So this isn't a lethal puzzle exactly, it's more of a "what gives the best chance for lethal?" I was watching Trump play Patron Warrior vs SilentStorm playing what looked like a Face Hunter. It was a close game and both players were racing. In the end Trump won with some lucky boom bot RNG. Here was the board state on the final turn (sorry I didn't get a screenshot): http://i.imgur.com/GxdHJYo.jpg
SilentStorm has 19 life, an Arcane Golem, Leper Gnome, and 3 hounds vs Trump's Dr. Boom and 2 boom bots and equipped Fiery War Axe. Trump has Whirlwind, Inner Rage, and Death's Bite in hand.
Trump chose to equip Death's Bite, Inner Rage the Boom, send everything to face leaving SilentStorm at 4, and finally played the Whirlwind to kill everything but the Arcane Golem and Dr. Boom. The boom bots went 1 to the Arcane Golem and 4 to face for lethal.
Immediately after chat started claiming that playing Inner Rage on the Arcane Golem rather than Dr. Boom gave a better chance of lethal, a play Trump did not appear to consider. I wasn't convinced so I did the math!
Inner Rage on Dr. Boom: opponent at 4 life 3/4 that 1 bot hits face and 1 hits golem (since if the golem is hit it will always die, the chance to go golem then face is 1/2, and the chance to go face then golem is 1/4) *In this case the 1 bot that hits face must hit for 4 to get lethal, this occurs 1/4 times *Therefore, this case contributes (3/4)(1/4) = 3/16 to our win probability when we cast Inner Rage on Dr. Boom 1/4 that both bots hit face *There are 16 different possibilities when both bots go face (1,1 2,2 3,3 4,4 1,2 2,1 1,3 3,1 1,4 4,1 2,3 3,2 2,4 4,2 3,4 4,3) *Of these outcomes, 13/16 deal 4 or more damage *Therefore, this case contributes (1/4)(13/16) = 13/64 to our win probability when we cast Inner Rage on Dr. Boom *Win probability = 3/16 + 13/64 = 25/64
Inner Rage on Arcane Golem: opponent at 6 life *100% that both bots go face, of the 16 possibilities 6/16 deal 6 or more damage *Win probability = 6/16 = 24/64
So it turns out that casting Inner Rage on Dr. Boom was the correct play by a very slim margin.
TL;DR: Trump is 1/64 better than chat
