Question: A garbler who makes 100 bets of $1, each at payoff odds of 8 to 1, wins 10 of these bets and loses 90.
a) How many dollars has the gambler gained overall?
b) What is the gambler's average financial gain per bet?
Suppose now that the gambler makes a sequence of $1 bets at payoff odds of rpay to 1. Define an empirical odds ratio nr ≠ to be the gambler's number of losses divided by the number of wind. So, in the numerical example above, rpay was 8 and r ≠ was 90/10 = 9. Show that the gambler's average financial gain per bet is $(rpay - r≠) / (r≠ + 1). Explain carefully the connection between this formula and the house percentage formula.