5-Card Poker Hand Odds

In a standard 52-card deck there are C(52,5) = 2,598,960 possible 5-card hands. The probability table above shows exact combinatorial counts and probabilities for each hand rank, from Royal Flush down to High Card.

Hand Rankings Reference

Rank	Hand	Combinations	Probability
1	Royal Flush	4	0.000154%
2	Straight Flush	36	0.00139%
3	Four of a Kind	624	0.0240%
4	Full House	3,744	0.1441%
5	Flush	5,108	0.1965%
6	Straight	10,200	0.3925%
7	Three of a Kind	54,912	2.1128%
8	Two Pair	123,552	4.7539%
9	One Pair	1,098,240	42.2569%
10	High Card	1,302,540	50.1177%

Outs and Equity

An out is any card remaining in the deck that will improve your hand. Counting outs and converting them to equity is the foundation of poker math. Use the Rule of 2 and 4:

One card to come (river only): multiply outs by 2 to get approximate equity %.
Two cards to come (flop → river): multiply outs by 4 to get approximate equity %.

Example: you have four cards to a flush after the flop (9 outs). With two cards to come: 9 × 4 = ~36% chance of making the flush.

Pot Odds

Pot odds are the ratio of the current pot size to the amount you must call. If the pot is $100 and you must call $25, your pot odds are 100:25 = 4:1, or 20% (25 ÷ 125). If your equity exceeds 20%, calling is mathematically profitable.

Compare pot odds directly to your hand equity: if equity > pot odds percentage, call; if equity < pot odds percentage, fold. This framework separates a break-even call from a profitable one.

Variance and Expected Value

Expected value (EV) measures the average outcome of a decision over many repetitions. A positive-EV call is correct even if you lose that hand — results and decisions are independent in the short run. Variance means a correct decision can lose money over hundreds of hands before the math evens out. Professional poker is won by making high-EV decisions consistently, not by chasing results.