Pot Odds and All That Jazz

No matter how you slice it, poker always revolves around this primary relationship: Does the pot offer enough money – or promise to offer enough money once all the betting rounds are concluded – to overcome the odds against making your hand? You can't escape it. The relationship between the pot and the chances of making the winning hand threads its way through every form of poker you play. It even winds its way through real life, too. The phrase, "Is the prize worth the game," encapsulates the essence of decision-making. In real life, the answer always "depends," since everyone's personal equation for relating the cost of something to its personal value differs. But poker metrics are less subjective, and one has the advantage of being able to count the pot and calculate the odds against making a hand, and then decide whether to fold, bet, call, or raise.

That's the very reason poker is a game you can beat. If you're shooting dice, each and every bet – from the bad ones like "hard ways" and the "Yo" to better wagers, like making a pass-line wager and taking the odds – carries a negative expectation. No system yet devised enables you to package a group of individual bets with negative expectations and rewrap them into a magic parcel of wagers that will pay off in the long run.

Poker is beatable, in part, because the odds are not immutable; they shift and change as each card is dealt off the deck. In some games, like seven-card stud, figuring the precise odds against making your hand can be difficult, especially in the heat of battle, because the calculations change with every betting round. You may start out with three hearts in your hand and not see another heart in of any of your opponents' exposed upcards. But on the next round of betting, four of your opponents might be dealt a heart, and that dramatically changes your hand's risk-reward ratio. After all, there are only 13 cards of each suit in a deck. You have three and need two more to complete your flush. Each heart dealt to one of your opponents is one that will never find it's way into your hand. You don't need to know much about poker or probability to realize that you stand a much better chance of receiving a heart when 10 of them remain in the deck instead of six – and you still need two of them.

It's a bit easier to figure the odds in hold'em, because there are only so many situations to be accounted for, and far fewer exposed cards to consider. If you work out the relationships in advance by memorizing the odds against making particular hands in commonly encountered situations – like flopping four to a flush or four to a straight – half of your work is already done. All that remains is counting the pot.

Michael Wiesenberg, in The Official Dictionary of Poker, defines pot odds as: "The ratio of the size of the pot to the size of the bet a player must call to continue in the pot." For example, if the pot contains $20 and you must call a $4 bet, you are getting pot odds of 5-to-1.

If there are no more cards to come, and no players remain to act after you, all you need do is consider the pot odds. If your chances of winning are better than the odds the pot is offering you, it pays to call. Otherwise, you should fold – unless you think a raise will cause your opponent to release his hand, in which case that's the preferred action. But let's ignore the impact of bluffing for a moment, and focus our attention on the relationship between pot odds and the chances of making your hand. If you figure to win once in three times when the pot is offering you 5-to-1odds, it pays to call, regardless of whether you win that particular hand or not. It's the long run that matters in poker, not the outcome of any given hand.

But on earlier betting rounds, when there are still more cards to be dealt, more players to act, and more betting rounds, it's difficult to know with any degree of precision how much it will cost to try to make your hand, since you can never be sure how the betting will proceed or how many opponents will stick around and pay you off if you make the winning hand.

That's where implied odds come into play. The Official Dictionary of Poker defines implied odds as: "The ratio of what you should win (including money likely to be bet in subsequent rounds) on a particular hand to what the current bet costs." Calculating implied odds is imprecise, and is really a form of reckoning at best, since one never knows how many opponents will remain in the hunt, or how much money will be wagered on subsequent betting rounds.

The more betting rounds there are in a particular game – all else being equal – the bigger the role played by implied odds. In games like draw poker or lowball, with only two rounds of betting, implied odds are not as significant as they are in hold'em, which has four betting rounds, or seven-card stud, which has five.

Implied odds are affected by a number of factors. Implied odds are better whenever your hand is hidden, because your opponents might not realize what you're holding and pay you off when they have inferior hands. If you're playing seven-card stud, you might have four unsuited, unrelated cards exposed on your board, and have a full house or even four of a kind. A hidden hand begets much higher implied odds than a hand that shouts out its strength for the entire world to see.

Suppose you're showing four jacks in your seven-card stud hand. Your implied odds are pretty much zilch, zero, nada, nil, and nothing at that point. Unless your opponent can beat four jacks, he's going to take his hand and toss it away. He can't beat you, he can't bluff you, and he won't pay you off, either.

