Alternatives to Mulligans in Magic: The Gathering

Question

!edited: Added non-opinion-based question

I am currently looking into ways of doing Mulligans in another way, or replace Mulligans altogether, for casual play around the kitchen table. I don't like the shuffling and reshuffling three times, for a two time mulligan.

I want to hear what to do, so that option is roughly equivalent to a normal Mulligan.

Here is my idea:

Draw (7+X) cards, keep (8-X) cards

Instead of having the option to take a Mulligan, at the beginning of the game, all players draw X additional cards, then shuffle (2X-1) cards back into their library (or put them on the bottom of their library). For each additional card draw, your starting hand size, which you may keep, decreases by 1:

Draw: (7) - 8 - 9 - 10 - 11 - 12

Shuffle back: (0) - 1 - 3 - 5 - 7 - 9

Starting hand: (7) - 7 - 6 - 5 - 4 - 3

(no mulligan taken)

Players can draw 8, and keep 7, but can decide to keep drawing until the decide to keep, and shuffle cards back/put them on the bottom of their library for each card they drew additionally.

For example: Timmy does not care about odds and draws 7 cards, no mulligan. Johnny wants to test his new combo deck, and decides to draw 10, keep 5. Spike draws 8, is not quite satisfied, draws to 10, decides to keep, and shuffle five cards back, starting with a hand of 5.

Handicapping idea:

• Timmy may draw up to 10 cards, and still keep 7.
• Spike may only draw additional cards, if he starts the game with 3 life less for each card drawn additionally. Starting hand size is either 7, or reduced as before.

How have I to tweak the number of cards drawn and discarded, so that the quality of hands is similar to that of a regular Mulligan?

Answer 1

Your proposed mulligan rule would be better for the quality of a hand compared to a single mulligan under current rules, but much worse for larger/more mulligans. I would expect the number of viable decks to decrease, especially decks and archetypes that rely on few key cards would suffer.

Generally, mulligans are a system to exchange card advantage for card quality. Card advantage in this context is obvious, it's simply the number of cards in your starting hand compared to in your opponent's hand. Since your new system makes sure to keep the ultimate number of hand cards the same after the same number of mulligans (shifted by 1), we can focus on the resulting card quality. Card quality is hard to define because it depends on the deck's strategy, but generally, holding at least one of a certain card is a good, generally applicable definition of card quality of your starting hand. That's why I will evaluate your scheme on that criterion.

You have designed the system such that the number of cards in hand after drawing an extra n+1 cards is equivalent to taking n mulligans under current rules. Threfore, it would be always optimal to draw 8 cards and shuffle 1 back to 7 rather than just keeping the 7. That means that the chance to draw at least 1 of a certain card in your starting hand of 7 goes from 39.9% to 44.5%, without downside. That means that if you already have a playable hand, you get a chance to further improve that hand for free.

However, if you have an unplayable hand, e.g. too much or too little or the wrong color of mana, and you would like to get rid of the whole hand, then you could only do so at large card disadvantage. Also, the chance to find a certain card increases much more slowly with your scheme than under the current one.

Under the current rules, the cumulative chance to get a certain card in your starting hand after n mulligans are roughly:

• 0 mulligans: 40% (7 hand cards remaining)

• 1: 61%

• 2: 73%

• 3: 80%

• 4: 83%

• 5: 85%

• 6: 87% (1 hand card remaining)

By contrast, if you draw an extra n+1 cards under your rules, the probabilities for at least 1 of a certain card in your hand are:

• 1 card drawn: 44.5% (7 hand cards remaining)

• 2: 48.7%

• 3: 52.7%

• 4: 56.5%

• 5: 60.1%

• 6: 63.4% (1 hand card remaining)

I have used the hypergeometric calculator with values (top to bottom) 60, 4, 7 (hand size, adjust for actual card draw), 1. The first list of probabilities is obtained by multiplying the probabilities for "x < 1" (i.e. the wanted card is not in hand) for hand sizes 7 through 1. The second list is simply the probability for "x => 1" for hand sizes 8 through 13, which results in the same final starting hand size as the respective current mulligan.

As an effect, I would expect the meta to adapt around such a drastic change of the maths behind mulligans. It would become much harder to get a certain key card on your starting hand. Deck construction would have to take that into acount, by not including disproportionately important cards into the deck's strategy. That would be counter the core idea of "build-around cards", which are usually found in the rare or mythic rare slots of a set. Arguably, that mulligan rule would reward homogenous decks, decks where cards can more or less stand in for each other, and therefore decrease the number of viable archetypes.

Answer 2

I would caution against using your variant based on the fact that you are trying to avoid shuffling decks. I think this suggests your playgroup is trying to solve the wrong problem.

The decks might not well balanced, especially land-wise. Honestly, the times I've found myself having to mulligan often with the same deck it's almost always because I didn't include enough lands. Or in a related problem, my mana curve is too high and I included too many flashy 6+ mana cards. A typical 2-color deck 60-card will require around 24 lands. Don't go much lower unless you have specific reasons (low mana curve, really good dual lands).

Your playgroup could be not proficient in shuffling, which might mean you are not shuffling thoroughly enough to randomize your decks. If your shuffling is not sufficiently random, your deck is likely to clump cards in bad ways leading to more mulligans. In this is the case, your proposed system could even backfire and force bad shufflers to start with fewer cards just to "guarantee" they have a chance.

As an aside, your system is similar to a partial-Paris mulligan, except it costs more cards to dig deeper and is non-repeatable. I know that partial-Paris mulligans (which used to be the go-to in Commander) fell out of favor because they empowered combo decks and let players get away with more unbalanced decks.

Answer 3

If you want to reduce shuffling for mulligans in casual, you can use the old commander mulligan rules:

Each time a player takes a mulligan, rather than shuffling his or her entire hand of cards into his or her library, that player exiles any number of cards from his or her hand. Then the player draws a number of cards equal to one less than the number of cards he or she exiled this way. Once a player keeps an opening hand, that player shuffles all cards he or she exiled this way into his or her library.

This means a maximum of 2 shuffles per player (the second of which can happen after the game has started) without changing the game substantially.