Depends what you do with the other 99.99% and the other three answers, I assume.
In a two-answer scenario, if I’m understanding bill’s version of the log scoring rule correctly, giving p=0.9999 to the right answer and p=0.0001 to the wrong answer should get you [log(0.9999)-log(1/2)]/log(2) ~= 0.99986 points. With four answers, giving p=0.9997 to the right answer and p=0.0001 to each of three wrong answers should get you [log(0.9997)-log(1/4)]/log(4) ~= 0.99978 points.
Depends what you do with the other 99.99% and the other three answers, I assume.
In a two-answer scenario, if I’m understanding bill’s version of the log scoring rule correctly, giving p=0.9999 to the right answer and p=0.0001 to the wrong answer should get you [log(0.9999)-log(1/2)]/log(2) ~= 0.99986 points. With four answers, giving p=0.9997 to the right answer and p=0.0001 to each of three wrong answers should get you [log(0.9997)-log(1/4)]/log(4) ~= 0.99978 points.