386 THE HANDBOOK OF PORTFOLIO MATHEMATICS
0. 75 × 0. 75 × 1. 5 × 1. 5 × 1. 5 = 1. 8984375 (ruin)
0. 75 × 0. 75 × 1. 5 × 1. 5 × 0. 75 = 0. 94921875 (ruin)
0. 75 × 0. 75 × 1. 5 × 0. 75 × 1. 5 = 0. 94921875 (ruin)
0. 75 × 0. 75 × 1. 5 × 0. 75 × 0. 75 = 0. 474609375 (ruin)
0. 75 × 0. 75 × 0. 75 × 1. 5 × 1. 5 = 0. 94921875 (ruin)
0. 75 × 0. 75 × 0. 75 × 1. 5 × 0. 75 = 0. 474609375 (ruin)
0. 75 × 0. 75 × 0. 75 × 0. 75 × 1. 5 = 0. 474609375 (ruin)
0. 75 × 0. 75 × 0. 75 × 0. 75 × 0. 75 = 0. 237304688 (ruin)Now my probability of ruin hasrisento 10/32, or .3125. This is very dis-
concerting in that the probability of ruin increases the longer you continue
to play.
Fortunately, this probability has an asymptote. In this two-to-one coin-
toss game, at the optimalfvalue of .25 per play, it is shown the table below:
Play # RR(.6)2 0.25
3 0.25
4 0.25
5 0.3125
6 0.3125
7 0.367188
8 0.367188
9 0.367188
10 0.389648
11 0.389648
12 0.413818
13 0.413818
14 0.436829
15 0.436829
16 0.436829
17 0.447441
18 0.447441
19 0.459791
20 0.459791
21 0.459791
22 0.466089
23 0.466089
24 0.47383
25 0.47383
26 0.482092