When Magic the Gathering gamers create infinite useful resource combos, they usually identify numbers akin to 1 million, 1 billion, or 1 trillion. Often this ends in Participant A creating that many permanents, gaining that a lot life, and many others.
Clearly if Participant B can even create an infinite combo to supply a counteracting useful resource (extra attackers than Participant A’s blockers, extra injury than Participant A’s life, and many others.), then the unique quantity can all the time be out-enumerated. Nevertheless, it appears believable to me that Participant A may even be in peril if Participant B’s combo isn’t infinite. For instance, if Participant B may double a creature’s energy each flip for 40 turns, then it may simply wipe away 1 trillion life with a single assault, nevermind that it may have been attacking every flip alongside the way in which. Participant A would possibly be capable to survive assaults and doublings over 120 flip by naming 1 duodecillion, which feels like greater than sufficient turns to cowl any recreation of Magic. Nevertheless, if Participant B may double their creature’s energy a number of instances per flip, then this nonetheless will not be sufficient. In actual fact, if every flip Participant B may create a brand new copy of the supply which doubles their creature’s energy, then greater-than-exponential progress might be achieved. Right here my instinct is {that a} Googol life will not be sufficient to ensure Participant A indefinite security, whereas a Googolplex could also be, however is impractical to work with.
How rapidly is it attainable for Participant B to deal life loss to Participant A, utilizing any non-infinite mixture of playing cards? After all, I’m not solely within the life case, but in addition within the circumstances of making an arbitrary variety of permanents, or different assets, which can have totally different thresholds for security. For every sort of useful resource an infinite combo that doesn’t win a recreation outright can create, what quantity is so giant that it’s nearly not possible to remorse not naming a bigger quantity?
