A game is said to be fair if the expected value for winnings

A game is said to be \"fair\" if the expected value for winnings is 0, that is, in the long run, the player can except to win 0. Consider the following game. The game costs $1 to play and the winnings are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following probabilities apply. What are your expected winnings? Does the game favor the player or the owner? A gambler claimed that he had loaded a die so that it would hardly ever come up 1. He said the outcomes of 1, 2, 3, 4, 5, 6 would have probabilities 1/20, 1/6, 1/6, 1/6, 1/6, 1/6

Solution

the winnings are    $5 for red,$3 for blue,$2 for yellow,$0 for white

and the game costs $1 to play

hence we have

outcome:         Red    Blue    Yellow White

probability:       0.02     0.04     0.16     0.78

winning:             $5       $3        $2         $0

the game costs the player $1

hence the expected winning is 0.02*5+0.04*3+0.16*2+0.78*0-1= -$0.46 [answer]

it means that the game costs the player $0.46 . hence the game favor the owner [answer]