@Imaginator: That is indeed true, but in our case, as we are dealing with cardinals, IF they are infinite, they are countably infinite (and thus bijective/equal in size)

@lettucemode: That number is not ALWAYS infinite, for both players. suppose a situation where neither player has any cards left in his spellbook and no way to heal or generate life. imagine there is a ghoul rot on one of the players - that game will end in a finite number of turns bounded by (HP of Mage left)/2+1,  and in each turn, there are only finitely many options, therefore you are indeed looking at a situation where there are only finitely many possible outcomes. In fact, i have heard (from AI research guys) that playing a few random games from a position can be somewhat viable as a measure for how good the position is, even in go (this amounts basically to a Monte Carlo simulation of the game space).