The Math of Mulligans

Olav Rokne says, the English philosopher and Bishop Joseph Butler once commented that probability was the guide to life. Although I remain unconvinced of this in the big picture, his attitude would have served him well when playing Vs. System.

Often, the first and most important decision of the game is whether or not to mulligan. Sadly, a vast number of players make this decision based only on a gut feeling or instinct about their Draft or Sealed decks. Is it a good hand or a bad hand? Is what you are giving up worth what you might get? Such determinations can only really be worked out through probability.

A quick search of the Internet for “probability,” “statistics,” “card games,” “CCGs,” or “TCGs” yields a shockingly large number of different ways to get entirely incorrect calculations of probability. For card games such as Vs. System, binomial distribution does not apply. Take a simple example of binomial distribution: tossing coins. The result of one toss does not affect the result of the next, which is accounted for in binominal distribution. The events are said to be independent.

However, in a TCG, selection of successive cards is not independent because the cards are not put back into the deck. Finding the odds of drawing a particular card on one draw is relatively easy. If there are 60 cards in the deck and 1 copy of the card you are looking for, any joker can tell you that you have a 1 in 60 chance of receiving that card. Read more.


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