Wednesday, January 05, 2005

Useful Math in Hold-em

A Strategy Primer for New Hold'em Players
By Lou Krieger

As poker's popularity continues to grow in the United States and overseas, experienced home game players as well as those who are new to the game itself, continue to sidle up to casino poker tables asking to be dealt in. Although new and exciting, playing poker in a casino can be confusing at first, and new players are usually full of questions. This is particularly true, and quite understandable, when that newcomer is playing hold'em for the first time, since even experienced home game players may either be more familiar with stud or have played such a wide variety of home poker games that they may never have studied, or even thought about hold'em to any measurable degree.

Some newcomers think they know it all. Others ask a lot of questions, particularly when they are attempting to learn hold'em the right way. Rather than simply sitting down and paying for lessons at the table, many new players - in an attempt to fast-track their own learning process - are reading books and using computer software to learn essential poker principles before attempting to put them in action in live games.

Some new players have read so extensively about poker that their questions are quite sophisticated. While these players are the exception rather than the rule, you can usually tell how schooled they are because their inquiries are aimed at sorting out information hierarchically, so they'll know what's important and how to apply that knowledge in the heat of battle. Players who haven't read much about the game, or even thought about it at all, generally bounce their questions all over the lot; some are important, while others range from trivial to the completely insignificant.

Stop me only if you haven't heard this one before: "I had A-K and raised. The dealer turned over three small cards - unconnected and unsuited. One player bet and another called. What should I have done?" I'll bet you've even heard that same mantra from experienced players. The big pair question is almost as popular: "I raised with Q-Q, but another player made it three bets. The flop was ragged. What should I do, check and call, come out betting, or check with the intention of raising?"

What should he do, indeed? If you are new to casino poker, new to poker in general, just learning to play Texas hold'em, or even if you happen to be an experienced player and these questions seem baffling at times, here are some guidelines to consider when faced with what appear to be vexing choices.

Basic Arithmetic: You can't escape it. Many of the choices you have to make in hold'em are based on numbers. Regardless of how you phrase it, you always need to answer the Prime Question: "Are the odds against making my hand offset by the money in the pot, or the money that figures to be in the pot by the end of the hand?" If you know the correct answer to this question, you are well on your way to resolving many of the dilemmas you'll encounter at the poker table.

If, for example, the odds are 2-to-1 against making your hand, but the pot will pay three dollars for each dollar you must invest in order to try and catch that winning card, it pays to call. In fact, if you figure to attract more than two dollars for each buck you wager on that particular betting round, it pays to bet your draw aggressively. Yes, that's right. If you have three opponents who are all wearing signs saying, "I call all bets," go ahead and bet your draw. If you're heads up, but there's already enough money in the pot so that it figures to pay you more than 2-to-1 on future investments, try to make your draw inexpensively - all other considerations notwithstanding - by checking and calling, or better yet, by getting a free card.

If the relationship between the odds against making your hand and the pot were different, and you figured to make your hand only one time in four attempts, you'd better not call if the pot only appears to be offering a 2-to-1 return on your money.

One comforting feature about hold'em is that situations frequently repeat themselves, so even if you are innumerate - a word that describes those of us who are "illiterate" where numbers are concerned - you can simply memorize the odds against catching the card you need in certain situations, compare it to the pot odds, and your answer becomes obvious. Just as an aside, we'll ignore those instances when it pays to bet, or even raise, when the relationship between the pot odds and the odds against making your hand are not justified arithmetically, but you think there's a good chance that betting or raising will cause your opponent to fold. That way we can keep this analysis Simon pure and simple, and unconfound with subtleties.

Don't worry if you have a hard time counting the pot. You don't need to be all that precise about it anyway and a close estimate will usually suffice. But when you do count the pot, be sure to consider how many additional bets you're likely to win from those opponents who will probably call if you make your hand. The first column in the following chart describes some common situations you'll encounter playing hold'em, along with the chances of making your hand. Those chances have been expressed as percentages. The second column of figures shows these same percentages expressed in terms of the odds against making your hand, which have been rounded, for simplicity's sake.

For example, if you are dealt a pair before the flop, you have a 12 percent chance of making a set on the flop. The odds against flopping that set are 7.5-to-1.

