank and pull out the correct figure. And anytime you find yourself fighting a tinge of self-doubt, you can always double-check yourself by using the "outs times 2 plus 2" approximation.

If you want to estimate your chances on the flop without the need for much arithmetic, try this: If you have between one and eight outs, quadruple them. Eight outs multiplied by four yields 32, while the precise answer is 31.5 percent. With four outs, the quadrupling method yields 16 percent, while the accurate answer is 16.5 percent.

With nine outs – a common situation, because it represents the number of outs to a four-flush – quadruple the number of outs and subtract one. You'll be spot-on when you do, since the arithmetic answer is 35 percent. You can use this method for up to 12 outs – although with 12 outs, our shortcut method yields 47 percent, while the precise answer is only 45 percent.

For 13 through 16 outs, quadruple the number of outs and subtract four, and your results won't be any more than two percentage points off dead center. And remember, anytime you find yourself with 14 outs or more, you are an odds-on favorite to make your hand, and pot odds of any size become worthwhile.

This chart shows odds against making your hand in hold'em with two cards to come (the turn and the river), as well as with one card (the river) remaining.

Hanging on to unprofitable draws for whatever reason – and many players persist in drawing to long shots even when they really do know better – can be a major leak in one's game. For many, it's the sole reason they are lifelong losing players instead of lifelong winners.

There's no real excuse for that kind of play. Even if you are not mathematically inclined (and if you're in this category, you're in the majority; most people I know loath doing calculations while playing poker), you now have two surefire ways to get the answers without having to do anything more difficult than multiplying by two or four, or memorizing a simple chart. Now, all you have to do is count the size of the pot, or even approximate it, compare one to the other, and make your decision. It's that easy – really.

Raise your game with Lou Krieger, author of Poker for Dummies, at http://www.royalvegaspoker.com. His newest books, Internet Poker: How to Play and Beat Online Poker Games and Winning Omaha/8 Poker, as well as all of his books, are available www.Cardplayer.com.