Douglas Zare writes:
Suppose to start off each match, you make a blunder worth 20% mwc, but
then you and your opponent play perfectly. Then you will win 30% of the
time, and every time you win, your net luck will be +70%. Every time you
lose, your net luck will be 30%. If you win 3 games in 10, then your
total luck would be 210%210%=0%.
The total luck should average to 0 in the long run. However, the stronger
player will be luckier most of the time. In a match between players who do
not play at a novice level, the luckier player wins, so it is not useful
to check who is luckier if you already know who won the match. What is
useful is to see how much luck was used.
