Odds & Probability | Calculate Poker Odds | Pot Odds | Implied Odds | Outs | Count Outs | Odds You’ll Make Your Drawing Hand | Probability Tables | Odds Tools
To improve your game, you need to make calculating poker odds and counting your outs a priority every time you sit down at the poker table to play poker.
All winning poker players have a solid knowledge of math, which goes far behind just playing poker. Some are able to calculate odds in their head like a computer, others use simple methods (even using their fingers), and when playing online some use high-tech poker odds calculation software.
I guess the question is, can you calculate odds and count your outs in every situation you face at the poker table? If not, take a little time and read through this section. You’ll find useful links, articles, cool tools and some pretty nifty tricks that will take your game to the next level! Even if you’re not a genius, you can still learn how to calculate odds for every situation.
To really understand how to calculate odds, you need to first understand poker odds and poker probability. There are times when it is appropriate to use “probability”, and times when it’s appropriate to use “odds”.
Odds is just an alternative way of expressing the likelihood of an event occurring. The odds of getting tails when you flip a coin are even, or 1 to 1. There is one outcome that is not tails (against) and one outcome that is tails (for). The odds of rolling a four on a six-sided die is 5 to 1. There are 5 possible outcomes that are not four, and 1 outcome that is four.
odds = # of chances against / # of chances for
Reward:Risk = Pot is $1, Bet to you is $1; Your Reward is $2:Your Risk is $1 [2 reward:1 risk] Pot Odds 2:1
Lose:Win
Round down when calculating pot so you are pessimistic towards your decision.
Probability is the ratio of the number of actual occurrences to the number of possible occurrences. The probability of getting tails when you flip a coin is 50% or 1/2. 1 is the number of actual occurrences and 2 is the number of possible occurrences. The probability of rolling a die and getting a four is 1/6, or 16.6%. 1 is the number of actual occurrences and 6 is the number of possible occurrences.
probability = # of actual occurrences / # of possible occurances
You should get comfortable with odds and probabilities as both are useful depending on the situation.
Do you know how likely you are to complete your flush if you hold 2 of a suit and the flop comes with 2 more?
What is the likelihood that another of your suit will come up on the turn or river?
Here are poker odds charts and probability tables. To learn how to calculate these answers on your own, continue reading and you will find this info will help you make the correct decision and dictate your actions at the poker table.
On most flops, you won’t make a complete hand…that is, you still need at least one more card to improve the strength of your hand and give you a made hands. In other words, you’re on a draw.
So how do you know what to do? Just wing it and throw all your chips in the middle and hope you hit? Well, you need to make a decision based on the information you have. So let’s learn how to calculate odds and give yourself one more piece of information to use to defeat your opponents.
Explanation of Pot Odds in Poker. Also, calculating pot odds.
When you hear poker players say they know how to calculate odds, what does that really mean? Well, mostly it is in reference to pot odds and out counting..
Pot odds is defined as the ratio of the money in the pot against the cost to call.
Pot Odds = current size of the pot (including the bet to you) / cost to call
If the current size of the pot is $10, and someone bets $2 to you, you would need to call the $2 to continue in the hand. So using our formula for pot odds:
pot odds = $10 + $2 / $2
pot odds = $12 / $2
pot odds = 6 to 1
In this example your pots odds are 6 to 1. Other ways to express your pot odds are:
– – you are getting 6 to 1 on your money
– – the pot is laying you 6 to 1
Now that you have calculated your pot odds, you need to determine if that is good or bad. Is it worth it to you to call the bet or not, or to continue playing in the hand by raising?
In order to answer these questions, we need to learn about implied odds, outs, how to count your outs and how to approximate the odds you’ll make your drawing hand.
Implied Odds
How To Calculate Pot Odds - Nicky Numbers
Pot Odds In Poker Explained - Goku Poker
Implied odds are similar to pot odds except they require speculation on your part as to how much money is going to be put into the pot when everything is said and done. You cannot exactly calculate implied odds, because they are dependent on your opponents calling bets.
How much money is the total pot going to be worth if you showdown the winner on the river?
If you are playing at a very loose passive game, it is ok to call a bet without proper pot odds if the implied odds are still in your favor. Suppose that the pot is laying you 3:1 odds right now, but your flush draw is a 4:1 dog… If you are confident that your opponents behind you will also call the bet then for every opponent that calls the implied odds are in your favor.
Counting your Outs is another step in calculating pot odds
Outs are ‘technically’ defined as the number of cards left in the deck that gives you the winning hand.
