London Mulligan Math: Exact Odds and Where Serum Visions Fits

The London mulligan changed what a mulligan costs. Under the current rule you always look at seven fresh cards and choose which ones go to the bottom, so a six-card hand is the best six of seven, not a random six. That selection is easy to quantify. Every percentage below comes from an exact hypergeometric calculation (whole-number combinatorics, no simulation), and the formula is spelled out so you can check it or rerun it in our hypergeometric calculator.

What the rule actually says

The mulligan is defined in rule 103.5 of the Comprehensive Rules (the version effective September 25, 2026). The key sentence reads:

"To take a mulligan, a player shuffles the cards in their hand back into their library, draws a new hand of cards equal to their starting hand size, then puts a number of those cards equal to the number of times that player has taken a mulligan on the bottom of their library in any order."

Three details in 103.5 matter for the math:

• Every new hand is a full shuffle of the whole library, so each attempt is a fresh, independent draw. That is what makes the probabilities below multiply cleanly.
• You always draw your full starting hand size (normally seven) and only then put cards on the bottom. You choose which cards; you are not stuck with whatever the top six happen to be.
• The rule ends with: "A player can take mulligans until their opening hand would be zero cards, after which they may not take further mulligans."

Once a player keeps, the rule says "that player may not take any further mulligans." There is no scry after keeping under the current rule.

From Vancouver to London: the dated history

The scry after a mulligan belonged to the previous rule, informally called the Vancouver mulligan. Wizards of the Coast's Battle for Zendikar Release Notes (published September 23, 2015) announced that "the traditional rules for mulligans are changing beginning with Battle for Zendikar Prerelease events," and that the change taking effect on September 26 was an addition to the existing rule: after keeping, "each player who kept fewer cards than his or her starting hand size looks at the top card of his or her library" and may put that card on the bottom. A Wizards guide for returning players (April 24, 2018) summarized that system: you "draw one fewer card each time" you mulligan, and keeping fewer than seven "allows that player to scry 1 before the game begins."

The London mulligan replaced it. In "The London Mulligan" (June 3, 2019, by Ian Duke), Wizards summarized it as: each time you take a mulligan, "you draw up to seven cards, then put a number of cards from your hand equal to the number of times you have mulliganed this game on the bottom of your library in an order of your choice." The same announcement said it had been tested at Mythic Championship II in London, that "Magic Online will begin using the London mulligan on July 2," and that tabletop play would use the new mulligan starting with the Core Set 2020 Prereleases on July 5.

The formula behind every number here

Drawing cards without replacement from a shuffled library follows the hypergeometric distribution. With a library of N cards containing K lands, the chance that a hand of n cards contains exactly k lands is:

P(X = k) = C(K, k) × C(N − K, n − k) / C(N, n)

where C(a, b) is the number of ways to choose b items from a. Worked example for a 60-card deck with 24 lands and a seven-card hand: C(24, 3) = 2,024 ways to pick three lands, C(36, 4) = 58,905 ways to pick four nonlands, out of C(60, 7) = 386,206,920 possible hands. That gives exactly 30,107/97,527, or 30.9%, for exactly three lands. The expected number of lands in seven cards is simply 7K/N, which is 2.80 for 24 of 60.

For Commander we use a 99-card library: rule 903.5a requires exactly 100 cards including the commander, and rule 903.6 has the commander start in the command zone, so with one commander the shuffled library is the other 99. For Limited we use 40 cards, the minimum deck size in rule 100.2b.

Across every row of this table, between 20.5% and 29.3% of opening sevens fall outside two to four lands.

Defining "keepable" and what bottoming buys

A probability needs a definition. In this article a hand is keepable if, after putting cards on the bottom, it holds 2, 3 or 4 lands. That is deliberately simple: it ignores colors, curve and what the spells do, so treat it as a land-count floor, not a full keep-or-mulligan rule.

Under the London rule, the land count you can end with depends on how many lands are in the seven you draw (call it L) and how many cards you bottom (m). You can bottom lands, nonlands or a mix, so:

• Seven-card keep (m = 0): keepable when L is 2, 3 or 4.
• Six-card keep (m = 1): keepable when L is 2 to 5. With five lands, bottom one land and keep four; with one land, bottoming a spell still leaves one.
• Five-card keep (m = 2): keepable when L is 2 to 6.

So the keepable chance for a London six is the sum of P(X = k) for k = 2 to 5 with n = 7, not k = 2 to 4 with n = 6. The last column shows what a plain six-card draw with no selection would give, the hand a player saw under the older one-fewer-card rules before any scry:

The counterintuitive result: under this definition, a London six is more likely to have a workable land count than a fresh seven, because the bottom card rescues every five-land draw. What the mulligan costs is a card, not mana stability. A six-card hand has one fewer spell to cast, and that card-count cost is something no land table measures.

Chaining mulligans

Because each mulligan reshuffles the whole library, the attempts are independent. If you mulligan exactly when a hand is not keepable, the chance of having a keepable hand by a given point is 1 − (1 − p₇)(1 − p₆)…, using the per-attempt values above. In a two-player game:

Land count is only one reason to mulligan, so real mulligan rates for a given deck can be higher than these numbers suggest. They are a floor set by mana alone.

Commander and multiplayer: the free first mulligan

Rule 103.5c adds a multiplayer exception:

"In a multiplayer game and in any Brawl game, the first mulligan a player takes doesn’t count toward the number of cards that player will put on the bottom of their library or the number of mulligans that player may take. Subsequent mulligans are counted toward these numbers as normal."

Rule 100.1b defines a multiplayer game as one that "begins with more than two players," and rule 903.2 says a Commander game "may be a two-player game or a multiplayer game." So under the Comprehensive Rules a typical Commander pod of three or more gets the free mulligan, while a two-player Commander game does not (Brawl gets it either way). In a multiplayer game the sequence is seven, seven, then six (bottom one), then five (bottom two):

With 36 lands, a two-player game reaches a keepable hand by six 94.5% of the time; in a multiplayer game the free mulligan reaches 93.3% while still holding seven cards.

Where Serum Visions fits

Serum Visions is a one-mana blue sorcery ({U}) whose entire Oracle text is "Draw a card. Scry 2." Rule 701.22a defines scry N as looking at "the top N cards of your library," then putting "any number of them on the bottom of your library in any order and the rest on top." So one cast puts a card in your hand and lets you see and arrange the next two: three cards seen for one mana. It debuted as a common in the Fifth Dawn expansion (released June 4, 2004, per Scryfall), and it has since been reprinted in sets including Modern Masters 2017 and Commander 2021.

As of October 2, 2026, Serum Visions is legal in Modern, Legacy, Vintage, Commander and Pauper, and not legal in Standard or Pioneer.

It is not a mulligan tool in the rules sense: the current mulligan has no scry, and Serum Visions is cast during the game. What it does is smooth a keep that is light on lands. For a 60-card, 24-land deck that kept two lands, cast on turn one on the play (53 cards left, 22 of them lands), the exact chances of seeing at least one land are:

The top-three figure is 1 − C(N − K, 3) / C(N, 3). Seeing a land is not the same as drawing it: the drawn card is random, and a land found by the scry sits on top for your next draw. On the play, the starting player of a two-player game skips the first draw step (rule 103.8a), which is why the library still holds 53 cards here.

Run your own numbers

The tables above use a fixed definition of keepable. To test a different one, such as needing exactly three lands or a specific color source, plug your deck into the hypergeometric calculator. To decide how many lands and sources to play in the first place, the manabase calculator applies the same hypergeometric math to colored sources for Commander and 60-card formats.