Gaming · Card game odds
Mulligan probability calculator.
Tell the calculator your deck size, how many of the cards are lands (or whatever resource card you count) and the range of lands you would keep, and it works out how often your first seven is keepable and how the London mulligan changes that. It uses the Magic: The Gathering Comprehensive Rules for the mulligan: draw a new seven, then put one card on the bottom for each mulligan taken. Example: a 60-card deck with 24 lands and a keep range of 2 to 5 lands has a keepable first hand 84.4% of the time, so you mulligan 15.6% of the time.
Deck and keep rule
Result
Working out the result.
How the mulligan odds are calculated
Rule 103.5 of the Magic Comprehensive Rules describes the London mulligan: you shuffle your hand into your library, draw a new hand of the starting hand size, then put a number of those cards equal to the mulligans you have taken on the bottom, in any order. So a hand after one mulligan is seven drawn cards minus one you choose to bottom.
The tool first uses the hypergeometric formula for the number of lands l among the seven cards drawn: C(lands, l) × C(deck − lands, 7 − l) ÷ C(deck, 7). A drawn hand with l lands and 7 − l other cards can be turned into a kept hand of s = 7 − m cards holding anywhere from max(0, s − (7 − l)) to min(l, s) lands, depending on which cards you bottom. The hand is keepable if that range overlaps your keep range (your minimum is lowered to s if the hand is smaller than that minimum). The final hand-size odds multiply the chance of rejecting each earlier hand.
Worked examples with real numbers
- 40 cards, 17 lands, keep 2 to 5. The first seven is keepable 87.8% of the time. The chance of exactly 0 lands is C(23,7) ÷ C(40,7) = 1.31% and of 7 lands 0.10%.
- 60 cards, 24 lands, keep 2 to 5. Keepable 84.4% at seven. After one mulligan, the chance that the new seven can be turned into a keepable six-card hand is 85.6%, and the expected final hand size with up to 3 mulligans is 6.818 cards.
- 99 cards, 37 lands. Keepable 80.4%.
Worked table: 60 cards, 24 lands, keep 2 to 5, up to 3 mulligans
| Mulligans taken | Cards kept | Keepable when drawn | Chance you end here |
|---|---|---|---|
| 0 | 7 | 84.4% | 84.4% |
| 1 | 6 | 85.6% | 13.4% |
| 2 | 5 | 85.7% | 1.9% |
| 3 | 4 | 85.7% | 0.3% |
Common deck setups, keep 2 to 5 lands
| Deck | First hand keepable | Mulligan at least once | Expected final hand (up to 3 mulligans) |
|---|---|---|---|
| 40-card limited deck, 17 lands | 87.8% | 12.2% | 6.864 |
| 60-card constructed deck, 24 lands | 84.4% | 15.6% | 6.818 |
| 99-card singleton deck, 37 lands | 80.4% | 19.6% | 6.760 |
Lands in the first seven, 40-card deck with 17 lands
| Lands | Chance |
|---|---|
| 0 | 1.31% |
| 1 | 9.20% |
| 2 | 24.55% |
| 3 | 32.30% |
| 4 | 22.61% |
| 5 | 8.40% |
| 6 | 1.53% |
| 7 | 0.10% |
What this calculator leaves out
It counts lands only. It treats every non-land as interchangeable, so it cannot tell a hand of five unplayable spells from a hand of five cheap ones, and real keep decisions depend on exactly that. It assumes you bottom the best cards for your land range, and that you mulligan whenever the drawn seven cannot reach your range. Rule 103.5c says that in multiplayer and Brawl games the first mulligan is free and does not count toward the cards bottomed, which this page does not model. It covers the London mulligan described in the Magic rules; other games and older mulligan rules work differently.
Common mix-ups
-
Often assumedAfter a mulligan you draw a smaller hand, six cards and then five.
What the source saysThe Comprehensive Rules say you draw a new hand of cards equal to your starting hand size, normally seven, and then put one card per mulligan taken on the bottom of your library. [1]
-
Often assumedYou can only mulligan a couple of times before you are forced to keep.
What the source saysThe rules say a player can take mulligans until their opening hand would be zero cards, after which they may not take further mulligans. [1]
-
Often assumedEvery mulligan costs a card in every format.
What the source saysRule 103.5c says that in a multiplayer game and in any Brawl game, the first mulligan a player takes does not count toward the number of cards put on the bottom or the number of mulligans allowed. [1]
Checked against these sources on .
Frequently asked questions
What is the chance of a keepable opening hand in Magic?
It depends on deck size, land count and what you call keepable. With 24 lands in 60 cards and a keep range of 2 to 5 lands, the first seven is keepable 84.4% of the time. With 17 lands in 40 cards it is 87.8%.
How does the London mulligan work?
Per rule 103.5 you shuffle your hand back, draw a new hand of seven, then put one card on the bottom of your library for each time you have taken a mulligan, choosing which ones. A first mulligan keeps six cards, a second keeps five.
How many mulligans can you take?
Until your opening hand would be zero cards, according to the Comprehensive Rules. In practice the calculator lets you cap it at 0 to 5 to see how often you would still be stuck.
Why does bottoming cards raise my keepable chance?
Because you choose the cards. A drawn seven with five lands and two spells can become a six-card hand with four lands and two spells by bottoming a land, so more drawn hands can be fixed than the first-seven odds suggest.
What land range should I keep?
That is your call, not a rule. The calculator takes any minimum and maximum and shows the result, so you can compare keep ranges such as 2 to 5 and 3 to 4 for your own deck.
Does the first mulligan cost a card in every game?
No. Rule 103.5c says that in multiplayer and Brawl games the first mulligan you take is free and does not count toward the cards put on the bottom. This calculator does not model the free mulligan.
Sources
Retrieved
- Magic: The Gathering Comprehensive Rules, rule 103.5 (Nov 8, 2024 edition) — mulligan procedure, hand size, bottoming, free first mulligan in multiplayer and Brawl (103.5c) (read 2026-10-26)
- Wikipedia: Multivariate hypergeometric distribution — hypergeometric counting used for the first seven cards (read 2026-10-26)
Fan-made tool, check the current rules
Not affiliated with Wizards of the Coast. Magic: The Gathering is a trademark of its owner. Rules read from the Comprehensive Rules effective 8 November 2024 and checked on 26 October 2026; later rules updates may differ. Nothing you type is sent or stored.