The probability of winning a 15 frame match was shown to be 0.2131 if the probability of winning a single frame is 0.4. To win an 11 frame match the player must be the first one to win 6 frames. The probability is

p6 + æ ç è 6 5 ö ÷ ø p5(1-p)p + æ ç è 7 5 ö ÷ ø p5(1-p)2p + æ ç è 8 5 ö ÷ ø p5(1-p)3p+ æ ç è 9 5 ö ÷ ø p5(1-p)4p+ æ ç è 10 5 ö ÷ ø p5(1-p)5

For p=0.4 and 1-p=0.6 this becomes

0.46[1 + 6*0.6 + 21*0.62 + 56*0.63 + 126*0.64 + 252*0.65 = 0.2465018

A player with a consistent chance of 0.4 of winning each frame is the weaker player in the match. The calculated chance of 0.2465 of winning over 11 frames gives him a better chance than 0.2131 of winning over 15 frames.