lyonhaert wrote: ↑3 years ago
tstorm823 wrote: ↑3 years ago
...because Arcbond damage isn't going to deal the same damage to every player.
How so?
Players with lower life totals can die first to Arcbond even without Taunter damage aimed at them, which means they don't contribute to the calculation at all. If the opponents all have less life, you don't need to calculate. If the opponents all have more life, the calculation becomes simple arithmetic after some algebra:
Total Damage = Arcbond + Taunter; substitute in the calculations for how much of each type of damage we can do.
Total Damage = [our life - 1]*[# of opponents] + [our life + 1]; rearrange terms a bit
Total Damage = [our life - 1]*[# of opponents + 1] + 2; then redefine the second brackets
Total Damage = [our life - 1]*[# of players] + 2.
Which if we take a 4-player game, means we can do damage to opponents equal to 4*(current life total) - 2.
Or if we want to rearrange to answer "how much life do I need to win", you get:
Our life = (sum of opponents' life totals - 2)/(# of players) + 1
So to beat 3 opponents with a total of 102 life, we'd need 26 life yourself, so we can do 25 Arcbond damage to each and 27 Brash Taunter damage, for 102 total.
BUT all that would be wrong if our life total is in the middle, because any opponent with less that 25 life will die before the last Arcbond and mess up the math. So if the opponents had 102 life because they had 50, 42, and 10 life, the player with 10 would take 10 damage, the other two would take 25 Arcbond damage for 60 total Arcbond damage, and less than 42 Taunter damage to finish the job. So there is no single step equation where you can just plug in all the numbers and call it a day. You have to do it in 2 steps, where the first step is ignoring any player with less life than us. So instead, we'd need:
Amount of life needed to win = (sum of all higher life totals than ours - 2)/(# of opponents with more life +1) + 1
So if we had opponents with 10, 42, and 50 life, and we were at 30 and wanted to know if that was enough, we do:
Is 30 > (42 + 50 -2)/(2 +1) + 1.
Is 30 > 31
Answer is no, we'd need to be at 31 to win that game, so we could do 30 Arcbonds and 32 Brash Taunter damage (12 to the player with 42, 20 to the player with 50) before dying ourselves.
Another perspective is to take out the arcbond damage first, add up the remainder, and compare it to possible taunter damage. Doing [our life -1] arcbond damage to each, so the difference is (opponent's life - [our life - 1]), so if we were to say our life total is u, and an opponent's life is t, and n is the number for opponents, we'd look for:
u ≥ Σ(t - u + 1) - 1, for all values of t > u.
And if you put the example numbers above, you get 30 ≥ 33 which is false again, or 31 ≥ 31, which is true. But again, you can't just shove each players' life total into a single equation and pop out the right answer, it's a multi-step analysis, which means you can't ever condense it to "here's the equation in every instance, do some arithmetic".
