Poker Odds Probabilities
Some people may argue that poker is a game of chance, instead of a skills game. And you know what? These people are actually right, since most of the time you will not be able to predict the outcome of the next card which will determine if you’ll win – or lose a hand.
But knowing how to calculate odds and probabilities in poker will help you ‘guessing’ the next card based on a few simple formulas which are described below. If you play more than just a few hands of poker you will learn to understand that skill is actually a huge part of the game, and luck becomes a lot less significant.
Knowing this, poker indeed is a game of skill. If poker is played seriously, skill simply dominates luck.
Here are some related pages and posts:
Probabilities
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The following calculates the frequency of each poker hand for all combinations that can be made out of 5 cards drawn at random from a full deck of 52 playing cards, without the use of wild cards.
The probability in poker is determined based on the number 2,598,960, which represents the total number of five card combinations that can be created. In this case, the probability is the frequency of a hand divided by the total number of five card hands, and the odds are defined by the formula ((1 / p) – 1 : 1), where p corresponds to the probability.
Frequency of Five Card Poker hands
In the following table, the frequencies are precise, while the probabilities and the odds given are approximate.
Also, the royal flush is included in the table as a straight flush, since the royal flush can be made in four different ways (hearts, spades, clubs and diamonds). This calculates a probability of 0.000001539077169 and odds of 649,739 : 1.
| Hand | Frequency | Probability | Odds against |
|---|---|---|---|
| Straight flush | 40 | 0.00154 % | 64,973 : 1 |
| Four of a kind | 624 | 0.0240 % | 4,164 : 1 |
| Full house | 3,744 | 0.144 % | 693 : 1 |
| Flush | 5,108 | 0.197 % | 508 : 1 |
| Straight | 10,200 | 0.392 % | 254 : 1 |
| Three of a kind | 54,912 | 2.11 % | 46.3 : 1 |
| Two pair | 123,552 | 4.75 % | 20.0 : 1 |
| One pair | 1,098,240 | 42.3 % | 1.37 : 1 |
| No pair | 1,302,540 | 50.1 % | 0.995 : 1 |
| Total | 2,598,960 | 100 % | 0 : 1 |
The probability of a straight flush or an ace low straight will be reduced in case they won’t be counted. They will become 9/10 as common as they usually would be.
This pages will tell you more about card outs:
Pot odds
In poker, pot odds are used to determine the expected value of a play. Poker players use pot odds to calculate the profitability over the long term. Generally, odds are expressed as a win:loss ratio. The following formula can be used to calculate the percentage probability:
win:loss odds = win / (win + loss) % probability
For instance, this means that 1:4 odds equals 1 / (1 + 4) = 20% probability.
Instead, odds are also expressed as a loss:win ratio, or also known as odds against (see table above). To make it totally clear, we have used win:loss odds in remainder of this explanation.
The correct poker playing strategy is influenced by pot odds for every possible table action (check, fold, call or raise) at every single moment during a poker game.
Most likely, calling is the correct play when facing a call with higher pot odds, just like folding is the correct play when facing a call with lower pot odds.
For instance, if you can win a $1000 pot by making a call for just $1, essentially no hand should be folded, since you only have to win this call one time every thousand hands for it to be profitable.
The probability of winning is equal to the chance that a player will win with either the best hand at showdown or simply because the opponents will fold out of the hand before opening up.
Be sure to also read:
Pot odds in Texas Hold’em Poker
The approximate percentage probability that a player hits one of his outs on the first coming card in Texas Hold’em is calculated as follows:
Poker And Probability
(number of outs) x 2 + 1
In case you have the outs for a potential flush, i.e. 9 cards could improve your hand, then you’ll have about 19% chance to complete your flush with the next card (9 x 2 + 1 = 19).
With two more cards to come (the turn and the river), the approximate percentage probability is calculated as follows:
(number of outs) x 4 – 1
Poker Odds
This means that you’ll have 35% roughly to hit a flush with two more cards to come (9 x 4 – 1 = 35).
Poker Odds And Probabilities
For a correctly classified table action, the odds for winning a hand should never be lower than the applicable pot odds.