When you are sitting at the poker table though, an out, is any card left in the deck that gives you a made hand. A made hand means ‘you made the hand you were drawing to’. It doesn’t mean it’s the winning hand, it just means you made the hand that ‘you feel’ is the winning hand.
The difference here is when you’re sitting at the poker table, you don’t know if your made hand is the winning hand or not, so the outs that you have determined may be totally wrong. You may count 7 outs (for your drawing hand), but in all reality you could be drawing dead.
Counting outs is different when you’re sitting at home watching the WSOP, because you can see each players’ hole cards and you know what cards in the deck will give a certain player the winning hand. But if you’re sitting at the poker table, you don’t know for sure. Even if you hit your drawing hand, you may not have the winning hand.
But hey, that’s poker!
With that being said, over time, as a poker player, you will be able to determine with some certainty (based on the board cards, your opponents, betting patterns, etc.) if your drawing hand will be a winner or a loser.
Count Outs Explained
Let’s look at the example from Clonie Gowen’s “Approximate the Odds You’ll Hit Your Hand” article to see how to count your outs:
Step 1: Count Your Outs
Suppose you hold A 8 and the flop comes Q 9 4.
You have a flush draw. There are 13 clubs in the deck and you are looking at 4 of them (the 2 in your hand, and the 2 on the board). That leaves 9 clubs left in the deck and thus gives you 9 outs.
So now that we know what outs are, and how to count them, what do you do with it? We’ll use the number of outs to determine the odds you will hit your drawing hand.
The Odds You’ll Make Your Drawing Hand - Evaluating Draws
Approximate The Odds You’ll Make Your Draw
A quick lesson in counting your outs and how likely you are to make the hand you’re drawing to. Start your odds education by reading this short article by Clonie Gowen. It is very difficult to calculate the exact odds of hitting a drawing hand when you’re sitting at the poker table. Unless you’re a genius with a gift for mathematics, you will not be able to do it unless you practice.
Approximate The Odds You’ll Make Your Drawing Hand
So, you have 9 outs and 2 chances (the turn and river) to hit one of your outs.
The trick to figuring out the approximate odds you’ll hit the flush is to multiply your outs (9) times the number of chances to hit it (2), or 9 *2 = 18. Then take that number, multiply times 2, and add a percentage sign (18 * 2 = 36).
The approximate percentage of the time you will make the flush is 36%. (The exact percentage is 34.97%.)
In Texas Hold ‘Em, you need to be able to calculate your outs and pot odds often. This is the starting point for those who want to learn more about poker odds. The above examples are very generic and their are many other factors that will determine whether or not you play a hand, whether you just call or you raise, etc. The next statement sums up pot odds and counting outs:
The basic idea is that when your likelihood of catching one of your outs (or making your hand) is better than the odds the pot is ‘laying’ you, you should draw to your hand. More discussion and explanation of Pot Odds with an example.
Example: If a player is facing a $5 raise by his opponent (and must therefore pay $5 to call the raise), and the total amount of money in the pot (including the uncalled raise) before his potential call is $30, then he is facing 6-to-1 pot odds for the call. If he is contemplating raising another $5 (making his potential bet $10), then he is facing 3-to-1 pot odds for the raise.
For every potential action (fold, call, raise) at every point in a game of poker, your strategy is influenced by the pot odds. For example, the lower the pot odds facing a call, the more likely it is that folding will be the correct play, and the higher the pot odds facing a call, the more likely it is that calling is the correct play. An extreme example, if you can call for $1 with a $1000 pot, there is essentially no hand that would be correct to fold, because you only have to win one time in a thousand in similar situations for the call to be profitable. Similarly, small pot odds favor bluffing, because they make it less correct for an opponent to call.
Learning to determine how likely you are to complete your draw and comparing that to the odds that the pot is offering you is vital to winning in the long run. If you have a flush draw on the flop, you are a 2:1 dog to complete your flush by the river. If there is $25 in the pot, and there is a $5 bet to you, it is correct to call this bet. The $25 dollars already in the pot, plus the $5 bet gives a total of $30 in the pot. It costs you $5 to continue in the hand. 30/5 = 6, this means that as long as your drawing hand is more likely than 6:1 you are getting proper odds to call.
