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No sophisticated formula - @SimpleStacker's math is 100% correct. We use LMSR.
I think my cost estimates for multi outcome markets may be misleading though. I realized that the order you buy shares and the amounts you buy them in matter. I think to minimize costs when executing a multi outcome strategy would be to buy the shares one by one, is this correct? Since this is cumbersome, maybe there should be a way to simultaneous buy shares in multiple outcomes with one trade.
There is reason we do it one-by-one is:
- The cost to buy bundled shares across multiple outcomes is always less than the cost to buy one-by-one.
- Bundled shares will be boon to the traders but bane to the creators. In other words, the creator will loose more sats.
That makes sense as a choice to make for your business. But it also means my calculator is wrong because it uses a bundled price. Something I'll need to go back and change.
(I guess the user can replicate it by buying one share at a time, but that is way too much work; also racks up transaction fees.)
Oh wait, both ChatGPT and Gemini are telling me that the cost function for LMSR is path independent. So executing a bundled trade using multiple single-outcome trades only costs more because of transaction fees, not because of the probability paths. If that's the case, my calculator is fine, since it ignores fees right now anyway.
Thanks for pointing that out. I'll have to re-visit my assumption regarding bundled shares.
Yes - you are right: https://chatgpt.com/share/6950836b-ca60-800e-8c48-16b9bb842be5
The optimal bet is only optimal if you have the correct beliefs, which you likely don't, so there isn't really an arbitrage opportunity here. The "expected profit" could be wrong if your beliefs are wrong.
Afaict, my math is the same as theirs. But I simplified the presentation a bit (with my discussion of phantom shares which abstracts from the parameters)
So cool!
I think Predyx uses more sophisticated formula, I mean maybe some adition to the formula. It's not that you can always win or there's always some arbitrage on a market. I'm not sure though. My maths is too weak to understand formulas a lot.
I'll still try this tool and see if it works.