Disney Lorcana Odds: Opening Hands, Mulligans, and Ink

Welcome to Level 3. At Level 2 you built a deck with a plan. Now you learn what that deck will actually draw. Every number here comes from the same simple math, worked out for a 60-card deck and a 7-card opening hand. You do not need to do the math at the table. You need to know the shape of it.

How often you see a card

Say your deck has 4 copies of one card. How likely are you to have at least one by a given turn? The starting player sees 7 cards on turn one and one more each turn after. The second player draws on turn one too, so they are always one card ahead.

Nine cards is turn three for the starting player. Ten is turn three for the second player. These are the chances without a mulligan.

Two lessons jump out:

• A single 4-of is a coin flip by turn three. If your plan depends on one specific card, you will often not have it.
• Groups are reliable. If 12 cards in your deck do the same job, such as 2-cost characters, you see one in the opening hand about 4 times in 5.

That is why good decks are built around groups of cards that do the same job, not around one card.

Altering your hand

You may alter your hand once: put any number of cards on the bottom of your deck, then draw back to 7. The new cards come from the rest of your deck, so the ones you sent back will not return.

Here are the chances that the replacement cards include at least one card from a group you are missing, after a hand with none of them:

More cards sent back means better odds of finding what you need, at the cost of losing cards you already had. Sending back the whole hand finds one of 12 cards 85% of the time, but it also throws away any ink and plays you liked.

A mulligan method

1. Name what the hand needs. Usually: two or three inkable cards, and something to play on turns one to three.
2. Keep what fills those needs. A cheap character and two inkable cards are worth keeping.
3. Send back the rest. Expensive cards you cannot play for many turns, and situational cards, go to the bottom.
4. Do not keep a hand out of fear. A hand that cannot do anything early is often worse than a random 7.

Because the mulligan is all at once, you cannot send cards back in two waves. Decide everything before you draw.

How many inkable cards?

You want to ink every turn for the first four or five turns. On turn four the starting player has seen 10 cards and needs 4 of them to be inkable, plus some to play. The second player has seen one more, so their odds are a little better. Here is the chance of seeing at least 4 inkable cards in your first 10 cards:

So reaching four ink is rarely the problem, even with 40 inkable cards. The problem is choice. With few inkable cards, the card you ink is often one you wanted to play. More inkable cards give you room to ink the right one. That is the real reason most decks run a large majority of inkable cards.

How to use this

Do not memorize the tables. Remember three shapes:

• One copy of a card is rarely there when you want it. Four copies are there about half the time by turn three.
• Twelve cards that do the same job show up almost every game.
• A smart mulligan meaningfully raises your odds, but costs you the cards you send back.

These numbers come from the hypergeometric distribution, the standard math for drawing without replacement. If you want to run your own, any online hypergeometric calculator works: deck size 60, the number of copies, and the number of cards seen.