Poker Hand Odds
Poker Hand Probabilities
ITs been said before that the higher mathematics of poker hand odds are not very important. It doesn't help a player much to know the chances of being dealt a straight flush or a full house or even a pair. Yet most of the published tables of poker probabilities are confined to that kind of information.
It does help to know the odds against improving any particular hand. Memorize those odds, (See Bottom of page 2 Other Poker Hand Odds). At the very least they will tell you when the pot is offering you good odds on a speculative play.
The following are some special phases of poker mathematics.
Possible Poker Hands in a 52-Card Deck
Straight Flush ........................................................... 40
Four of a Kind.......................................................... 624
Full House................................................................ 3,744
Flush ....... _....................................................................... 5,108
Straight............................................................................ 10,200
Three of a Kind........................................................ 54,912
Two Pairs....................................................................... 123,552
One Pair....................................................................... 1,098,240
No Pair, less than above................................................ 1,302,540
Total ............................................................. 2,598,960
Possible Poker Hand Odds of Less Value Than One Pair
IF ACE COUNTS HIGH IF ACE CO UNTS LOW
Ace High.................. King High........................... 502,860
King High................. Queen High ................. 335,580
Queen High............... Jack High .................... 213,180
Jack High.................. Ten High .................. 127,500
Ten High................... Nine High ........................ 70,380
Nine High................. Eight High .................... 34,680
Eight High................. Seven High .................. 14,280
Seven High............... Six High ............................... 4,080
Total.............................................................. 1,302,540
Chances of Being Dealt Poker Combinations in the Original Five Cards
Royal Flush...................................................... 1 in 649,740
Straight Flush .................................................. 1 in 64,974
Four of a Kind................................................. 1 in 4,165
Full House ..................................................... 1 in 694
Flush ............................................................ 1 in 509
Straight............................................................ 1 in 255
Three of a Kind............................................... 1 in 47
Two Pairs ....................................................... 1 in 21
One Pair ....................................................... 1 in
No Pair ............................................ _............. 1 in 2
Blind-Opening Draw Poker
Chance of beating one opponent who has not bet voluntarily (that is, chance of beating the blind raiser when you are the blind opener:)
If you draw 5 cards................................... 9 to 1 against you
If you draw 4 cards to an ace.................... to 1 against you
If you draw 3 cards to an A-K.................... Z to 1 against you
If you draw 2 cards to a flush..................... 8 to 1 against you
If you draw 2 cards to a straight................. 8 to 1 against you
If you draw 2 cards to a straight flush......... 6 to 1 against you
If you draw 3 cards to a low pair (4, 3, 2).... Even
If you draw 3 cards to a medium pair
(5 to 9)........................................ 11/2 to 1 for you, On any better hand than a medium pair you should raise.
Comment: The pot usually offers 4 to 1. It will be seen that the usual plays stand to lose. However, the figures are complicated by the high cards in the hand that may pair.
The same principles and poker hands odds apply to straight draw poker, when you are next-to-last man and everyone but the dealer is out.
Every additional opponent reduces the odds in your favor on a particular hand. But every additional opponent has to put his money into the pot, thus increasing the odds you are getting for your own money.
All poker calculations come to the same thing, though in varying degree: If you had the high hand to begin with, you figure to win. The more players there are against you, the fewer pots you will win but the more you will win each time you win the pot, and in the long run you still show a profit.
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