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Playing the Odds in Texas Holdem Learning how to properly calculate poker odds is a fundamental requirement of Texas Holdem. While the math aspect of odds might sound scary to most new players, it really isn't as hard as it looks. In fact, most of the calculations only require that you know basic math. Why Odds Are ImportantKnowing odds is important because it gives you an idea when you are in a good or bad situation. Let's say you and a friend are flipping a quarter and he gives you 1:1 odds that the next flip will land on heads. You already know that 50% of the time it will land on heads, while the rest of the time it will land on tails. In this case he's giving you an even bet, because nobody has the advantage. However let's say your friend offers you 2:1 that the next coin flip will be heads. Would you take this proposition? Of course you would, because the chances of heads or tails coming up are still 1:1, while he's paying you at the 2:1 rate. If your friend gambles with you long enough, he'll be losing his shirt with these kind of odds. While the above example is trivial, remember that the only reason it was such an obvious good deal is that you already knew the odds of a coin flip are exactly 50-50. If you didn't know that, you might have passed up a very advantageous situation. Or even worse, you might have been the one offering 2:1! This kind of thing actually goes on all the time in poker. Players often don't know the real odds they are facing, and unwittingly put themselves on the wrong side of the wager. Always remember this important principle: In poker, there are two types of players. The first type are players who take bad odds in hopes of getting lucky. The second type are players who cash in on the good odds offered by the first type. Drawing HandsAt the heart of most odds considerations in Texas Holdem are so-called "drawing hands." These are hands that don't figure to be the best hand at the moment, but have some definite way to improve to become the probable winning hand. The most common examples are straight draws and flush draws. These hands usually start out extremely weak, but with the right card they become sudden monsters. Playing drawing hands correctly is one of the keys to winning at Texas Holdem, and one of the areas where new players make their biggest mistakes. The principles outlined below will help you to avoid these errors in your own play. Pot OddsThe relationship between the current size of the pot and the current bet is called the pot odds. For example if the pot is $100 and the bet is $10, the pot odds are 10-to-1. Pot odds are used to calculate whether a certain play has a positive expected value. You should always know the pot odds when either making or calling a bet. As you'll see below, knowing the pot odds is crucial to making the correct decisions regarding drawing hands. OutsOuts refers to the cards in the deck that will make your hand if they show up on the turn or river. If you have 10 outs, it means that there are 10 different cards that can come that will complete your hand. Sometimes calculating the number of outs is very simple--for example if you need an ace to make your hand and all four aces are still in the deck, you have 4 outs. Sometimes it takes a little more thought. Take a standard flush draw--say you have two spades in your hand and two spades appear on the flop. Altogether there are 13 spades, and you've seen 4 of them. That leaves 9 spades unaccounted for, so you have 9 outs to make your flush. To save time it is useful to memorize the most common situations such as flush draws and straight draws. The table below shows the number of outs for some typical hand types.
Hand OddsHand odds are simply the odds of completing your hand. This is based entirely on your number of outs--the more outs you have, the better the odds of completing your hand. Hand odds can be expressed as either a ratio (like "3-to-1") or as a percentage (like "25%"). As a rule of thumb, every out gives you about a 2% chance of hitting on either the turn or river, or about a 4% chance on the turn and river combined. For example, 5 outs gives you about a 10% chance of improving on the next card, or 20% on the next two cards. The table below shows exact values for each number of outs, and it is well worth memorizing the most common ones.
Expected ValueWhen playing a drawing hand, the most important factor to consider is the ratio between the pot odds and your hand odds. Simply put, if the pot odds are bigger than your hand odds then you should continue with the hand because you have a positive expected value. It doesn't mean that you will make money on this hand, of course. But the times when you hit your draw will make enough profit to cover the losses from the times you don't. However if the pot odds are less than your hand odds, you should fold the hand because you now have a negative expected value. This means that the money you win when you hit your draw will not be enough to cover the losses from the times you don't.
Putting It All TogetherLet's say you have a flush draw on the flop and need to decide whether to call a bet with it. This is 9 outs, and refering to the odds table you will see that you have a 19.6% chance of hitting a hand with 9 outs on the turn. This is approximately 1 in 5 times, or 4-to-1. So now you know that the size of the pot needs to be bigger than 4 times the size of the bet to make this a profitable play. If it costs you $10 to call and the pot is more than $40, drawing for the flush is the correct move. If there is less than $40 in the pot, you should fold.
