Your deck
Probability
A Yu-Gi-Oh probability calculator answers the deck builder’s big question: how often do I open a starter? Run nine one-card starters in a 40-card deck and you open at least one 74% of the time with a five-card hand. Push it to twelve and it’s 85%. Fifteen gets you to 92%. Set your own numbers in the free calculator above and it shows the full spread, from bricking to opening three.
Using the Yu-Gi-Oh probability calculator
Put your Main Deck size in the first box and the total number of copies that count in the second. If you run three copies each of three different starters, that’s 9. Going first you see five cards. Going second you draw a sixth, so change cards in hand to 6.
It’s the hypergeometric formula, the same one card players use everywhere:
P(exactly k) = C(copies, k) × C(deck − copies, hand − k) ÷ C(deck, hand)
What the numbers say about deck size
A single card run at three copies shows up in your opening five 33.8% of the time in 40 cards. In 42 cards it’s 32.3%. Two extra cards don’t sound like much, but over a whole tournament that’s a few more bricked hands. This is the maths behind “play 40”.
Going second helps more than you’d think. That same three-of jumps to 39.4% with six cards.
The calculator treats each card as either a hit or not. If your combo needs one starter and one extender, check each part separately and remember the two aren’t independent, so the true chance of both is a little different from multiplying them.
Playing Magic too? The MTG hypergeometric calculator counts draws by turn. The hypergeometric calculator works for any deck.