the game Egg Roulette play player initially 2r raw egg 2C cook egg place randomly carton the shell leave way distinguish raw egg cook egg one time player select egg smash egg hisher forehead if egg cook happen egg raw mess this continue player break R raw egg point player declare loser player winsthe order player turns describe stre A b character ith character tell player choose ith egg Traditionally player turn go that follow order ABABAB this is not fair second player win We d like find well order player turn Lets define unfairness order absolute difference player win probability second player win probability Were interested ordering minimize unfairness we consider order valid contain number as BsYou give stre s length 2rc contain a b character an ordering say match S differ S position S contain of valid ordering minimize unfairness match S