The Odds

Article has been taken from PokeriInfo website with their permission.

1. The Odds
2. Pot Odds
3. Implied Pot Odds
4. Winning Odds
5. Probabilities and Winning Odds
6. Overcards

1. The Odds

The winning strategy in loose low-limit games is to play aggressive and tight mathematical poker. Therefore, you have to know the probabilities, the winning odds, and the pot odds.

The probability is the likelihood of something happening, expressed as a percentage. For example, when counting the probability of a flush on the river, there are 46 cards in the deck and 9 of them will make the flush. Accordingly the probability is 9/46 = .196 or 20%.

The probability is expressed better as a ratio, making it easier to relate it to the pot size. This value is called the winning odds.

Winning odds are the ratio between the positive and the negative outcome. If the winning odds are 2:1 you are the favorite to win twice for every time you lose. If the odds are 1:2 you are the underdog, winning one out of three times or winning once and losing twice. The winning odds for a flush draw on the river are 9/(46-9) = 9/37 = 1:4.

2. Pot Odds

Pot odds show the ratio between the bet and the size of the pot. For example, if the bet is $2 and there is $10 in the pot, the pot odds are 2:10 or 1:5. You can play your hand profitably if the pot odds are higher than the winning odds. In the example above, the winning odds for the flush draw were 1:4. If the pot odds are 1:5, you can play your draw and make a profit in the long run. You'll lose one unit four times, but win five units the fifth time, making an average profit of 20¢ per game in the long run. This is mathematical poker, and in loose low-limit games it is the winning strategy.

The pot odds must be higher than the winning odds. But how much higher? It depends on the strength of the hand and on the threat cards on the board. For example, if the flush draw above is A-high and there is no pair on the board, the draw is to the nuts, the pot odds 1:5 are high enough and you'll make a nice profit in the long run. If the flush is something like J-high, there is a risk of losing to a higher flush. The pot odds must be somewhat higher, depending on the opponents. If there is only one opponent who has bet all the way, he is not on a draw. The more passive calling opponents there are, the higher the risk that one of them is on a flush draw, too.

If the board is threatening, the pot odds must be higher accordingly. If you are on a flush draw and the board pairs up, someone can have made a full house. The probability depends on the texture of the board. For example, if the paired cards are aces in a multiway pot, there is a great risk someone having a full house, because an ace can make a playable starting hand with any other card suited and with the big cards unsuited, too. On the other hand, if the paired card is e.g. a 7, the risk is much lower, because a 7 needs an A, K, Q, 8 or 6 suited or another 7 to be playable as a starting hand. Especially if none of these supporting cards occurs on the board, the risk of a full house is minimal and 1:5 are acceptable pot odds.

3. Implied Pot Odds

The pot odds in the examples above are current pot odds, expressing the ratio between the bet and the size of the pot for the time being. In fact, you have to estimate the size of the pot in the showdown and calculate the implied pot odds. For example, if you have on the flop an inside straight draw to the nuts, the winning odds are 1:11, the bet is $1 and there is $6 in the pot with four opponents when the first player bet, the current pot odds are 1:6. Seemingly a very poor play. But if you can count on the other opponents to call also on the flop and one of them to call all the way, there will be $13 (6+3+2+2) in the pot, excluding your own bets. The implied pot odds are 1:13 and you can play your draw profitably in the long run.

Suppose now, that the next card doesn't hit your draw. There is $12 in the pot now when the first opponent has bet, the bet is $2, and you estimate that the other opponents will fold and the first one will call on the river as well even if you make your straight. The final pot will then be $14, excluding your own bets. The implied pot odds are 2:14 or 1:7, and you have to give it up.

Estimating the final size of the pot is very difficult but crucial, particularly in no-limit games, because the pot can grow substantially during the coming betting rounds and the implied pot odds can therefore be significantly higher than the current odds. In loose games, the pot can also grow fast if many players stay on until the showdown and the implied pot odds can often justify a seemingly unfavorable play.

One of the most common cases where you are essentially better off playing according to the implied pot odds is when you have a small or medium pair in the pocket. Suppose you have 3-3 in the pocket in late position, three players have limped in, the bet is $1 and there is $4.50 in the pot. The current pot odds are 1:4.5. The winning odds for making at least a set on the flop are 1:7.5. Since a set is usually quite vulnerable, the pot odds have to be significantly higher, perhaps up to 1:10. Can you even think about playing this hand?

A set is always well concealed and usually gets a lot of action. If you can assume that the small blind will call as well, four of the opponents will call on the flop, two on the turn, one on the river, there will be finally $15 in the pot in the showdown, excluding your own bets. The implied pot odds are 1:15 and you have an edge.

On the other hand, raising has always a devastating effect on the implied pot odds. If the pot is raised before the flop, you have to pay $2. Although paying more, there are fewer participants and the pot may not include more than the same $15 in showdown. The implied pot odds go down straight away to 2:15 or 1:7.5 and you have to throw away your pocket pair.

In tournaments, you sometimes face an opponent who goes all-in or almost all-in. In this case the current pot odds are the same as the implied pot odds, since the player can't put more money into the pot later on. As a result, you may have to fold some generally playable hands and play some hands that would have been unprofitable under normal circumstances. For example, on the turn in a no-limit game you are on a nut flush draw against one player. Your opponent has gone all-in with 400 and there is 1200 in the pot. The current and the implied pot odds are 1:3. The winning odds are 1:4. If you don't have anything at all, such as a bottom pair or something, you may have to give it up. But if you are on the flop with the same draw against one opponent who has gone all-in with 400 and there is 1200 in the pot, you can take the challenge. The current and the implied pot odds are again 1:3, but in this case you'll get two cards to complete your flush and the winning odds are 1:2. You have the edge.

4. Winning Odds

You don't need to be able to calculate the winning odds yourself. They can be found in every poker book as well as on this site. Nevertheless, it may be useful to understand the principle beyond them.

We have used rounded values below, because there are so many uncertainties and assumptions to be made in poker, so there is no reason whatsoever to show unnecessary decimals. Furthermore, in some cases we have used a simplified method, not quite exact, but exact enough in practice.

The draws are common hands, and playing them correctly is crucial for success. For example, an open-end straight draw has 8 outs. The odds are 8/(47-8) = 1:5 on the flop and 8/(46-8) = 1:5 on the turn as well. A flush draw has 9 outs. The odds are 9/(47-9) = 1:4 on the flop. Completing the flush draw until the river there are 2x9 = 18 outs and the odds are 18/(47-18) = 1:2.

With a small pocket pair you'll need a set. There are two outs and three cards dealt on the flop. Consequently, you have 2x3 = 6 possibilities to get one of these two cards. The odds are 6/(50-6) = 1:7. On the flop, the odds are 2/(47-2) = 1:23. If you understand these odds, you'll also understand to give up if the flop doesn't hit.

5. Probabilities and Winning Odds

In the table below, there are the probabilities and the winning odds for the most common hands. The number of different outs is in brackets.

In the table below, you can find the probability of an overcard flopping when you have a pocket pair and it doesn't make a set.