As you play more poker, counting your outs and comparing them with the pot odds will become easier and easier. Make a habit the next time you sit down to play poker that you will make an effort to calculate the pot odds for every hand you are in, and if you are really focused you need to count the pot odds for the hands that you are not in. Not only will this improve your game substantially, it will also give you a feel for if your compeition is considering pot odds in their decision making process.
Example: If you flop 4 to a flush draw and there is $10 in the pot and it costs you $2 to continue should you call?
Let’s take a look. A flopped 4 flush is a 2:1 dog to complete the flush by the river. You need to call $2 dollars to continue with the hand. There is currently $10 in the pot, so your $2 dollar call is fine in this situation, as 10/2 = 5/1. The pot is laying you 5:1 odds for the call. If you had to call $6 instead of only $2, or if the pot was smaller, then it would be incorrect to call, as the pot would only be laying you 1.6/1 odds, and your flush draw remains 2:1.
You have to figure that if you don’t hit your flush on the turn you will most likely face a bet before you can see the river.
The easiest way to calculate your odds is by simple division. The numerator will be the number of outs you have. The denominator is the number of cards left that we haven’t seen. The result will be the percentage chance of making one of those outs. Therefore, the most math you’ll be doing will be dividing your outs by 50 (pre-flop), 47 (after the flop), or 46 (after the turn). Again, we refer to this great article on quickly calculating your outs easy.
Example: You hold TT but the flop misses you completely. What is the likelihood that you will catch a 3rd ten on the turn. Well there are 2 Tens left in the deck, and the deck is currently has 47 cards. 2/47 = .0426 or 4.3%. There is a 4.3% chance you will catch a 3rd jack on the turn. On the river there are now 46 unknown cards, 2/46 = .0434, or 4.3% (just slightly higher)
Poker Odds – Tools and Software
CardPlayer magazine has some great poker odds calculators that will surely help your game. Here are the highlights…
• Calculate the odds of one hand beating another.
• Calculate the odds of whether your hand becomes stronger or weaker with more players.
• Calculate the odds after the flop.
• Calculate the odds after the turn.
• Change any variable and see whether you are still the favorite.
You can also use the free tool over at twodimes.net to match up any combination of hands, pre-flop, on the flop or the turn. It is very handy.
For a list of more good reading, visit our Poker Tips section.
The probability that you’ll be dealt… Expressed as a percent is… Expressed as an odds…
pocket aces.
any pocket pair.
AK suited.
AK offsuit.
AK suited or offsuit.
any two suited cards.
suited connectors.
either pocket aces or pocket kings.
either pocket aces, pocket kings or AK. .45%
5.9%
.30%
.90%
1.2%
24%
2.1%
.90%
2.1% 220 to 1
16 to 1
331 to 1
110 to 1
82 to 1
3.3 to 1
46 to 1
110 to 1
46 to 1
The probability your pocket pair improves to… Expressed as a percent is… Expressed as an odds…
a set.
a full house.
quads. 11.8%
.74%
.25% 7.5 to 1
136 to 1
407 to 1
The probability the FLOP will contain… Expressed as a percent is… Expressed as an odds…
three of a kind.
a pair.
three suited cards.
two suited cards.
no suited cards (rainbow).
three cards in sequence.
two cards in sequence.
no cards in sequence. .24%
17%
5.2%
55%
40%
3.5%
40%
56% 424 to 1
5 to 1
18 to 1
.8 to 1
1.5 to 1
28 to 1
1.5 to 1
.8 to 1
The probability your hand improves from _ to _ from the FLOP to the RIVER… Expressed as a percent is… Expressed as an odds…
From a set to a full house or better.
From two pair to a full house or better.
From one pair to a set or better.
From a four-flush to a flush.
From a three-flush to a flush.
From an open-ended straight draw to a straight.
From a gutshot straight draw to a straight.
From two non-pair cards to a pair or better (overcards).
From the same pair as your opponent (but are outkicked) to a second pair. 33%
17%
8.4%
35%
4.2%
32%
17%
24%
13%
2 to 1
5.1 to 1
11 to 1
1.9 to 1
23 to 1
2.2 to 1
5.1 to 1
3.2 to 1
7 to 1
The probability your hand improves from _ to _ from the FLOP to the TURN… Expressed as a percent is… Expressed as an odds…
From a set to a full house.
From two pair to a full house.
From one pair to a set.
From four-flush to a flush.
From an open-ended straight draw to a straight.
From a gutshot straight draw to a straight.
From non-pair cards to a pair.
