[Utah]

[ QUOTE ]
The answer is easy: which option maximizes your expected growth?

[/ QUOTE ]That doesn't seem to be an easy question to answer because it is dependent on the +ev of the bet with the expected winrate of the bet. For the bet in question, the edge is 4.2% and Kelly says the optimal bet is $1000. So, I expect to make $42 dollars on the bet. But, that doesn't seem right because I can instantly arb for $20 with zero risk.

So, in order to make the softside bet only, I need to give back the $20 I can get for basically doing nothing. In essence, I am being charged $20 for the bet upfront and thus in lowers the rate to something under 4.2%. If it is lower than 4.2% then the kelly value drops below $1000 and I am betting too much.

I believe kelly compares between betting and not betting. But, I don't think it accounts for the alternative of, "don't take any risk and you get X amount for free".

To summarize:
false - take bet and expect $42. Don't take bet and expect nothing
True - take bet and expect $42. Don't take bet and get free $20.

Something seems amiss. Again, I could be missing something completely obvious and my logic could be 100% wrong.