How to Calculate Poker Odds


Every winning poker player understands the odds of winning in most situations. Though it may sound difficult at first, after reading this article, you will know your odds in any given situation in no time. Remember that all poker games are games of percentages and probability. Many players play under the incorrect assumption that poker is a game of luck.

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Poker must be viewed as one long lifetime game instead of many short sessions. The reason for this is over the course of thousands of
hands, the best hand will win the correct amount of time. Poker, however, is full of short-term variance (often called luck), which can be extremely frustrating. Despite losing when the odds are overwhelmingly in your favor, the goal of winning poker is still to put yourself in this type of situation as many times as possible because when you do, you will win most of the time.

In this article you will learn the basic percentages you will use time and time again in your poker playing. We will begin in the next section with a basic discussion of pot odds and how to use them to become a winning player.

For more information on poker odds and winning at poker, try the following links:
  • To see all of our articles on poker rules and advice, go to our main article on How To Play Poker.
  • For an introduction to the game, skim over these Poker Basics.
  • So you think you've got the best hand. Maximize your winnings with these Poker Betting Tips.
  • Have you calculated that your hand is a loser, but you think you can fake out the opposition? Be sure you know How to Bluff in Poker.

Pot Odds Made Simple

Figuring pot odds (the pot is all the money that has been bet for a single game) is one of the most misunderstood and misused concepts for beginning poker players. In this section, simple and straightforward computations are used. And for all examples, unless otherwise noted, Texas Hold'em is the poker game being played. For a comprehensive look on how to play Texas Hold'em, click here.

Learning how to calculate pot odds puts the concept of risk and reward into a numerical computation. For those of you who aren't confident in your math skills, don't worry. It is not complicated, and with a little practice you will be able to figure your pot odds in no time. The following examples will illustrate pot odds. We will use a minimum bet of $1 and a maximum bet of $2 Hold'em for simplicity.

You are betting last of the six players in the pot for $1 each to see the flop. This makes the pot $6. You hold
A-Q, and the flop comes K-Q-6.

Possible ace-high flush
©2006 Publications International, Ltd.
A pair of queens with a possible ace-high flush.

The first player bets $1, two players call, and two players fold to bring the total in the pot to $9. It is now your turn to act. You must decide whether to fold, call, or raise. At this time you should assume that at least one of your opponents holds a king and that your hand must improve in order to win.

Now you must decide how many unseen cards can help you win. These cards are called your "
outs," and this terminology will be used from here on. (One question that is often asked is: "The other players have cards in their hands that cannot come to me on the turn or the river, so how can I count them in the cards that will improve my hand?" The answer is: You must count all cards that can help you because you have no way of knowing what cards are in your opponents' hands, even if it is quite likely that they hold certain cards. Therefore, all unseen cards need to be counted.)

Because you have a
pair of queens, you must assume that if either of the other two queens hit, it will improve your hand to make you the winner. There are also three remaining aces that will improve you to two pair. This makes five outs. In addition, if any club hits, it will give you an ace high flush. So you have nine other outs (the remaining clubs). This gives you 14 outs. Now you have seen five cards (your hole cards and the three on the flop) out of a 52 card deck. This leaves 47 unseen cards before the turn. This means that 14 out of 47 cards can come on the turn and improve your hand, and 33 will not help you at all. This makes the odds roughly 2.4 to 1.

The easiest way to figure this is to see how many times your 14 outs will divide into the 33 cards that will not help you. You don't have to figure this out exactly to know if it is correct to call or not.

Because 2 times 14 is 28, which is a little less than 33, and 3 times 14 equals 42, you know the number is closer to two than three, or your odds of winning are closer to 2 to 1 than 3 to 1. This means that for it to be correct for you to call, there must be at least 2.4 times the amount you must call in the pot. In other words, the amount you must risk, in this case $1, must have a reward of at least $2.40 when you hit your hand. In the example above, there is $9 in the pot, and you have to call only $1 to see the turn. Since the pot is offering you 9 to 1 odds, the correct play is to call or raise, which we will discuss shortly.

