Economic and Game Theory
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There are two gladiators groups. Group A and Group B. Let assume that group A have 20 gladiators and group B have 30 gladiators. Every gladiator have a mark that represent his power in positive integer - 100, 140, 200, 80, 210 etc. The gladiators fight each other in couples.
The odds to win are:
If gladiator with 100 "power" fight against "150" gladiator, his odds to win is 100/(100+150). This is because that stronger gladiator have bigger chance to win. If 2 gladiators with the same "power" fighting, for example 100 Vs 100, the odds of each one to win is 50%. as the "power" gaps are bigger the odds if the one with the more "power" to win bigger.
Every group, A and B have a coacher that decide in which order to send the gladiators to the fight. he can send the stronger first and vice versa.
by The game rules the gladiator that wins go back to the end of the line - thats means that it is not possible that the strongest will fight all the battles. He stays with the same power that he had PLUS the power og the gladiator he won, and the gladiator that lose just leave. The battle continued until there are no more gladiators in one of the teams, and this is the losing group.
The question is, What will be the best strategy, and what will be the best order that the coacher should choose the gladiators he sending for the battle. (try to think before you continue to read).
The answer is very surprising. There is no need in a coacher at all. The order is totally not important. The odds of each group to win have nothing to do with the order of the gladiators fights. The odds to win equal to the total "power" of all the gladiators in the group divided by the total "power" of the gladiators in both of the groups together. Coachers are important... But maybe not that important.
THE BIG QUESTION: HOW CAN YOU PROVE THAT THE ODDS OF EVERY GROUP TO WIN IS NOT DEPENDS IN THE ORDER OF THE GLADIATOR ORDER? [Manage messages]