> Or put in another way, if you know the distribution is normal, you can bet on the the result being near the center and come out on top, but if it’s uniformly random distribution all hopes are out.
That’s just because the payout distribution and real distribution are different, and there’s a place the payout is at a loss.
If you bet on a uniform distribution of 2 through 12 that payed out according to a normal distribution, you’d make a killing betting on 2 or 12 (the “outliers”). If you roll 2d6 (normalish) and get paid according to a uniform distribution, you’ll make a killing betting on 7.
That’s just because the payout distribution and real distribution are different, and there’s a place the payout is at a loss.
If you bet on a uniform distribution of 2 through 12 that payed out according to a normal distribution, you’d make a killing betting on 2 or 12 (the “outliers”). If you roll 2d6 (normalish) and get paid according to a uniform distribution, you’ll make a killing betting on 7.