Things To Watch Out ForOne of the most common mistakes players make when evaluating odds is consider only the current bet but compare it against the hand odds for the turn and river combined. For example many players have memorized the fact that a flush draw will hit by the river 35% of the time. That's about one time in three, or 2-to-1 odds. That number implies they need at least 2-to-1 pot odds to call. So if the bet is $10 and the pot is $25, the call seems correct. But that is actually a mistake, because they are forgetting that if they don't hit their flush on the turn they will likely have to face an additional bet to see the river. Never compare hand odds based on seeing two cards with pot odds based on seeing one card. The simplest way to correctly consider the situation is to compare the current pot odds ($25 to $10, or 2.5-to-1) with the odds of making your flush on the very next card (4-to-1, not 2-to-1). So now we can see that calling is only going to cost money in the long run. Another common mistake is to count more outs than you really have. This can take two forms. One is simply a miscalculation based on counting the same card twice when adding together two different draws. Let's say you have 4s5s in your hand and the flop is 3h6sKs. That gives you both a flush draw and an open-ended straight draw. That's 9 outs and 8 outs, respectively. But it's not 17 outs total, because the 9 outs (for the 9 spades left in the deck) already counted the 2s and the 7s, which are also part of the 8 outs to make the straight. Thus you really have 15 outs rather than 17. More often, players overestimate outs by assuming any of them are equally good. Often that is not the case. For example if you hold 8c9c and the board is Jc5c8h you have 9 outs to make the flush. But if your opponent is holding AcQc, none of those 9 outs will actually give you the winning hand! In fact you would be much better off if an 8 came than if a club came, so those 2 outs are "stronger" outs than the 9 flush outs. What this means is that even if a certain card will improve your hand, it should not be counted as a full out if the improved hand may still not win. To count as a real out a card should ideally give you the nuts; the further away from the nuts you get, the less that card should be considered as a true out. Naturally this can get rather subjective and there is no clear-cut way to distinguish a "good" out from a "bad" out without knowing exactly what cards your opponent is holding. Just be aware that when counting outs, you should only count cards that give you a likely winning hand, and not just any cards that improve your hand in some way. Implied OddsOnce you're comfortable with basic odds, you can include the concept of implied odds (or implied pot odds). The basic pot odds formula given above only took into account how much money was actually in the pot. This may be different from how much you truly stand to win because if you hit your draw, you can often raise the bet or make a bet at the end and get called. Since this extra money only goes into the pot when you make your hand, it makes some draws a bit more playable than they might first appear. However, evaluating implied odds can be very subjective and can depend heavily on the specific situation. For example some opponents will almost never call your final bet if they think you just made your flush, while others might actually make a bet of their own and allow you to raise. Also implied odds tend to be much more important in no-limit than in limit games, since in limit all you can ever hope to get is one extra bet while in no-limit you might get your opponent's entire stack. It's best not to worry too much about implied odds until you're completely comfortable with basic pot odds, and above all don't make the mistake of using implied odds to justify chasing draws you know are losers.
Manipulating the Pot in No-Limit HoldemFinally, it's time to consider the opposite side of the coin--that is, playing against drawing hands. This is another area where new players have a lot of trouble, but the basic idea is pretty simple. If you have some kind of a made hand--say, top pair--and you suspect your opponent has a drawing hand, you can size your bet to manipulate the pot odds he will be getting. As a general rule, you want to make his draw unprofitable so he will either fold or make a mistake by calling. If you knew his exact cards you could size your bet perfectly to be just above what he could correctly call. Of course you can't really be this exact, but by betting at least 1/2 the size of the pot you can cover most draws. Let's say the pot is $100 and you bet $50. That puts $150 in the pot. He has to call $50, so as you can see his pot odds are now 3-to-1. The most common draws are about 4-to-1 to hit on the turn, clearly not enough to continue in this situation. So by sizing your bet appropriately you have shut your opponent out of his draw (or induced him to make a mistake by calling, which is even better). What about a bigger bet? Anything up to the size of the pot is probably fine, but above that is probably just forcing him to make a correct decision and fold, as well as simply risking more money than is necessary. What about betting less? A little less may be fine, and might even be more likely to induce a mistake. But too much less and you might be the one making the mistake. For example if there is $100 in the pot and you bet $30, your opponent's pot odds will be $130-to-$30 or a bit over 4-to-1. That's good enough to make any standard draw profitable to pursue. In the long run, your $30 bet is a money loser! Of course this kind of pot manipulation is usually impossible in a limit game, which is the primary reason limit Holdem is much more of a drawing game than no-limit Holdem.
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