You play a gambling game with your friend in which you win 30% of the time and lose 70% of the time. When you lose, you lose $1.

Question

What profit should you earn when you win in order for the game to be fair? (Round your answer to the nearest cent.)
$

 

 

Answer 1

Ivy,

 

Let p = probability of winning each time you play the game = 0.30

(1-p) = probability of losing each time you play the game = 0.70

     W = $ you get when you win a game (the unknown)

      L = $ you pay when you lose a game ($ 1.00 )

     N = Number of times the game is played (large number, say over 100, to get a tight estimate (small std. deviation)

           around the computed mean.

 

To be considered fair, your mean gains from games won must balance your mean losses from games lost, when N games are played.

 

Mean or average gain over N plays = pWN

Mean or average loss over N plays = (1-p)LN 

 

Balancing these two, gives the solution   W = (1 - p) L/p = 0.70 ($1.00)/0.30 = $2.33  as the N's cancel out.

 

Because a win is rarer than a loss, its payout has to be greater to make the game fair.