So there is this excellent flash game, Monster's Den. In order to make a high score, I must complete many battles..this question is about battles with the Legendary Monsters.
The target is to reduce the single enemy's HPs to 0 as quickly as possible. To do this, physical damage is very slow (these are strong enemies) - we are going to use poison, which leads in an arithmetic progression style of attack.
T is a time constant used below.
H is the enemy health.
P is the poison attack.
The game is turn based. Each turn, each character gets to either make an action (takes T time), pass (do nothing, takes T/2 time), or leave the battlefield without being able to return (takes 0 time).
Enemy: Every time will make an attack (which we dont care about) which takes T time. Each round, its HP is reduced by its accumulated poison.
Mariah: Can attack in order to increase the enemy poison accumulation by P.
George: Can make an attack with unimportant damage. There is a 25% probability that nothing else happens, and then the round will have taken T time. Else, there is a 75% probability that Mariah is led to make a follow up attack, causing P as before, and this whole thing will have taken 2T time. As an exception, George may NEVER leave the battlefield.
Regina: Can make an attack with unimportant damage, with 100% probability of leading Mariah into attacking, and this whole thing will have taken 2T time.
What is the tactic that minimizes the time of the battle? Provide a formula for that minimum time.
From the comments, I gather the question is not clear enough. I will thus pose some thoughts:
In the beginning, one should find the optimal character setup for rapid poisoning. George must always be there, and Mariah must be too in order to poison, so the first question in: is regina's time worth the extra poison she generates?
Near the end, the poison accumulation is so large that increasing it is not worth its time. It is sure that in the optimal strategy, the final step is to have George pass and wait until the poison does its job. The thing is, when is the sweet time spot for each character to leave.