By “better than 50% accuracy” I am trying to convey “Provide an algorithm such that if you ran a casino where the players acted as ROB, the casino can price the game at even money and come out on top, given the law of large numbers”.
(Perhaps?) more precisely I mean that for any given instantiation of ROB’s strategy, then for any given target reward R and payoff probability P<1 there exists a number N such that if you ran N trials betting even money with ROB you would have P probability to have at least R payoff (assuming you start with 1 dollar or whatever).
You can assume ROB will know your algorithm when choosing his distribution of choices.
How is “better than 50% accuracy” defined?
You need to have it on every possible ROB’s strategy?
Or in general, with some measure on the (uncountable) set of strategies? In this case, what measure?
By “better than 50% accuracy” I am trying to convey “Provide an algorithm such that if you ran a casino where the players acted as ROB, the casino can price the game at even money and come out on top, given the law of large numbers”.
(Perhaps?) more precisely I mean that for any given instantiation of ROB’s strategy, then for any given target reward R and payoff probability P<1 there exists a number N such that if you ran N trials betting even money with ROB you would have P probability to have at least R payoff (assuming you start with 1 dollar or whatever).
You can assume ROB will know your algorithm when choosing his distribution of choices.