Card draw probability calculator

How to use it

Pick the game and the page fills in the deck size and the opening hand for you. Then enter how many copies of the card are in your deck and how many you want to find: the result updates as you type. The big number is the probability of having those copies in your opening hand, and the table below shows how it grows turn by turn, with every card you draw.

“Copies” can also be a group of cards that do the same job for you. If you run 24 lands in a 60-card Magic deck, enter 24 copies and ask for at least 2: you will see how often your opening hand has enough of them to get going. With the second card box the page works out the odds of having two different cards together, like the two pieces of a combo.

The maths behind it

When you draw you don't put cards back in the deck, so every card drawn changes the odds of the next one. The right calculation for this case is called the hypergeometric distribution: you count every possible hand and see how many of them contain what you want. There is no simulation, the result is exact.

An example. With 4 copies in a 60-card deck and a 7-card hand, the hands without a single copy are 60.1% of the total: so at least one copy shows up in 39.9% of games. With 3 copies it drops to 31.5%, with 2 to 22.1% and with just one to 11.7%. If you want to count the combinations by hand, there is Combinations and permutations.

The built-in rules

Magic: The Gathering is played with a deck of at least 60 cards and an opening hand of 7, and in Limited formats, that is draft and sealed, the deck is at least 40. In a two-player game the player who goes first skips the draw of the first turn. In Commander the deck is exactly 100 cards, but the commander sits outside the deck, so you draw from 99, and in multiplayer games everybody draws on the first turn too.

Pokémon uses a 60-card deck and a 7-card hand, then 6 Prize cards are set aside. You draw a card every turn, including the first.

Yu-Gi-Oh! has a deck of 40 to 60 cards and a 5-card hand, and the player who goes first does not draw on the first turn.

One Piece has a deck of exactly 50 cards plus the Leader, a 5-card hand and as many Life cards as the Leader says, usually 4 or 5. The player who goes first does not draw on the first turn.

Disney Lorcana has a deck of at least 60 cards and a 7-card hand, and here too the player who goes first skips the first draw. We reread the rules of Magic, Yu-Gi-Oh!, One Piece and Lorcana in the official rulebooks on 11 November 2026. If your deck is different, change the numbers by hand.

The mulligan

The mulligan is the chance to change your opening hand when it is no good, and every game has its own. In Magic and in One Piece you put the whole hand back in the deck, shuffle and draw a new one. In Magic, for every mulligan taken, you then put one card on the bottom of the deck, but you choose it, so the card you wanted stays in your hand. In Lorcana you choose which cards to put under the deck and draw that many, only once. In Yu-Gi-Oh! there is no mulligan, and in Pokémon you redraw only when the hand has no Basic Pokémon at all.

The page counts a single mulligan, taken every time the opening hand does not have what you want. With 4 copies in a 60-card deck the probability goes from 39.9% to 63.9% by shuffling the whole hand back, and to 66.5% with the Lorcana rule, where the new cards come from the rest of the deck. That is the most a mulligan can give you: in a real game you keep or change a hand looking at everything else as well.

Prize cards and Life cards

In Pokémon six cards of the deck become face-down Prizes, in One Piece a few become Life cards: they are cards you cannot draw until the game hands them to you. The odds of finding a card in your hand do not change, because Prizes and Life are cards taken at random like all the others. But the card you need may well have ended up right there.

With a single copy in a Pokémon deck the probability that it is among the six Prizes is 10%, that is one game in ten. With 4 copies at least one ends up in the Prizes in 35.1% of games, while all four ending up there is next to impossible. The page does this calculation whenever the cards set aside are more than zero.

A few numbers worth remembering

In Magic, 24 lands out of 60 give you at least 2 lands in the opening hand in 85.7% of games. In Yu-Gi-Oh! three copies of a card in a 40-card deck show up in the 5-card hand in 33.8% of games, and in 39.4% if you go second and draw the sixth. In Pokémon, with 12 Basic Pokémon the opening hand has none in 19.1% of cases, and with 8 Basics that goes up to 34.6%.

Two different cards together are much rarer than they seem: with 4 copies of each in a 60-card deck, having both in the opening hand happens in only 14.5% of games. If you also get your cards graded, before shipping them you can measure the borders with Card centering calculator.