Pot odds boil down to percentages. The pot must be large enough to pay enough extra on the times you do hit your hand to make up for the losses when you don't. The key is to get your money into the pot when you have the best hand. If you use pot odds correctly, you will be well on your way to becoming a lifelong winner.

Continuing the above example, you call the bet on the flop, increasing the pot to $10. The turn card is
8, which does not improve your hand. You still have the same number of outs, 14, but one less unseen card, 46. Notice that your pot odds are almost the same, roughly 2.3 to 1. The first player bets $2, making the pot $12, and the other two players fold. The bet you must now call is $2 into a $12 dollar pot. This reduces down to 6 to 1 odds (12 divided by 2 equals 6, and 2 divided by 2 equals 1). Once again the correct play is to call. Notice that at this time, if you don't improve on the river, you can fold, and if you do improve, you can bet or raise.
The above example is fairly simple, but what has been said is not everything you must consider.

Actually, after the flop you can improve on either the turn or the river cards. This means that you have 14 outs two times, which if you consider both the turn and the river, your pot odds are actually .95 to 1. Any time your pot odds are less than 1 to 1, you are a
favorite to win. In this case the correct play is often a raise instead of a call.

Some players use the combined odds for both the turn and river while others use them separately. If you use the turn odds on the turn, reevaluate the situation after the turn card is revealed, and use the pot odds on the river separately. The problem when using the combined odds is that you almost have to call on the turn to see the river even if you don't improve. This can lead to a dangerous mindset, and you can become a calling station. First, consider each situation by itself, and then, add in other factors.

In the next section we will discuss more about pot odds, including
implied odds and raising to give yourself correct pot odds.

For more information on poker odds and winning at poker, try the following links:
  • To see all of our articles on poker rules and advice, go to our main article on How To Play Poker.
  • For an introduction to the game, skim over these Poker Basics.
  • So you think you've got the best hand. Maximize your winnings with these Poker Betting Tips.
  • Have you calculated that your hand is a loser, but you think you can fake out the opposition? Be sure you know How to Bluff in Poker.

Implied Odds and Advanced Techniques

This is a good time to point out something that is often confusing to beginning players when computing pot odds. The beginning player often thinks he already has so much money in the pot and believes that this somehow goes into the computation of the pot odds. The fact of the matter is any money already in the pot is not yours. It was yours before you put it into the pot, and the only way you will get it back is to win the pot. This is the reason that money you have already placed into the pot is not used in computing pot odds.

Another factor to consider is something called "
implied odds." Implied odds take into account not only the money in the pot and the amount of the bet but also the possibility of collecting extra bets when you hit your hand. For instance, in the previous example, if all four players act before you call on the turn, more than likely one or more of them will call a bet or raise by you on the river if you hit your hand.

Their calls on the river actually improve your pot odds because you can add these bets into your calculations. In this instance, you can safely figure on adding at least one and probably two bets to the pot. Be careful with your use of implied odds in close situations. It is very important not to assume future bets of which you aren't certain. Many players misread the situation and/or their opponents and rely too heavily on implied odds resulting in poor decisions. Knowing your opponents' tendencies is a must when using implied odds.

Some advanced players raise on the
flop in order to give them correct pot odds to call on the turn if their hand does not improve. This is an advanced play and should be done only when you are a favorite to win the hand or have tremendous implied odds. If you are a novice, simply mastering your ability to understand and use pot odds should be your goal. As you grow as a player, you will start to see situations in which you can use advanced plays such as this.

Now that we have discussed pot odds, it is time to see how much you have learned. In the next section, you will be presented with three hands and asked to calculate your own pot odds.

