Problem 2697. Probability of winning single-elimination tournament

Find the probability that the p^{th} player will win a single-elimination tournament with 2^n players where M(i,j)=probability that player i will beat player j in a head-to-head matchup. In the first round player 1 plays player 2, player 3 plays player 4 and so on. (In each round each surviving competitor plays his surviving "next door neighbor" in the bracket.)

See also problem 2254.

Trivial example :

if

M = [ NaN 0.7 ; 0.3 NaN ]

then

winprob(M,1)=0.7 

and

winprob(M,2)=0.3