Poker Hand Calculator

Hand

Five cardsRank then suit, separated by spaces: "As Ks Qs Js Ts". Suits are s, h, d, c.

OutsCards still in the deck that complete your hand. A four-flush after the flop has 9.

Unseen cards47 after the flop in hold’em (52 less your two cards and the three board cards); 46 after the turn.

Cards still to come

Pot size before your callEverything already in the middle, including the bet you have to call.

Amount you must call

Your chance of winning the potOptional. Supply your equity to see whether calling has a positive expectation.

Pay table (coins returned per coin bet)One payout per winning hand, in the same order as the frequencies.

Probability of each paying hand under your strategyFrom your own strategy analysis or the game’s published return report. These are game- and strategy-specific and are never assumed here.

Hand

Royal flush

Poker Odds Calculator

Probability of the hand

0.000002

Probability of the hand

0.000154 %

Odds against (X to 1)

649,739

Number of such hands

Total five-card hands

2,598,960

Strength rank (10 is best)

Chance of completing the draw

0.349676

Chance of missing

0.650324

Draw odds against (X to 1)

1.859788

Equity needed to call

0.25

Pot odds (X to 1)

Minimum defence frequency

0.666667

Alpha (bluff success needed)

0.333333

Worked out from Exact enumeration of the 2,598,960 five-card hands from a 52-card deck and 3 other sources.

These are exact mathematical probabilities for a fair, well-shuffled deck. They are not betting advice, and no probability makes a wager profitable on its own.

How this is worked out

4 steps

The five cards As Ks Qs Js Ts make royal flush, strength rank 10 of 10.
There are 4 such hands among the C(52,5) = 2,598,960 five-card hands.
Probability = 4 / 2598960 = 0.0000015391, i.e. 0.000154% or 649739 to 1 against.
The ten category counts total 2,598,960, which is exactly C(52,5).

Frequency of every handtable

hand	rankOrder	combinations	probability	oddsAgainst
Royal flush	10	4	0.000002	649,739
Straight flush (not royal)	9	36	0.000014	72,192.333333
Four of a kind	8	624	0.00024	4,164
Full house	7	3,744	0.001441	693.166667
Flush (not straight)	6	5,108	0.001965	507.801879
Straight (not flush)	5	10,200	0.003925	253.8
Three of a kind	4	54,912	0.021128	46.329545
Two pair	3	123,552	0.047539	20.035354
One pair	2	1,098,240	0.422569	1.366477
High card (no pair, no straight, no flush)	1	1,302,540	0.501177	0.995301

Results are general information, not financial, tax, legal, medical or engineering advice.