(1) From the block diagram, we know that this is a block diagram with two conditions, combined with the conditions given in the title.

The first condition box in the program block diagram should be filled with M=2, and the second condition box should be filled with n = 6.

According to the meaning of the question, when A wins two games in a row or B wins two games in a row, the game ends at the end of the second game.

With p2+( 1? p)2=59。

P = 23 or p = 13.

∫p > 12，

∴p=23.

(3) According to the meaning of the question, all possible values of ξ are 2, 4 and 6.

Let every two games be a round, then the probability that the game will stop at the end of the round is 59. 5%.

If the game will continue at the end of this round, both parties must score one point in this round.

At this time, the result of this round of competition has no influence on whether the next round of competition will stop.

So p (zeta = 2) = 59,

P(ξ=4)=( 1？ 59)(59)=208 1,

P(ξ=6)=( 1？ 59)( 1? 59)? 1= 168 1.

∴ The distribution list of random variable ξ is:

∴eξ=2×59+4×208 1+6× 168 1=2668 1.