把每2盘看成一回合
甲胜: (2/3)*(2/3) = 4/9
乙胜: (1/3)*(1/3) = 1/9
平: 1 - 4/9 - 1/9 = 4/9

若出现胜负，结束；若平，继续下一回合

n回合后
甲胜概率为:
4/9 + (4/9)*(4/9) + [(4/9)^2]*(4/9) + ... + [(4/9)^(n-1)]*(4/9) = (4/5)*[1-(4/9)^n]
乙胜概率为
1/9 + (4/9)*(1/9) + [(4/9)^2]*(1/9) + ... + [(4/9)^(n-1)]*(1/9) = (1/5)*[1-(4/9)^n]
平局概率为
(4/9)^n

n取无穷大，则
甲胜概率80％，乙胜概率20％

n=6，则...自己算吧

……第5000贴竟然是这样的……