If you think you are serious about poker and you don't know how to calculate odds, then you are a fish. Plain and simple. Look in the mirror and practice your fishy face.
Here is a simple analogy. Suppose someone wants to bet with you on coin flips. If he offered to pay you $1 whenever it's heads, and you pay $1 whenever it's tails, you would accept because that is a fair bet. Why is it a fair bet? Because there is a 50% chance of coming up heads, also known as odds of 1:1. This means that whatever amount he is willing to pay for heads, you should be willing to pay an equal amount (or less, but who would accept that) for tails (= 1:1).
Now suppose he wanted to flip two coins. You win if they are both heads and lose otherwise. You can see that you lose when one coin is heads and the other is tails, or both are tails. What are the odds and what is an appropriate bet? Well, there are two ways that the coins can come up heads and tails: the first coin is heads and the second coin is tails, or the first coin is tails and the second coin is heads. There is one way that they can both come up tails. And there is one way that both can come up heads. This means that he has 3 ways to win and you have 1. This is odds of 3:1 against you winning. In order for the bet to be fair, for every $1 you must put up, he should pay $3.
How does this apply to poker? When you call a bet, you are paying the amount of the bet in order to win the whole pot. So if someone bets $5 and there is now $25 in the pot, then you are paying $5 to win $25. The pot is laying you $25 to $5 which is odds of 25:5 or 5:1. This means that as long as the odds against you winning are 5:1 or better (lower), this is a fair bet, and you should call the bet.
Of course, most of the time you will lose, but it doesn't matter in the long run. Suppose you take the above bet 6 times. Odds are that you will pay $5 and lose 5 out of 6 times. One time you will win $25. So you lose a total of $25 (5*$5) the five times that you lose and win $25 one time - you have broken even.
Now that you know how to calculate the odds that the pot is laying, you still need to know the odds of making your hand to determine if it's a fair bet. The general assumption here is that you don't think you have the best hand and are drawing to the best hand, such as when you have a flush draw or a straight draw, or just overcards. When you think you already have the best hand, such as top pair, you should bet or raise in order to prevent your opponents from having the proper odds to chase their draws. So how do you calculate the odds against making your hand? It's simple - it's the number of cards that don't help you vs. the number of cards that help you. It's easiest when there isn't another potential draw. For example, you have Ts9d and the flop comes Jc8d2h. You have an open-ended straight draw. How many cards will help you? The four 7s and the four Qs will make you a nut straight. A T or 9 will give you a pair, but it will also put a possible straight on the board and both are underpairs, so I wouldn't count those as outs (cards that will help you). Therefore, with the 7s and Qs, you have 8 outs. How many cards don't help you then? Well, we've seen 5 (2 in your hand and 3 on the flop), so there are 47 left in the deck. OK, technically, they are not all in the deck, some are in other players' hands, burned cards, etc., but if you can't see a card, then it doesn't really exist. Look up Schrodinger's Cat if you don't believe me. Anyway, there are 47 cards left and 8 help you, which means that 39 don't help you. Thus the odds against you making your hand are 39:8 which is very close to 5:1 (it's actuall;y 4.875:1). Approximations are close enough for these decisions unless you suck as approximations. Since you are 5:1 against making your hand, then you are getting the correct price from the pot as long as it's paying you 5:1 or more on your bet. If there's $30 in the pot and the bet is $5, then you can call because the pot is paying you 6:1 to hit your 5:1 shot. If you miss on the turn, then you MUST recalculate because in limit poker, the turn bet is bigger, and you might no longer have the correct odds for your draw.
Is this hard to do? It takes some learning but becomes automatic after awhile. And you can't call yourself a decent poker player unless you can calculate odds. This is one reason why online poker is easier, because the pot always has the $ amount right next to it. It's harder to determine how much money is in the pot in a live game when there's three different colors of chips in the pot. But you eventually get good at doing that too.
Outs are cards that will improve your hand. You really want these outs to improve your hand to the best hand. Here's an example in hold'em: you have JTo (this means jack and ten "offsuit". JTs is jack-ten suited). You are heads-up and the flop comes Ah8c9d. Your opponent bets and you feel confident that he has an ace. This means that catching a J or T won't help you. But you have a nice straight draw. Any 7 or Q will give you the nut straight. There is no flush draw (right now) because the board has 3 different suits. There are four 7s and four Qs left, so you have 8 "outs". This means that 8 cards will help you and all remaining cards will hurt you. How many remaining cards are there? You subtract from 52 all the cards that are known. There are 3 on the flop and 2 in your hand, and if you are confident enough, you can count the ace in your opponent's hand. That means 6 cards are known, leaving 52-6 = 46 cards unknown. Of the 46, 8 will help which means 38 will hurt. The odds against making your hand on the next card are 38:8 = 4.75:1 (estimating is ok, and by the way, this is always the odds of making an open-ended straight draw in hold'em). So if your opponent bets $3 and the pot is now $10, the pot is laying you 10:3 = 3.33:1 to make your hand. That's not enough and you should fold. You need to get 4.75:1 or better from the pot.
Suppose we are playing the above hand but the flop is Ah8c9h, and there are four players in the pot. Now there is a flush draw, and someone might have it since there are a lot of players. That means some of your outs won't help you. You can't count all the 7s and Qs because the 7h and the Qh will make someone a flush. Now you have 6 "clean" outs = 40:6 = 6.66:1.
No, I didn't get into implied odds, reverse implied odds, or even implied tilt odds yet. More on those later.
You can also apply odds to calling bets on the river. Suppose it's heads-up and there is $90 in the pot. Your opponent bets $10. You can only beat a bluff - maybe you have a pair of 3s or maybe even just Ace high. But the pot is offering you 9:1. This means that if you just catch your opponent bluffing in this same situation 1 time for every 9 times that you are wrong, you will break even. Basically it means that if there is a 10% chance that your opponent is bluffing, you should call. And there is almost always at least a 10% chance that your opponent is bluffing. You need to call in these situations, especially in limit poker, unless you know the opponent is very tight and therefore has you beat, or doesn't bluff.
In big bet poker, you can sometimes bluff out an expert opponent on the river with a small bet rather than a big bet. Suppose that on the river, there is a possible flush, and you make a pot-sized bluff. That actually looks like a bluff. If you really had a flush, most players would bet the amount that you think your opponent would call, since you expect to win, and that would not be a pot-sized bet, but more like 1/4 or 1/3 of the pot. The a bluff of 1/3 or 1/4 of the pot can be more scary to your opponent IF he is an expert and IF he thinks you are a good player too.
Conversely, if you are playing against morons and are holding the nuts, you might want to bet hugely because they are stupid enough to call.
- schneid
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