More About Ability Checks (POSP)

__NOTOC__
One problem with ability checks as they now stand follows:
“Leon, see if your 17 Muscle fighter can lift that iron chest.”
(Rolling a d20) “Missed it. I rolled a 19.”
“Tomas, check if your 6 Muscle wizard can do it.”
“Yes!—I made it with a 4!”
The above reflects that sometimes a character with a high score will fail, only to have a character with a lower score get lucky and succeed. Depending on the number of points in each subability score, the character can make additional attempts at feats. The rule is: for each point in a subability above 15, the player can roll an additional 1d20 for checks against that subability. For example, because Leon's fighter has a 17 Muscle, the character can make up to three checks—the initial check, plus two more. So if Leon's fighter wants to force open a trap door, Leon rolls 3d20. If any of the dice register a successful check, the fighter opens the door. Tomas' character, with a 6 Muscle only rolls 1d20.
This multiple d20 system does not eliminate the possibility of a character with a low ability score succeeding where a character with a higher ability score fails. But the system does reduce the number of times such an improbable incident will occur.