Sorry to go mathy on everyone. But here goes.
Assuming that the cursed individual takes all opportunities to wear panties regardless of the consequences, then they have a 1 in 2 chance of wearing panties on a given day. Per the rules of probability, this means that the chance of wearing panties n days in a row is 1/(2^n). Therefore, for the varying difficulty levels, the probability of wearing panties for the correct number of days in row is:
- n=3, P= 1/8
- n=4, P= 1/16
- n=5, P= 1/32
- n=6, P= 1/64
- n=7, P= 1/128
- n=8, P= 1/256
The rule of thumb that I learned for estimating an expectation value is that we expect to see a successful result, on average, after as many trials as the number in the denominator. That is to say, if you are trying to roll a specific number on a six sided die, you will average about 6 rolls per trial. Obviously, sometimes you will get it in one try, but sometimes it will take ten or more.
Coming back to this dare, it means that we can (and this is an oversimplification, but should give a rough estimate) expect to see the cursed individual freed after number of days equal to the denominator of the probabilities above. This would mean that the expected duration of this dare for each difficulty is:
Very Easy: 8 days
Easy: 16 days
Medium: 32 days (~1 month)
Hard: 64 days (~2 months)
Very Hard: 128 days (~4.25 months)
Impossible: 256 days (~8.5 months)
As I said, though, this is a simplification, and if anyone else out there knows a better way to work through the probabilities, I'd love to hear about it. Just maybe in the lounge, for the sake of everyone who would have to listen to us.
P.S. By the way, Sodium, nice dare, and Squirell, thanks for the adaptation. It makes me wish I had a submissive I could subject to it.