\par An expected value of the game is the total of all of expected payoffs of the consequences in the flips; thus, there is an infinite number of dollars a player can win in the game. Assume that the measurement of utility throughout the game can be put in a function $u(w)$. As mentioned before, the expected utility decreases as the total winning prize increases; thus, Bernoulli suggested the use of a logarithmic function, $u(w) = ln(w)$ to show the graph of the paradox. According to Ole Peters, who contributed in the writing of “The Time Resolution of the St Petersburg Paradox”, Bernoulli proposed the idea of the logarithmic function with the perception of an increasing in the player’s wealth correlates with the increase in utility, in which
