Page 210 - Probability Demystified

CHAPTER 11 Game Theory 199

19p ¼ 16

19p 16
¼
19 19
16
p ¼
19
Hence, the player (offense) should run 16 of the time, and pass 3 of
19 19
the time.
The value of the game when p ¼ 16 is
19

16 16
2p þ 10ð1 pÞ¼ 2 þ 10 1
19 19

16 3
¼ 2 þ 10
19 19

5
¼ 3
19

Let s ¼ the probability of defending against the run and 1 s ¼ the
probability of defending against the pass; then

2s þ 5ð1 sÞ¼ 10s 6ð1 sÞ

2s þ 5 5s ¼ 10s 6 þ 6s

3s þ 5 ¼ 16s 6

3s 16s þ 5 ¼ 16s 16s 6

19s þ 5 ¼ 6

19s þ 5 5 ¼ 6 5

19s ¼ 11

19s 11
¼
19 19
11
s ¼
19