Say I roll $100$ dice. Make a market on the sum of all the dice.
How does one go about approaching these types of problems? Here's my approach:
I expect the sum to be $350$, so this is where my market will be centered around. The variance of a dice roll is $2.9$, so in total, I expect the variance to be $290$. Square root of this is around $17$, so that is $1$SD. I'll make my market centered be $2$SD wide on each side, so I'll make my market be $[350-(17)2, 350+(17)2]$.
Another question: Why wouldn't I just make the lower end of the market equal to 0, so that I can buy it for even $0?