I was playing tennis with my brother. We were playing in a format such that in order to win you have to score $X$ number of points. I gave my brother a handicap.
Scenario 1: We play until $7$ points. He gets a $5-0$ lead.
Scenario 2: We play until $10$ points. He gets a $7-0$ lead.
In the first scenario, I only get two chances to err. In the second scenario, I have a buffer of 3 points. However, in the first scenario, I have to win less points to catch up. Whereas in the second scenario I have to win more points to catch up. How do I quantify the tradeoff between the margin of error and the raw number of points needed to win?