In the game Hearthstone there is a playing board containing friendly and enemy minions, and two heroes - yours and the enemy's.
To generalize and simplify, we will assume it's your turn, the opponent has 0-7 minions with given health values on the board, and is at H life points. We will ignore our side of the board entirely.
Now we will cast a supercharged version of Arcane Missiles. This ability shoots a random enemy (uniformly selected from all alive minions and the hero) for 1 damage, repeated A times. Note that if a target dies (reduced to 0 health), it can not be hit again.
Given H, A and a list L containing the health values of the minions, output the probability as a percentage accurate to 2 digits after the decimal point that either or both the hero dies, or every minion dies (clearing the board).
Some examples logically derived:
H: 30, A: 2, L: [1, 1] We have no chance of killing our opponent here. To clear the board, both shots must hit a minion. The first shot has a 2/3 chance of hitting a minion, then that minion dies. The second shot has a 1/2 chance. The probability of clearing the board or killing our opponent is thus 2/6 = 33.33%. H: 2, A: 3, L: [9, 3, 4, 1, 9] We have no chance of clearing the board here. 2/3 shots must hit the hero. However, if any of the shots hit the 1 health minion, it dies, increasing the odds for future shots. 4/6 the first shot hits a health minion. The next two shots must hit the hero, for a total probability of 4/6 * 1/6 * 1/6. 1/6 the first shot hits the 1 health minion and it dies. The next two shots must hit the hero, for a total probability of 1/6 * 1/5 * 1/5. 1/6 the first shot hits the hero. Then there are three options again: 1/6 the second shot hits the hero. 4/6 the second shot hits a healthy minion. The last shot must hit 1/6. 1/6 the second shot hits the 1 health minion. The last shot must hit 1/5. This last option gives a probability of 1/6 * (1/6 + 4/6 * 1/6 + 1/(5*6)). The total probability is the chance of any of these scenarios happening, or: 4/6 * 1/6 * 1/6 + 1/(6*5*5) + 1/6 * (1/6 + 4/6 * 1/6 + 1/(5*6)) = 7.70%
As you can see, it gets complicated quickly... Good luck!
Your score is the number of bytes of code of your answer. If your code computes a probability exactly rather than simulating boards, halve your score. Lowest score wins.