For more information on poker odds and winning at poker, try the following links:
  • To see all of our articles on poker rules and advice, go to our main article on How To Play Poker.
  • For an introduction to the game, skim over these Poker Basics.
  • So you think you've got the best hand. Maximize your winnings with these Poker Betting Tips.
  • Have you calculated that your hand is a loser, but you think you can fake out the opposition? Be sure you know How to Bluff in Poker.

Quiz Hands

The following three quiz hands will help you get the feel of the thought process involved in using pot odds. See if you can compute the pot odds, and decide whether to call or fold. For simplicity's sake, we will not take blinds into account. (The suggested answers can be found in the next section.)
  1. In a 1/2 Hold'em game, your hole cards are J-T, and the flop is K-Q-6. There are two other players, $3 in the pot before the flop, and one player bets and the other calls. What are the odds the pot is offering you? What are the odds of improving your hand? Should you call or fold?

  2. In a 1/2 Hold'em game, your hole cards are J-T, and the flop is A-K-6. There is one other player, $2 in the pot before the flop, and your opponent bets $1. What are the odds the pot is offering you? What are the odds of improving your hand? Should you call or fold?

    how-to-calculate-poker-odds-2
    ©2006 Publications International, Ltd.

  3. In a 1/2 Hold'em game, your hole cards are Q-Q, the flop is 2-T-7, and the turn is A. You are the last to act and must call a $2 bet to see the river. There is $34 in the pot. What are the odds the pot is offering you? What are the odds of improving your hand? Should you call or fold?

    how-to-calculate-poker-odds-2
    ©2006 Publications International, Ltd.

These examples are fairly simple, and hopefully you can see how pot odds can work for you. Once you have a good understanding, use the chart on the last page and practice. Pot odds are the only difference between some winning and losing players -- they are that important. So learn to compute them or memorize the chart, but make the commitment to use pot odds when playing poker. You'll never regret it, and neither will your bankroll.

In the next section we will talk about
expected value and reveal the answers to the questions above.

For more information on poker odds and winning at poker, try the following links:
  • To see all of our articles on poker rules and advice, go to our main article on How To Play Poker.
  • For an introduction to the game, skim over these Poker Basics.
  • So you think you've got the best hand. Maximize your winnings with these Poker Betting Tips.
  • Have you calculated that your hand is a loser, but you think you can fake out the opposition? Be sure you know How to Bluff in Poker.

Expected Value and Pot Odds Answers

Many poker players talk about EV, which stands for "Expected Value." Expected value is the amount you can expect to win on average every time you are in a particular situation. It is included here because as you spend more time playing poker, you will hear EV tossed around, and you should know what it is.

Using an earlier example in this article, assume you have a
pair of aces, and you place a $100 bet and one player calls with AK. The way to determine your EV is as follows: Put yourself in this situation 100 times. (It costs you $10,000 [$100 times 100] to enter this situation 100 times.) You will win 92 times and receive your $100 in return plus your opponent's $100 for a total of $18,400. You will lose your $100 the other eight times. Therefore, your $10,000 investment nets you $8,400 in profit ($18,400 minus $10,000). Now divide the profit ($8,400) by 100 times, and this figure -- $84 -- equals your EV. What this tells you is that, on average, you will win $84 every time you are in this same situation. Good poker players maximize the times they have positive EV and minimize the times they have negative EV.

In the final section, we have provided a pot odds table for you to study. With a little memorization and a lot of practice, you can start putting pot odds to work for you!

For more information on poker odds and winning at poker, try the following links:
  • To see all of our articles on poker rules and advice, go to our main article on How To Play Poker.
  • For an introduction to the game, skim over these Poker Basics.
  • So you think you've got the best hand. Maximize your winnings with these Poker Betting Tips.
  • Have you calculated that your hand is a loser, but you think you can fake out the opposition? Be sure you know How to Bluff in Poker.

