Example 6.1a In some situations, the only type of wagers allowed are ones that choose one of the outcomes i (i = 1, ..., m) and then bet that i is the outcome of the experiment. The return from such a bet is often quoted in terms of odds. If the odds against outcome i are oi (often expressed as oi to 1), then a one-unit bet will return either oi if i is the outcome of the experiment or 1 if i is not the outcome. That is, a one-unit bet on i will either win oi or lose 1.

Exercise 6.5 In Example 6.la, show that if m 1 #1 1+ 0; then the betting scheme (1 +0;)-1 xi 1- 21-1(1+0;) -1 i = 1, ...,m, will always yield a gain of exactly 1. Exercise 6.5 In Example 6.la, show that if m 1 #1 1+ 0; then the betting scheme (1 +0;)-1 xi 1- 21-1(1+0;) -1 i = 1, ...,m, will always yield a gain of exactly 1