3

Suppose the board consists of the following cards and relics:

  • 1x Meteor Strike+
  • 2x Coolheaded+
  • 1x Snecko Eye
  • 1x Philosopher's Stone
  • 1x Callipers
  • (other relics less relevant)

While this seems like an infinite deck1, it actually is not, due to the 99 energy limit. It's a deck that deals a very large but finite amount of damage. Assuming the player currently has:

  • 4 energy
  • 99 energy
  • X energy (0 <= X < 99)

What is the currently expected amount of damage they would deal to an enemy with infinite health, assuming they play Meteor, Coolheaded, Coolheaded in a cycle?

Note: The answer isn't an infinite number because each cycle gives you 6 energy, but may consume anywhere from 0 to 9 energy. So if, 33 cycles in a row (99 cards in a row) you only roll 3's, then you run out of energy. The probability of that is 1 in 1/3 ^ 99 = 1.72E47 If meteor strike gave out four orbs, then the expected damage, given P expected cycles, would thus be about 33 x 30 x 1.72E47 ~ 1.70E50. Of course, there are many other combinations as meteor strike gives you 3 orbs (6 energy): with a sufficient number of 3s you will run out of energy.

Markov chains could be useful to solve this problem.

1: It is assumed the enemy has 'Beat of Death' and thus you need to play two Coolheaded+ to generate enough Block.

2: When solved, this problem is useful to answer: How big does the Corrupt Heart need to be to give you a 50% chance of winning, if its damage limit is still 25% of its total hp? (slightly less than 17.5 times the expected damage).

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