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

${\displaystyle p^6+\left(\genfrac{}{}{0ex}{}{6}{5}\right)p^5(1-p)p+\left(\genfrac{}{}{0ex}{}{7}{5}\right)p^5(1-p{)}^{2}p+\left(\genfrac{}{}{0ex}{}{8}{5}\right)p^5(1-p{)}^{3}p+\left(\genfrac{}{}{0ex}{}{9}{5}\right)p^5(1-p{)}^{4}p+\left(\genfrac{}{}{0ex}{}{10}{5}\right)p^5(1-p{)}^5}$

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

${\displaystyle 0.4^6[1+6*0.6+21*0.6^2+56*0.6^3+126*0.6^4+252*0.6^5=0.2465018}$

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.