Opening hand and draw probability calculator for card games
With 4 copies in a 60-card deck, you see at least one in a 7-card opening hand 39.9% of the time; with 3 copies in a 40-card Yu-Gi-Oh! deck and 5 cards, 33.8%. Choose your game, enter how many copies you run and how many extra cards you will have drawn, and the calculator gives the exact probability.
How it is calculated
Drawing from a shuffled deck is sampling without replacement, so the tool uses the hypergeometric distribution. The chance of missing every copy is C(deck − copies, cards seen) ÷ C(deck, cards seen); one minus that is the chance of at least one. For “at least 2” or more, it adds up the exact cases below that number.
“Extra cards drawn” is how many cards you will have seen after the opening hand: for example, 2 if you want to know your odds by your second draw. Count only real draws, not cards searched from the deck.
Quick reference: at least one copy in the opening hand
| Deck · hand | 1 copy | 2 copies | 3 copies | 4 copies |
|---|---|---|---|---|
| 60 · 7 | 11.7 % | 22.1 % | 31.5 % | 39.9 % |
| 50 · 6 | 12.0 % | 22.8 % | 32.4 % | 41.1 % |
| 50 · 5 | 10.0 % | 19.2 % | 27.6 % | 35.3 % |
| 40 · 5 | 12.5 % | 23.7 % | 33.8 % | 42.7 % |
| 40 · 4 | 10.0 % | 19.2 % | 27.7 % | 35.5 % |
Mulligans, searching effects and first-turn draws change the real figure; the presets use each game’s standard deck and opening hand as explained in our rules guides.
Sources and checks
Deck and hand sizes checked on 27 October 2026 against our rules guides, which cite each official rulebook, and Riot’s Riftbound core rules guide. Flesh and Blood: Classic Constructed page read on 3 November 2026 (deck of at least 60 cards; you draw up to your hero’s intellect, 4 on most heroes).