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	1 1\2 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—see page 58.

The same principles apply to straight draw poker (page 54) 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.

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.

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.

Other Odds

The odds are 38 to 9 or 4 1/4to 1 against filling a four flush; 39 to 8 or almost 5 to 1 against filling a double-ended straight; 43 to 4 or 10 ¾ to 1 against filling an inside or one-ended straight; 43 to 4 or 10 ¾ 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 the odds are 2 to 1 against making a straight or better, 22½ to 1 against making a straight flush, 5 to 1 against making a flush, 6½ to 1 against making a straight.

With a one-ended straight-flush draw (such as ♥ A.K.Q.J. or ♥ 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 10-9-8.

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