Answer to Question #41959 in Math for Shashi Shekhar Sharma

Question

Consider a purely probabilistic game that you have the opportunity to play. Each time you play there are n potential outcomes x1, x2, ..., xn (each of which is a specified gain or loss of

euros). These outcomes x1, x2, ..., xn occur with the probabilities p1, p2, ..., pn respectively (where p1 + p2 + ... + pn = 1.0 and 0 <= pi <= 1 for each i).

Positive xi values mean a gain of |xi| euros and negative values mean a loss of |xi| euros. Assume that x1, x2, ..., xn and p1, p2, ..., pn are all known quantities. Furthermore, assume that each play of the game takes up one hour of your time, and that only you can play the game (you can't hire someone to play for you).

Let M be the game's expected value. That is, M = p1*x1 + p2*x2 + ... + pn*xn. Let S be the

game's standard deviation. That is, S = SquareRoot( p1 * (x1 - M)^2 + p2 * (x2 - M)^2 + ...

+ pn * (xn - M)^2 ).

1) In the real world, should a rational player always play this game whenever the expected value M is not negative? Yes/NO Explain please...