What this calculator does
This tool gives the exact probability of being dealt a specific poker hand in a single 5-card deal from a standard, well-shuffled 52-card deck (no jokers, no wild cards). It works for every ranked category, from the rare royal flush down to a plain high card, and reports the result as a percentage, a decimal probability, and easy-to-read "1 in N" odds.
How to use it
Pick a hand type from the dropdown and read the results. Categories such as "Flush" and "Straight" are counted inclusively (a flush count includes straight flushes), which matches the standard combinatorial tables most textbooks use. Select "Straight flush (incl. royal)" to see all 40 straight flushes, or "Royal flush" alone for just the 4 top-end versions.
The formula explained
The probability of any hand is simply the number of card combinations that produce it divided by the total number of possible 5-card hands. There are \(\binom{52}{5} = 2{,}598{,}960\) distinct 5-card hands. For example, four of a kind can be formed in 624 ways: 13 choices of rank for the quad, times \(\binom{48}{1}=48\) choices for the fifth card. So $$P = \frac{624}{2{,}598{,}960} \approx 0.024\%.$$
Worked example
Full house: choose the rank for the triple (13 ways), pick 3 of its 4 suits \(\binom{4}{3}=4\), choose a different rank for the pair (12 ways), and pick 2 of its 4 suits \(\binom{4}{2}=6\). That gives $$13\times4\times12\times6 = 3{,}744 \text{ ways}.$$ Dividing by 2,598,960 gives about 0.1441%, or roughly 1 in 694 hands.
FAQ
Are the flush and straight counts overlapping? The "Flush" figure (5,108) and "Straight" figure (10,200) include straight flushes. Subtract the 40 straight flushes if you want the exclusive count.
Does this account for community cards in Texas Hold'em? No. It models a single 5-card deal, like five-card draw, not the multi-stage drawing of Hold'em or Omaha.
Why does high card show 1,302,540 ways? That is the number of 5-card hands with no pair, no straight and no flush — the largest single category.
