Deck A is a 60-card deck, with every card current in just one or two copies. Deck B is a 120-card deck, consisting of two further copies of Deck A merged collectively. As a simplifying assumption, to illustrate there aren’t any playing cards within the decks that permit gamers to look; each occasion of accessing the library is random.

Deck A and Deck B ought to perform very equally. In phrases of win fee in opposition to different arbitrary decks, my speculation could be that Deck A performs considerably higher, because it ought to are typically dangerous, all else equal, to attract a number of consecutive copies of the identical card and even card kind (having lands and non-lands alternate appears optimum), and drawing a card in Deck B successfully solely removes half of that card from the library, relative to drawing a card in Deck A.

We may lengthen this setup by merging any variety of copies of Deck A, ignoring the precise sport guidelines, and within the restrict, the consequence ought to be an identical to operating Deck A, however drawing with substitute, as an alternative of with out substitute as buying and selling card video games are at all times performed in actuality.

Has there been any try to measure the impression of something on this ballpark, both drawing with substitute versus with out substitute or utilizing the notion of partial substitute captured by merging a finite variety of copies of a deck, on win fee? I’ve seen just a few A.I. algorithms making an attempt to emulate video games of Magic to match the impression of particular selections on win fee, and I used to be questioning if this has been examined, or whether it is even attainable to make use of arithmetic to place some sure on the reply.

I discover this query fascinating within the evaluation of Yorion decks, for instance. People typically focus on the downside of not drawing your greatest playing cards as typically in bigger decks, for the reason that ratio of these greatest playing cards to complete playing cards is lesser, however I’m excited about how a lot of a further detriment the substitute issue is.