Games of Chance. Given a fixed budget, how should we play the machines?

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Games of Chance

Given a fixed budget, how should we play the machines?

 What does ‘probability’ mean?  Relative frequency of occurrence of an event v Long term

Door 1Door 2Door 3If SwitchIf Stay

MACHINE 1MACHINE 2

MACHINE 1MACHINE 2 Costs $5 to play Pays you $105 with probability 1/5 Costs $1 to play Pays you $1001 with probability 1/50 Which one is the better machine to play?

MACHINE 1MACHINE 2 Average payoff = $16Average payoff = ~$18 So always play machine 2!

 Probability  ‘How likely am I to hit the jackpot?’  Expected value  `How much on average will I make playing this machine?’

 Two competing forces  ‘Exploration’ – try out a new machine  ‘Exploitation’ – stick with the reliable machine  Examples?