A man has to win two games in a row in order to win a prize. In total, he has to play only three games. The opponents are weak or strong. He has to at least play one strong opponent, and he cannot play consecutively two weak opponents. What sequence should he choose to play?

w: probability of winning against weak player
s: probability of winning against strong player

w>s>=0

now there are 3 ways to play which are
wss,sws,ssw

wss
the odds of getting two in a row are

w*s+s*s=s*(w+s)

sws
odds of getting two in a row here are
s*w+s*w=2*s*w

ssw
odds are the same as wss because of symetry

so which is the better order comes down to asking which is greater s*(w+s) or 2*s*w

start with our original assumption that w>s
w>s
w+w>s+w
2w>s+w
2sw>s(s+w)

thus sws is truely the bettter strategy  as Oskar pointed out

Posted by Daniel on 2006-08-01 09:14:46