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 a parameters)
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 a parameters)