From a the same pair as your opponent (bur are outkicked), to a second pair. 15%
9%
4.3%
19%
17%
9%
13%
6% 5.7 to 1
11 to 1
23 to 1
4.2 to 1
4.9 to 1
11 to 1
6.8 to 1
15 to 1
The probability your hand improves from _ to _ from the TURN to the RIVER…
Expressed as a percent is… Expressed as an odds…
From a set to a full house. 3.6 to 1
From two pair to a full house.11 to 1
From one pair to a set. 22 to 1
From four-flush to a flush.4.1 to 1
From an open-ended straight draw to a straight. 4.8 to 1
From a gutshot straight draw to a straight. 11 to 1
From non-pair cards to a pair. 6.7 to 1
From a the same pair as your opponent
(but are outkicked), to a second pair. 22%
The probability that… Expressed as a percent is… The odds against it are…
you will hold a Pair before the Flop.
you will hold suited cards before the Flop.
you will hold 2 Kings or 2 Aces before the Flop.
you will hold Ace-King before the Flop.
you will hold at least 1 Ace before the Flop. 5.88%
23.53%
0.90%
1.21%
14.93% 16 to 1
3.25 to 1
110 to 1
81.9 to 1
5.70 to 1
if you have four parts of a Flush after the Flop, you will make it.
if you have four parts of an open-ended Str-Flush after the Flop, you will make a Straight-Flush.
If you have four parts of an open-ended Str Flush after the Flop, you will make at least a Straight.
If you have Two-Pair after the Flop, you will make a Full House or better.
If you have Three-of-a-kind after the Flop, you will make a Full House or better.
If you have a Pair after the Flop at least one more of that kind will turn up (on the last two cards).
34.97%
8.42%
54.12%
16.74%
33.40%
8.42%
1.86 to 1
10.9 to 1
0.85 to 1
4.97 to 1
1.99 to 1
10.9 to 1
If you hold a Pair, at least one more of that kind will Flop.
If you hold no Pair, you will pair at least one of your cards on the Flop.
If you hold two suited cards, two or more of that suit will Flop.
11.76%
32.43%
11.79% 7.5 to 1
2.08 to 1
7.48 to 1
If you begin suited and stay through seven cards, three more (But not four or five more!) of your suit
will turn up.
If you begin paired and stay through seven cards, at least one more of your kind will turn up.
5.77%
19.18% 16.3 to 1
4.21 to 1
Pre-Flop, Hand-To-Hand Match-Ups
Explanation of the first match-up. The player who is dealt A A will win 81.3% of the time when going against a player who is dealt K K. The player who is dealt K K will win 18.7% of the time.
Pocket Aces
A A vs. K K
81.3% 18.7%
A A vs. 6 6
79.8% 20.2%
A A vs. A K
87.9% 12.1%
A A vs. A K
92.6% 7.4%
A A vs. J T
78.3% 21.7%
A A vs. J T
82.0% 18.0%
A A vs. 6 5
76.9% 23.1%
A A vs. 6 5
80.6% 19.4%
Big Slick
A K vs. A Q
74.0% 26.0%
A K vs. A Q
69.7% 30.3%
A K vs. K Q
74.2% 25.8%
A K vs. K Q
69.9% 30.1%
A K vs. A 6
73.5% 26.5%
A K vs. A 6
69.2% 30.8%
A K vs. K 7
75.0% 25.0%
A K vs. K 7
70.7% 29.3%
Pocket Kings
K K vs. A K
65.9% 34.1%
K K vs. A K
70.0% 30.0%
K K vs. A Q
67.9% 32.1%
K K vs. A Q
71.6% 28.4%
Pocket Tens
T T vs. A K
53.9% 46.1%
T T vs. A K
57.3% 42.7%
T T vs. A 2
71.1% 28.9%
T T vs. A 2
67.4% 32.6%
Pocket Sixes
6 6 vs. A 2
69.9% 30.1%
6 6 vs. A 2
66.2% 33.8%
6 6 vs. 7 6
64.2% 35.8%
6 6 vs. 7 6
60.5% 39.5%
6 6 vs. A K
52.1% 47.9%
6 6 vs. A K
55.4% 44.6%
Jack – Ten
J T vs. 2 2
54.0% 46.0%
J T vs. 2 2
51.2% 48.8%
• If you take two suited cards, you have a 15/1 (6.4%) chance of making a flush by the river.
• With unsuited cards, you have a 53/1 (1.8%) chance of making a flush by the river.
• With 14 outs, you are about even money to improve your hand with two cards to come.