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Poker Hand Odds
Chances of Improving in the Draw (Draw Poker)
Draws to One Pair
Drawing three cards to one pair—odds against making:
Two pair or better................................... to 1 against
Aces up or better..................................... 6 to 1 against
Three of a kind........................................ 8 to 1 against
Full house............................................... 97 to 1 against
Four of a kind.......................................... 359 to 1 against
Drawing two cards to one pair and an ace kicker-odds against making:
Two pair or better................................... 3 to 1 against
Aces up or better..................................... 4 to 1 against
Three of a kind........................................ 12 to 1 against
Full house................................................ 119 to 1 against
Four of a kind.......................................... 1,080 to 1 against
Comment: It will be seen that if the player is sure he must have aces up or better to win, his chance is slightly better by holding the Ace kicker.
Poker Hands Odds Draws to Three of a Kind
Drawing two cards to three of a kind—odds against making:
Full house or better................................. 82/3 to 1 against
Full house ............................................ 151/2to 1 against
Four of a kind......................................... to 1 against
Drawing one card to three of a kind and any kicker—
odds against making:
Full house or better................................. 103/4to 1 against
Full house .......................................... to 1 against
Four of a kind......................................... 46 to 1 against
Comment: Holding a kicker to three of a kind decreases the
chance of improvement and obviously can be advisable only for
deceptive or tactical purposes.
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Lowball
The following odds apply to lowball played with the bug. In each case it is assumed that the bug is not in the hand.
One card to 7-high......................................... 31/2 to 1 against
One card to 6-high......................................... .51/2 to 1 against
One card to 5-high......................................... …..9 to 1 against
Two cards to any three cards under 7,
to make 7-high or better................... 271/2 to 1 against
One card to 8-high......................................... …..2 to 1 against
One card to 9-high......................................... Even
Comment:. The more players there are in the pot, the more low cards can be assumed to have been dealt originally and the worse the chances are for improvement. The same fact decreases the danger of pairing, but this does not alter the fact that the chances of improvement are lessened.
Other Poker Hands Odds and Chances of Winning Poker Hands
The odds are 38 to 9 or to 1 against filling a fourflush;
39 to 8 or almost 5 to 1 against filling a double-ended straight;
43 to 4 or to 1 against filling an inside or one-ended straight;
43 to 4 or to 1 against filling a full house when drawing to two pair.
With a double-ended straight-flush draw (such as 8, 7, 6, 5, hearts) the odds are 2 to 1 against making a straight or better, to 1 against making a straight flush, 5 to 1 against making a flush, to 1 against making a straight.
With a one-ended straight-flush draw (such as hearts Ace, King, Queen, Jack or hearts 8-7-5-4), the odds are 3 to 1 against making a straight or better, 46 to 1 against making a straight flush, 5 to 1 against making a flush, 14 to 1 against making a straight.
Drawing four cards to an ace, the odds are 21/2 to 1 against making a pair of aces or better. (In stud poker the odds are 31/2 to 1 against pairing an ace if no other ace shows.) Drawing two cards to A-K, the odds are 21/2 to 1 against making aces or kings, or better.
It is 23 to 1 against making a flush on a two-card draw and 22 to 1 against making a straight on a two-card draw (both ends open twice, as 10-9-8). It is 11 to 1 against making a straight or better on a two-card straight-flush draw such as hearts 10-9-8.
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