A Good Hand in Poker
The probability for a five card poker hand begins with the proposition... 52 cards taken 5 at a time. Expressed mathematically that is (5215)! The math looks like this;
52*51*50*49*48
------------------------------ =2,598,960
5*4*3*2*1
There are 2,598,960 possible five card hands that can be dealt in a five card game. This means that the odds of being dealt a Royal Flush in Spades, (10, 1, Q, K, A) is I in 2,598,960. Understand that this also means the odds of being dealt “Any” called for five card hand is the same I in 2,598,960. Being dealt the 5d, 6c, As, I Oh, 9h in the first five cards is the same as the Royal Flush in Spades. Given that there are four (4) different suits that the Royal Flush could be made in, the correct odds for any Royal Flush in the first five cards is;
2,598,960 ./. 4 — 649,740 to 1
Similar calculations can be made for each of the other hand types. Take for instance the odds of being dealt a flush (five cards of the same suit...not in order). There are 13 cards in each suit. You need five of the thirteen cards In the first five dealt, to make a flush. The math looks like this;
13*12*11*10*9
--------------------- ‘= 1287 x 4 suits = 5148
5 * 4 * 3 * 2 * 1
The number above, however includes all Flushes.. .Royal Flushes and Straight Flushes as well.
You must now subtract the number of Royal and Straight Flushes to determine the accurate count for a standard flush.
5148
- 4...Royal Flushes
- 36. .Straight Flushes
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5108...... ..,......., . F1ushs |
