Hi! I’ve done a fair amount of betting beliefs for fun and calibration over the years; I think most of these issues are solvable.
A is a solved problem. The formulation that I (and my local social group) prefer goes like “The buyer pays $X*P% to the seller. The seller pays $X to the buyer if the event comes true.”
The precise payoffs aren’t the important part, so long as they correspond to quoted probabilities in the correct way (and agreed sizes in a reasonable way). So this convention makes the probability you’re discussing an explicit part of the bet terms, so people can discuss probabilities instead of confusing themselves with payoffs (and gives a clear upper bound for possible losses). Then you can work out exact payoffs later, after the bet resolves.
(As a worked example, if you thought a probability was less than 70% and wanted to bet about $20 with me, if you “sold $20 at 70%” in the above convention, you’d either win $2070%=$14 or lose $20-($2070%)=$6. But it’s even easier to see that you selling a liability of $20p(happens) for $2070% is good for you if you think p(happens)<70%.)
You’ve right that odds are a terrible convention for betting on probabilities unless you’re trying to hide the actual numbers from your counterparties (which is the norm in retail sports betting).
Hi! I’ve done a fair amount of betting beliefs for fun and calibration over the years; I think most of these issues are solvable.
A is a solved problem. The formulation that I (and my local social group) prefer goes like “The buyer pays $X*P% to the seller. The seller pays $X to the buyer if the event comes true.”
The precise payoffs aren’t the important part, so long as they correspond to quoted probabilities in the correct way (and agreed sizes in a reasonable way). So this convention makes the probability you’re discussing an explicit part of the bet terms, so people can discuss probabilities instead of confusing themselves with payoffs (and gives a clear upper bound for possible losses). Then you can work out exact payoffs later, after the bet resolves.
(As a worked example, if you thought a probability was less than 70% and wanted to bet about $20 with me, if you “sold $20 at 70%” in the above convention, you’d either win $2070%=$14 or lose $20-($2070%)=$6. But it’s even easier to see that you selling a liability of $20p(happens) for $2070% is good for you if you think p(happens)<70%.)
You’ve right that odds are a terrible convention for betting on probabilities unless you’re trying to hide the actual numbers from your counterparties (which is the norm in retail sports betting).