Poker Odds Answers
1. The odds the pot is offering you are 5 to 1. There is $5 in the pot, and you need to call with $1. Because any ace or nine will give you a straight, you have 8 outs of the 47 unseen cards or almost 4.9 to 1 odds to improve your hand. In a loose game where you can expect one or both of your opponents to pay you off when you hit, you should call. In a tight game with solid opponents, this is probably a fold. If you do decide to see the turn and another heart hits, your outs go from 8 to 17, and the pot odds probably improve enough to see the river.

Some may wonder why the possibility of a straight with a heart flush isn't an automatic call on the flop. While it's true that the possibility of two hearts hitting the turn and river (often called runner-runner) improve your odds slightly, the odds are knocked back down by the fact that if you hit a flush, it may not be the best flush because the A is out and may be in an opponent's hand; or if you improve to two pair, you could be beat by trips. Remember, don't ever let the possibility of runner-runner enter into your calculations until the first runner hits. When you need two cards to make a hand (often called a two-outer), you are getting terrible odds.

2. The odds the pot is offering you are 3 to 1. In all likelihood, your opponent holds an ace or a king, so making a pair will not help. Your only hope is making a straight. Therefore, you have only 4 outs (the 4 queens). This makes the odds 10.8 to 1 that you will hit your hand. This is an easy fold.

3. The odds the pot is offering you are 17 to 1. You are definitely up against at least a pair of aces and probably trips. You must have a queen on the river to win (unless your opponent has trip aces in which case you cannot win). This leaves you with 2 outs to win the hand and makes the odds 22 to 1. Though this looks like a fold, it is recommended calling in this situation despite the possibility of pocket aces because of the implied odds. Your hand is well disguised, and if a queen hits, none of your opponents will put you on trips, so you should be able to collect at least two or three more bets and possibly more since one of your opponents will almost definitely bet into you and you can raise.

Pot Odds Table

For the beginning player, calculating pot odds can be quite difficult while trying to keep track of all the other nuances in a poker game. You have to observe your other players, analyze the cards in your hand, and attempt to maintain an unreadable "poker face." The betting can come at you fairly quickly, and there is not always time to divide numbers in your head. Until figuring out the odds becomes second nature, you can refer to this chart.

Outs Turn River Turn & River Example
1 46-1
45-1
22.3-1

2
22.5-1
22-1 10.9-1

3
14.7-1
14.3-1
7-1

4
10.8-1
10.5-1
5.1-1
Gutshot straight
5 8.4-1
8.2-1
3.9-1

6
6.8-1
6.7-1
3.2-1

7
5.7-1
5.6-1
2.6-1

8
4.9-1
4.8-1
2.2-1
Open End Straight
9
4.2-1
4.1-1
1.9-1
Flush
10 3.7-1
3.6-1
1.6-1

11
3.3-1
3.2-1
1.4-1

12
2.9-1
2.8-1
1.2-1

13
2.6-1
2.5-1
1.1-1

14
2.4-1
2.3-1
.95-1

15
2.1-1
2.1-1
.85-1
Flush and Straight
16
1.9-1
1.9-1
.75-1

17
1.8-1
1.7-1
.67-1

18
1.6-1
1.6-1
.60-1

19
1.5-1
1.4-1
.54-1

20
1.3-1
1.3-1
.48-1


The skill of calculating pot odds can greatly improve your percentages as a winning player. You can never control what cards come out of the deck, and you never know when your solid hand will get beat by a miracle card. If you learn how to play the odds, however, you can be confident that your winnings will come to you eventually.

For more information on poker odds and winning at poker, try the following links:
  • To see all of our articles on poker rules and advice, go to our main article on How To Play Poker.
  • For an introduction to the game, skim over these Poker Basics.
  • So you think you've got the best hand. Maximize your winnings with these Poker Betting Tips.
  • Have you calculated that your hand is a loser, but you think you can fake out the opposition? Be sure you know How to Bluff in Poker.
©Publications International, Ltd.