Never Lucky

Probability Level 2

You're playing a game of Havenslate™, the digital card game. It's your turn, and you must win now because it is certain your opponent will win on his next turn. Your opponent has 6 health and a Frostbreath Sasquatch minion with 5 health. You have no minions and only one card in your hand: Vindicating Conniption. This card deals 8 damage randomly split among your opponent and your opponent's minions. What is the probability that you win the game?

Details and Assumptions: Vindicating Conniption deals 1 damage at a time, each time choosing randomly between the Sasquatch and your opponent. You win the game if your opponent goes to 0 health.

\frac{7}{64}

\frac{37}{256}

\frac{1}{4}

\frac{93}{256}

\frac{3}{4}

1 solution

Andy Hayes
Oct 4, 2017

You will win if 6, 7, or 8 shots go to your opponent. This can happen in $\binom{8}{6}+\binom{8}{7}+\binom{8}{8}=37$ ways. The total number of ways the shots can be chosen is $2^8=256$ Thus, the probability you win is $\boxed{\frac{37}{256}}.$

Note : In this example, it's OK to ignore the case in which the Sasquatch dies. The math works out the same as if you have the Vindicating Conniption continue firing shots at the dead Sasquatch, because you would lose if more than 2 shots go to the Sasquatch anyways.

Never Lucky

1 solution

0 pending reports