Before the Flop Percent Odds Against

* You hold A-K, your chances of flopping at least an ace or a king are: 32% 2-to-1
* You hold a pair, your chances of flopping a set are: 12% 7.5-to-1 With two cards to come
* You hold a straight flush draw, your chances of making a straight, a flush, or a straight flush by the river are: 54% 0.9-to-1
* You hold a flush draw, your chances of making a flush by the river are: 35% 1.9-to-1
* You hold an open-ended straight draw, your chances of making a straight by the river are: 32% 2.2-to-1

When you play hold'em, there are many other situations you'll encounter when your decision about whether to continue on with your hand once you see the flop will be based on the size of the pot compared to the odds against making your hand - but these will do for starters. If you memorize these odds, and can make a reasonable estimate about how many opponents will pay you off if you make your hand, you shouldn't go too far afield.

Count Your Opponents: The more opponents in the pot, the more straightforward you'll probably have to play. If you hold A-K, and the flop is comprised of three rags, what should you do? The answer depends, at least in part, on the number of opponents you are facing. If the flop didn't hit your hand, but there are seven other active players, you can be certain that the flop was kind to someone. If there's a bet and a call, consider this: To win, an ace or king needs to fall on the turn or the river, and it cannot give your opponents two pair. In addition, you have to hope you are not up against two pair - or better - already.

How do you assess whether you're up against two pair? Look at the flop. If the flop were 10-9-7 or J-10-9 chances of two pair are greater than they would be with a flop like J-6-3. Why? Most players will call with connected cards, or cards with a small gap, much more often than they will with an absolutely ragged hand like J-6, J-3, or 6-3.

Against only one or two opponents, your A-K may be the best hand regardless of whether the flop helps your hand. But if you are contesting the pot against more than two opponents, you need to be extremely careful. With a multitude of opponents, any flop that doesn't help you probably helps one of your opponents. When that's the case, "fit or fold" is usually the best course of action. If you need a metric to guide you, the breakage point is usually two or three. Two or fewer opponents and you stand a decent chance of winning even when big cards like A-K don't improve. Against three opponents or more, your chances will decrease progressively - from slim to none - based on the number of opponents contesting the pot.

The more opponents, the less bluffing you can do. It's nearly impossible to bluff seven players, and foolish to even try. After all, the flop that missed you probably hit one of your opponents, and he's the one who will call your bet. But if you are up against only one or two opponents, you might be able to steal the pot often enough to make a propitious bluff pay off.

What's Your Position? Life's a lot easier when you're in late position or last to act. After all, once your opponents have acted you know what it will cost to see the next card. If no one bets and you're last to act, you can even see the next card for free. If you are up against only one or two opponents you can bet and that might be enough for you to win the pot right there. When you are first to act or in early position, you usually need a strong hand to come out swinging. And you can't really assess the strength of your opponents' hands - real or purported - without some information.

Although every credible poker pundit advises selective and aggressive play, there are times when checking is advisable, and unless you have reason to think a bluff might win the pot right there, holding a marginal hand in early position is one of those times that discretion is often the better part of valor.

What Are My Opponents Like? There's no substitute for knowing your opponents. If you are playing against a habitual bluffer and you're holding any hand at all - even a marginal one, like second pair - you have to call when he comes out betting. While he's going to hold his share of big hands, just like the next guy, you will come out ahead in the long run by calling often enough to pick off his all too frequent bluffs.

Any time you have a good hand and a habitual bluffer bets, raising becomes mandatory. You'd ideally like to play him heads-up, since he might not even be holding a legitimate hand. After all, your raise might cause other opponents to fold, and that's a good thing, especially if they otherwise would call, get lucky, and draw out on you. While the world is full of poker players willing to stick around with weak hands in hopes of catching a miraculous card if the cost is only a single, solitary bet, that coterie narrows significantly when they have to cold-call two bets with a dial-a-prayer hand.

There's a lot more to feeling comfortable at the hold'em table than we've covered here. This is simply a primer - written with new players firmly in mind - as well as an easy way to keep your mind on the information you're likely to need in the heat of battle.

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