How much should you risk?

There is a closed form solution (it's just maximising some logs, so differentiable) but I just did it in excel which is much quicker.

GAT

 

I still wonder why your excel solution to the OP puzzle was so off.

 

Only the one for the first two moments was wrong ( the full distributional one was correct). And I didn't even use excel for that, just the nearest envelope.

GAT

 

Yeah, it's a 2 min job in excel.

 

No. It wasn't. botpro gave the correct answer.

 

In my world 77.793% versus 75% means diddly squat....

GAT

 

So how did you get 99.4% for the next puzzle?

 

In the first puzzle I just read the peak off a graph.

In the second puzzle I used solver to get a more precise answer.

While this is intellectually interesting, you and I both know that in the real world you'd be lucky to know your correct Kelly to within an order of magnitude.

GAT

 

The new Kelly formula does better than an order of magnitude in the real world. And it's perfectly safe at half-Kelly.

 

No closed solution for the puzzle in the OP. Too many outcomes.