Betting structures affect implied odds, too. When betting limits double on later rounds, implied odds increase. Since your opponent may call a bet on later rounds because of pot size alone, that extra bet increases the implied odds. Your opponents, just by virtue of their playing style, can increase or reduce implied odds. Players who seldom bet or raise but call to the bitter end increase implied odds, because you can draw to your hand cheaply, knowing all the while you'll get paid off if you make your hand.

If you're last to act, you can take advantage of what your opponents have done to increase your implied odds. But players who have the ability to discern what kind of hand you're holding even if they don't have the advantage of seeing exposed cards will reduce your pot odds as long as they have the discipline to release their hand once they know they are beaten.

Acting first doesn't help your implied odds, either. Whenever you act first, it's a guessing game of sorts. You never really know whether a wager will cause opponents to fold or if they'll play back at you by raising. When you're forced to act before your opponents, their actions can reduce the odds you're getting to draw for your hand.

There's another concept that comes into play, too, and that's the amount of money already in the pot. That money is the reason you might want to continue to play a hand even though you are not the favorite. Here's an example: If you flop a four-flush when playing hold'em, the odds are 1.86-to-1 against completing your hand. In addition, there's always the chance that you might make your flush but lose to a bigger hand. Even though you are not favored to win the hand, you are still a "money favorite." In other words, even though you might win the pot just once every three times you find yourself in that situation, it pays to draw as long as the pot promises to return $2 or more for each dollar you have to pay to draw to your flush.

Here's another example, and as absurd as it may seem, it makes it easy to illustrate the point about being a money favorite while not an outright favorite to win the pot. Suppose a wealthy eccentric is running around your favorite cardroom randomly tossing $5,000 chips into pots. Let's assume you have flopped a flush draw in a $20-$40 hold'em game against only one opponent, and you know with absolute certainty your opponent has flopped a set of kings. Normally, the relationship between the pot odds and the odds against making your hand would suggest that you fold, but with an additional $5,000 in the pot, you'll play – of course you will – calling all bets until the bitter end. After all, with three rounds of betting to go, you can lose a maximum of $20, $40, and $40 on each betting round – and you don't even have to call that last bet on the river if you fail to make your hand, since you know your opponent has you beaten unless you make your flush and the board fails to pair. Since you stand to win substantially more than the cost of a couple of bets, this is not the time to save a buck by folding. While I've never played a hand of poker in which the relationship between the pot odds and the odds against making my hand were this good, the fact remains that the amount of money currently in the pot is the third force to be reckoned with when considering pot odds and implied odds.

While there are always caveats that might cause you to deviate from these suggestions, here are three rules of thumb to think about when you're considering the pot odds/implied odds relationship.

• If you are a money favorite on new money – forget, for a second, about the money that's already in the pot – you should bet or raise to build the pot. If you've flopped a flush draw and are last to act, and four players have already called, go ahead and raise. You are getting a big enough price on this betting round alone to justify your action. Since the odds against completing your hand when flopping a four-flush are only 1.86-to-1 against you, but you're getting 4-to-1 on new money entering the pot – never mind whatever money is already in the pot – get some more money into the pot, and do it now.

• If you are a money favorite because of the size of the pot or the implied odds you think you'll get if you make your hand, calling is usually the best option. If you ignore the fact that raising may allow you to win the pot by causing your opponents to fold, raising in these situations only reduces your implied odds. Now is the time to make your hand inexpensively – even if some wealthy lunatic just sauntered by and dropped a few $5,000 chips in the pot.

• If you have neither pot odds nor implied odds, and are not a money favorite, fold and save your money.

When Oscar Wilde wrote, "The truth is rarely pure, and never simple," he was probably not thinking about a poker game, but his words hold true, nonetheless. These three rules of thumb are not the entire answer, of course, and while it's easy to come up with a raft of reasons to deviate from them on occasion, the fact remains that the relationship between pot odds, implied odds, the odds against making your hand, and the money that's already in the pot will go a long way toward answering that age-old poker conundrum: Shall I fold, bet, call, or raise?

My newest book, Internet Poker: How to Play and Beat Online Poker Games, is available through Card Player and at www.ConJelCo.com, and all of my books can be found at major bookstores and online at www.Amazon.com.