Originally posted on 06/03/2013:

Quote Originally Posted by mr.ed View Post
I would pick option #2 as profits would be greater because you imposed a very low wagering limits on option #1. Naturally, I would rather wager large amounts on option #1 while leaving option #2 and the (-EV) play out of it, but given the unusual parameters of the riddle, you have forced me to take option #2. Thank goodness these low limits aren't imposed in the real world!
And the point is

1. I did not impose anything. Math did.
2. Same conditions are absolutely present in a real world.

Here is why.

When you bet heads at 52% your edge is 4%
If you don't wont to expose yourself to a very substantial risk of ruin (going broke) math dictates that you cannot wager to win more than your edge. This is full Kelly. Very aggressive as it is.

So if you cannot win more than $100 with an edge of 4%, that means that your BR is $2500 max.
As I said, $100 limit is not imposed by me. It is just a function of your BR and your edge, if you want to be smart about it.

And that's where $1250 figure came from in option #2.
I did not dream it up. I just took your whole BR and divided it between two bets.
I can afford to do it now, since I can not lose.

This whole reasoning stays true in a real word exactly the same way.
Even though you have $2400 still "available" in a option#1, you can not touch it if you have any sense of self preservation.
Option #2 does not carry that burden and thus always preferable since it delivers higher EV in real money (although lower in %% terms, but who cares) with no additional risk. Actually, with no risk at all.

Unless your always bet limit, this type of analysis should always be performed when making decision to arb or not to make sure that your not shortchanging yourself.
And since betting limits is not something that done by overwhelming majority of readers in this thread, my point should be very useful indeed.

I really don't understand how something so obvious can be argued so intensely for such a long time.