• Poker Hands Probability Chart
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Poker Math & Probability Chart. This chart includes various probabilities and odds for many of the common events in Texas hold 'em. Committing these probabilities to memory can only be beneficial. Poker Drawing Odds Chart. Probability of making a specific hand (7 out of 52) The following chart shows the probability of getting a certain hand. Whereas a pair floats by often enough, getting a straight or royal flush is less likely. 7 out of 52 means, that although you build your hand using 5 cards, you still have 7. 1 The Ultimate Texas Hold’em Odds Calculator. 1.1 How is a Texas Hold’em poker odds calculator useful? 1.1.1 Simulate an instant example hand; 1.2 Why do you need to know poker odds?; 1.3 Poker Odds You Should Memorize; 1.4 How do you figure out pot odds in poker?; 1.5 What are poker outs?; 1.6 Poker odds chart. 1.6.1 Use the 2 and 4 “Hack” when you forget the odds.

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A list of the standard poker hand rankings, from best to worst. It can be printed off and used as a handy reference for beginners who are just starting out.

This chart includes various probabilities and odds for many of the common events in Texas hold 'em. Committing these probabilities to memory can only be beneficial.

This chart lists the mathematical odds of hitting your outs from the flop to turn / turn to river / flop to river and can be used as a handy reference when calculating pot odds.

A starting hand chart for standard full ring no-limit hold'em games with 9 or 10 players. To be used as a general guide. Game conditions must always be taken into account.

A beginners guide to starting hand selection in limit hold'em full ring games with 9 or 10 players. Game conditions must always be taken into account.

In the standard game of poker, each player gets5 cards and places a bet, hoping his cards are 'better'than the other players' hands.

The game is played with a pack containing 52 cards in 4 suits, consisting of:

13 hearts:
13 diamonds
13 clubs:
13 spades:

♥ 2 3 4 5 6 7 8 9 10 J Q K A
♦ 2 3 4 5 6 7 8 9 10 J Q K A
♣ 2 3 4 5 6 7 8 9 10 J Q K A
♠ 2 3 4 5 6 7 8 9 10 J Q K A

The number of different possible poker hands is found by counting the number of ways that 5 cards can be selected from 52 cards, where the order is not important. It is a combination, so we use `C_r^n`.

The number of possible poker hands

`=C_5^52=(52!)/(5!xx47!)=2,598,960`.

Royal Flush

The best hand (because of the low probability that it will occur) is the royal flush, which consists of 10, J, Q, K, A of the same suit. There are only 4 ways of getting such a hand (because there are 4 suits), so the probability of being dealt a royal flush is

`4/(2,598,960)=0.000 001 539`

Straight Flush

The next most valuable type of hand is a straight flush, which is 5 cards in order, all of the same suit.

For example, 2♣, 3♣, 4♣, 5♣, 6♣ is a straight flush.

Poker Hands Probability Chart

For each suit there are 10 such straights (the one starting with Ace, the one starting with 2, the one starting with 3, ... through to the one starting at 10) and there are 4 suits, so there are 40 possible straight flushes.

The probability of being dealt a straight flush is

`40/(2,598,960)=0.000 015 39`

[Note: There is some overlap here since the straight flush starting at 10 is the same as the royal flush. So strictly there are 36 straight flushes (4 × 9) if we don't count the royal flush. The probability of getting a straight flush then is 36/2,598,960 = 0.00001385.]

The table below lists the number ofpossible ways that different types of hands can arise and theirprobability of occurrence.

Ranking, Frequency and Probability of Poker Hands

Question

The probability for a full house is given above as 0.001441. Where does this come from?

Answer

Explanation 1:

Probability of 3 cards having the same denomination: `4/52 xx 3/51 xx 2/50 xx 13 = 1/425`.

(There are 13 ways we can get 3 of a kind).

The probability that the next 2 cards are a pair: `4/49 xx 3/48 xx 12 = 3/49`

(There are 12 ways we can get a pair, once we have already got our 3 of a kind).

The number of ways of getting a particular sequence of 5 cards where there are 3 of one kind and 2 of another kind is:

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`(5!)/(3!xx2!)=10`

So the probability of a full house is

`1/425 xx 3/49 xx 10 ` `= 6/(4,165)` `=0.001 440 6`

Explanation 2:

Number of ways of getting a full house:

`(C(13,1)xxC(4,3))` `xx(C(12,1)xxC(4,2))`

`=(13!)/(1!xx12!)` `xx(4!)/(3!xx1!)` `xx(12!)/(1!xx11!)` `xx(4!)/(2!xx2!)`

`=3744`

Number of possible poker hands

`=C(52,5)` `=(52!)/(47!xx5!)` `=2,598,960`

So the probability of a full house is given by:

`P('full house')`

`='ways of getting full house'/'possible poker hands'`

`= (3,744)/(2,598,960)`

`=0.001 441`