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There is reason we do it one-by-one is:

  1. The cost to buy bundled shares across multiple outcomes is always less than the cost to buy one-by-one.
  2. 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.)

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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.

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Thanks for pointing that out. I'll have to re-visit my assumption regarding bundled shares.