If your picks are coin flips my expected profit is $2.50 if you bet five games and 5 if you bet ten games with no forgiveness. But capping your losses at 55 (rather than the normal 110) still results in an EV of about 4 for me. In other words if you planned to bet five games with me, I substantially increase my “earn” if I let you bet five more for the same amount without increasing your maximum loss. Do you see why?
“Why” is because you only cost yourself $55 once in 1024, You cost yourself $34 (when he goes 1-9) ten in 1024, and $13, forty-five in 1024. Thats about a dollar in EV which brings your EV down to about $4. A dollar less than if he got no forgiveness, but about $1.50 more than if he wasn’t allowed to bet five extra games. Variations on this concept can be applied to almost any gambling game.