I’m not sure of the math OTTOMH but isn’t fractional Kelly equivalent to having some credence that your model is correct and some credence that the market is correct?
In your example, it seems like you’re assuming that the event has a 0% chance of occuring in the worlds where your model is wrong, but that doesn’t make a lot of sense—the worst case from a betting perspective is that the true odds are equal to the odds that the market assigns, because that means that any bet you make will be -EV.
I’m not sure of the math OTTOMH but isn’t fractional Kelly equivalent to having some credence that your model is correct and some credence that the market is correct?
Ah, seems promising!
So, with my credence in my own model being x, and my credence in the market being y, p−qb/a becomes:
I’m not sure of the math OTTOMH but isn’t fractional Kelly equivalent to having some credence that your model is correct and some credence that the market is correct?
In your example, it seems like you’re assuming that the event has a 0% chance of occuring in the worlds where your model is wrong, but that doesn’t make a lot of sense—the worst case from a betting perspective is that the true odds are equal to the odds that the market assigns, because that means that any bet you make will be -EV.
Here’s an interesting case study for fractional Kelly in real world betting scenarios
Ah, seems promising!
So, with my credence in my own model being x, and my credence in the market being y, p−qb/a becomes:
xp+ya−xq+ybb/a
=xp+ya−xqa/b−ya
=x(p−qa/b)+ya−ya
=x(p−qb/a)
So, yeah, makes sense.