Probability and Poker

In the standard game of poker, each player gets 5 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: ♥ 2 3 4 5 6 7 8 9 10 J Q K A
13 diamonds: ♦ 2 3 4 5 6 7 8 9 10 J Q K A
13 clubs: ♣ 2 3 4 5 6 7 8 9 10 J Q K A
13 spades: ♠ 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 Cnr .
Number of possible poker hands = C525 = 52!/(5!×47!) = 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, or 0.000002.
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.
For each suit there are 10 such straights (the ones starting with Ace, 1, 2, ... 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, or 0.000015.
The table below lists the number of possible ways that different types of hands can arise and their probability of occurrence.
Ranking, Frequency and Probability of Poker Hands
| Hand | No. of Ways | Probability | Description |
| Royal Flush | 4 |
0.000002 |
Ten, J, Q, K, A of one suit. |
| Straight Flush | 40 |
0.000015 |
A straight is 5 cards in order. An example of a straight flush is: 5, 6, 7, 8, 9, all spades. |
| Four of a Kind | 624 |
0.000240 |
Example: 4 kings and any other card. |
| Full House | 3,744 |
0.001441 |
3 cards of one denominator and 2 cards of another. For example, 3 aces and 2 kings is a full house. |
| Flush | 5,108 |
0.001965 |
All 5 cards are from the same suit.
For example, 2, 4, 5, 9, J (all hearts) is a flush. |
| Straight | 10,200 |
0.003925 |
The 5 cards are in order. For example, 3, 4, 5, 6, 7 (any suit) is a straight. |
| Three of a Kind | 54,912 |
0.021129 |
Example: A hand with 3 aces, one J and one Q. |
| Two Pairs | 123,552 |
0.047539 |
Example: 3, 3, Q, Q, 5 |
| One Pair | 1,098,240 |
0.422569 |
Example: 10, 10, 4, 6, K |
| Nothing | 1,302,540 |
0.501177 |
Example: 3, 6, 8, 9, K (at least two different suits) |
Question
The probability for a full house is given above as 0.001441. Where does this come from?
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