Ranking Order of Hands	Number of Possible Ways Hand Can be made	Chance of Being Dealt in Original 5 cards
Royal flush	4	1 in 649,740
Straight flush	36	1 in72,193
Four of a kind	624	1 in 4,165
Full house	3,744	1 in 694
Flush	5,108	1 in 509
Straight	10,200	1 in 255
Three of a kind	54,912	1 in 47
Two pairs	1,23,552	1 in 21
One pair	1,098,240	1 in 2 2/5
No-pair hand	1,302,540	1 in 2
Total	2,598,960

In the chance column above, fractional figures have been rounded out to the nearest 2/5 or whole number. The probability of being dealt a pair or better in the first five cards dealt is almost even and the probability of being dealt a no-pair hand is practically the same. So it’s almost a three-to-one chance, when playing against two opponents, that one of them will hold a pair or better in the first five dealt cards. The probabilities vary slightly depending on what you hold.
The 1,302,540 possible five-card no-pair hands are divided as follows:

POSSIBILE POKER HANDs oF LESS VALUE THAN ONE PAIR
IN A 52-CARDS DECK

Ace Counting High	King Counting High, ace Low	Number of Possible No-Pair hands
Ace high	King high	502,860
King high	Queen high	335,580
Queen high	Jack high	213,500
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
		1,302,540

CHANCES OF HOLDING ANY PARTICULAR HAND OR BETTER
IN FIRST FIVE CARDS DEALT

	Approximately Once in
Any pair or better	2 deals
Pair of jacks or better	5 deals
Pair of queens or better	6 deals
Pair of kings or better	7 deals
Pair of aces or better	9 deals
Two pairs or better	13 deals
Three of a kind or better	35 deals
Straight or better	132 deals
Flush or better	273 deals
Full house or better	590 deals
Four of a kind or better	3,914 deals
Straight flush or better	64 ,9deals
Royal flush	649,740 deals

CHANCE OF BENING WITH THE FIRST FIVE CARDS DEALT, PERCENT

	Number of Opponents
Players hand	1	2	3	4	5	6	7	8
Three of a kind	98	94	92	89	87	84	82	80
Two pair	93	86	80	74	68	63	59	53
Pairs
Aces	89	79	70	62	55	49	43	39
Kings	88	78	69	61	54	48	42	36
Queens	83	68	56	46	38	32	26	20
Jacks	79	63	55	40	32	25	20	15
Tens	76	58	44
Nine	73	53	38
Eights	70	49
Sevens	66	43
Sixes	63	40
Fives	60	36
Fours	57	32
Threes	53	28
twos	51	25

The above table presents the chance of a specific hand being high at Five-Card Draw Poker against one to eight opponents. This is expressed in percent thus 98 means 98 percent, or this will happen 98 times out of 100.
The lowest - ranking regular five-card Poker hand when an ace is both high and low is comprised of six, four, three, two, ace in mixed suits. The above table is particularly helpful to players who play high-low-poker variants of Poker. In the short run each additional active player in the game increase the odds against you on any particular hand. But in the long run, since all players have to put an equal sum into the pot, thus increasing the size of the pot in direct ratio to the increased odds, it doesn’t make much difference, as far as odds are concerned, if you are bucking one or seven players. To simplify matters, the figures in the following tables have been rounded out when necessary to the nearest 1/10 or whole number.

ODDS AGAINST IMPROVING THE HAND IN DRAW POKER
WHEN DRAWING THREE CARDS TO ONE PAIR

Odds against any improvement	2 ½ to 1
Odds against making two pairs	5 to 1
Odds against making three of a kind	8 to 1
Odds against making a full house	97 to 1
Odds against making four of a kind	359 to 1

ODDS AGAINST IMPROVING THE HAND IN DRAW POKER
WHEN DRAWING TWO CARDS TO A PAIR AND A KICKER

Odds against any improvement	8 ½ to 1
Odds against making a full house	15 ½ to
Odds against making four of a kind	22 ½ to 1

CHANCES OF IMPROVING THE HAND IN DRAW POKER
WHEN DRAWING ONE CARD TO THREE OF A KIND PLUS A KICKER

Odds against any improvement	11 to 1
Odds against making a full house	15 to 1
Odds against making four of a kind	46 to 1

The two tables above show that the best chance for improvement with three of a kind is to draw two cards and not hold a kicker. Holding a kicker increases the odds against the player for any improvement.

