Poker Hand Calculator
Poker hand calculator works out Probability of the hand and Odds against (X to 1) from Hand, Five cards and Outs. The default figures on this page give hand of Royal flush; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow 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 |
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the poker hand calculator calculates
Exact poker probabilities: the frequency of every five-card hand from a 52-card deck, the chance of completing a draw from a number of outs, the pot odds and equity a call requires, and the expected return of a video-poker pay table.
How to use this poker hand calculator
Enter Hand, Five cards, Outs and Unseen cards. Probability of the hand updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Probability of the hand, Odds against (X to 1) and Number of such hands.
The method follows Exact enumeration of the 2,598,960 five-card hands from a 52-card deck, Packel, E.W. (2006), The Mathematics of Games and Gambling, 2nd ed., Mathematical Association of America, Hypergeometric draw probability: P(miss) = C(unseen - outs, cards to come) / C(unseen, cards to come) and Pot odds and minimum defence frequency: required equity = call / (pot + call); MDF = pot before the bet / (pot before the bet + bet).
What you can compare
Change one input at a time to see how it affects Probability of the hand, Odds against (X to 1) and Number of such hands. The inputs you can vary are Hand, Five cards, Outs, Unseen cards, Cards still to come and Pot size before your call.
Understanding Probability of the hand, Odds against (X to 1) and Number of such hands
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.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
What information do I need for the poker hand calculator?
You need Hand, Five cards, Outs, Unseen cards, Cards still to come, Pot size before your call, Amount you must call and Your chance of winning the pot. The page opens with default figures that give hand of Royal flush, so you can see the scale before entering your own.
What does this poker hand calculator show?
It shows Probability of the hand, Odds against (X to 1), Number of such hands, Total five-card hands, Hand, Strength rank (10 is best), Frequency of every hand and Chance of completing the draw, with the working and any warnings for your entries.
Can I check how the poker hand calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.