What would the lottery prize need to be for our expectation to be positive ?
From example 6, we have E = Zp - 1 + p.
So, E > 0 → Zp > 1 - p → Z > ( 1 - p ) / p → Z > c - 1 = 13,983,815
The prize would have to be greater than $13,983,815.
For prizes bigger than this amount the advantage would be in our favor if we could afford to play a large number of times ( see exercise 5 ). Most of us could never afford to do this, and it is unrealistic to expect such a big prize to be offered for the thousands of trials it might take us to achieve our first win.