ODDS AGAINST FILLING IN A FOUR-CARD STRAIGHT
IN DRAW POKER WHEN DRAWING ONE CARD

Odds against filling a straight open at one end	11 to 1
Odds against filling a straight open in the middle	11 to 1
Odds against filling a straight open at both ends	5 to 1

ODDS AGAISNT MAKING A STRAIGHT FLUSH
IN DRAW POKER WHEN DRAWING ONE CARD

The odds against making a flush by drawing one card or the same suit are about 4 ½ to 1. If you insist on drawing to a three-card flush, the odds against your catching two cards of the same suit are approximately 23 to 1.

ODDS AGAINST MAKING A STRAIGHT FLUSH
IN DRAW POKER WHEN DRAWING ONE CARD

Odds against making a straight flush open at one end	46 to 1
Odds against making a straight flush open in the middle	46 to 1
Odds against making a straight flush open on both ends	22to 1

CHANCES OF HOLDING VARIOUS POKER HANDS IN THE FIRST FIVE CARDS DEALT WHEN THE FOUR CARDS DEALT WHEN THE FOUR DEUCES ARE WILD

Rank of hand	Number of each	Chance
Five of a kind	672	1 in 3868
Royal flush	484	1 in 5370
Straight flush	4,072	1 in 638
Four of a kind	30,816	1 in 84
Full house	12,672	1 in 205
Flush	13,204	1 in 197
Straight	66,236	1 in 39
Three of a kind	355,056	1 in 7
1 in Two pairs	65,040	1 in 27
One pair	1,222,048	1 in 2 1/10
No-pair hand	798,660	1 in 3 1/4
Total	2,598,960

CHANCES OF HOLDING VARIOUS POKER HANDS IN THE FIRST FIVE CARDS DEALT WHEN THE JOKER IS WILD (53 CARD PACK)

Rank of hand	Number of each	Chance
Five of a kind	13	1 in 220,745
Royal flush	24	1 in 119,570
Straight flush	216	1 in 13,286
Four of a kind	3,120	1 in 920
Full house	6,552	1 in 438
Flush	7,768	1 in 369
Straight	20,532	1 in 140
Three of a kind	137,280	1 in 21
Two pairs	123,552	1 in 23
One pair	1,268,088	1 in ½
No-pair hand	1,302,540	1 in 2
Total	2,869,685

A very unusual mathematical situation arises in Deuces Wild and also in a 53-card deck with the joker wild regarding the relative value of three of a kind and two pairs. In Deuces Wild, as detailed in the table, the chances of drawing three of a kind are one in 7 deals and the chances of drawing two pairs are one in 27 deals. In Joker Wild, you see that the chances of drawing three of a kind are one in 21 deals and the chances of drawing two pairs are one in 23 deals. This peculiar situation is caused by the fact that in one-pair hands the player holding a wild card will naturally call three of a kind instead of the lower-ranking two-pair hand.

Five-Card Stud Poker Probabilities

The chances against holding a given hand in Five-Card Stud are the same as in Five-Card Draw. However, it must be noted that players will drop out before receiving their fifth card if they have potentially weak hands. Therefore, the player who stays until the showdown in Five-Card Stud has a higher average winning potential than those who remain until the showdown in Five-Card Draw.
The following table gives the chances that a certain card (ace, king, queen, jack) is the high–hole (down) card depending on the number of players. This table is expressed in percent

CHANCE OF BENING WITH THE FIRST FIVE CARDS DEALT, PERCENT