BJFan: BJA3 Optimal Kelly

[Don Schlesinger]

> Don,

> You say that change in EV is based purely on the
> playing expectations and that bet size isn't used here
> I can deduct two things:

> 1) if CF=2*(E1-E2)/(V1-V2) depends on bet sizes as you
> say in the book, and E1-E2 doesn't, then V1-V2 must be
> calculated based on bet sizes. This implies that my
> method was wrong (my V1-V2 was done with a unit bet)
> but the results match!

In order to simplify, there is an assumption, to get just a single index, instead of several, that you are betting optimally at all times. I think MP mentions that on p. 373.

> 2) if 1) is true I can't understand why CF is
> calculated with a part that doesn't depend on bet size
> (E1-E2) and another part that depends on bet sizes
> (V1-V2)

> There's another possibility and it's that I'm talking
> nonsense which is possible!

> Sorry to bother you but I'd like to be convinced of
> what I'm doing, that's me.

It might be easier if you followed the step-by-step procedure of MP in the book, and then followed that with an example of your own attempt to replicate what he is done. Then, we might compare the two, to see if there is a problem.

Don

[BJFan]

Don,

I'm taking a second look at your RA text and I have this question:

I can't figure out the units of f because the units of CE and E are [$], V is [$ squared], so f should be [1/$], but you put [%] in table 13.13. Am I missing something?

BJFan

[Don Schlesinger]

> Don,

> I'm taking a second look at your RA text and I have
> this question:

> I can't figure out the units of f because the units of
> CE and E are [$], V is [$ squared], so f should be
> [1/$], but you put [%] in table 13.13. Am I missing
> something?

Not sure. MathProf defined f, at the bottom of p. 371, as "the size of the wager, expressed as a fraction of the Kelly-equivalent (optimal) bankroll." As such, it wouldn't have any units, would it?

Later, on p. 378, in the charts, it seems to me that Opt. f is given as percentage of the optimal $10,000 bankroll. So, if it is given, as, say, 2.0%, that would eventually equate to $200.

Frankly, I've never given much thought to the units and have always concentrated on the numbers.

Don