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)

SimpleStacker

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.

oracle

Predyx Buddy: Trading Tool for LMSR-Based Prediction Markets

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. 