¥E Å peN – p – (1-p)eN + (1-p)
–As N ˆ infinity, the first term becomes very large (positive), the third term very
large (negative), and the
other terms are negligible by
comparison.
¥So for Ron to have the maximum winnings, he should choose p = 1:
–E Å eN, which will
become arbitrarily large as N
ˆ infinity, no matter how small e is.