Friday, November 19, 2010

Combinations with types

A natural way to specify card combinations refers to both specific cards and generic card types. For example, to power 1BB you need to draw two swamps and one other land. The killer combination from Reign of Vampirism requires a Captivating Vampire and four other Vampires. Deck-u-lator was designed to automatically try all the different ways of drawing extra cards. For these two cases above, we need to restrict how cards are drawn.

Here is one way to approach this problem. Since there is only one Captivating Vampire in the deck, the other four Vampires must be different cards. We can pretend there is a card called Vampire from which we need to choose four. The same trick does not work for land. Two lands need to be Swamps. The third could be either a Forest or a Swamp. We can use our usual technique for calculating or combinations here. Calculate once with three Swamps (18%), once with two Swamps and a Forest (19%), add the results, and subtract a hand with three Swamps and a Forest so we do not double count (18%), for a total result of 19%

All this would be easier if Deck-u-lator could recognize card types and use them automatically in calculations.

Using a Captivating Vampire

have need card
Captivating Vampire

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