1. blackjack crusader: NO? for Don

Hi Don,

A two part question.

Does NO consider fixed bets or optimal resizing bets?

From an article by Brett Harris:

For a given ratio of max bet to min bet, a spread can be found which maximises the log growth of the bankroll, this corresponds to the spread which minimises the ratio of VAR/EV^2=NO for the entire system, with the growth rate given by G = 1 + 1/(2*NO).

I don't quite follow the second equation:
G = 1+1/(2*N0)

Is this the growth rate when betting optimally (resizing)?
Can you give an example using the formula with a NO of 14,000?

good cards

2. Don Schlesinger: Re: NO? for Don

> Hi Don,

> A two part question.

> Does NO consider fixed bets or optimal resizing bets?

N0 can be applied to any form of wagering; you just have to stipulate your terms. For all of my Chapter 10 charts, the bets are fixed, and the N0s that are provided assume such fixed-bet wagering.

> From an article by Brett Harris:

> For a given ratio of max bet to min bet, a spread can
> be found which maximises the log growth of the
> bankroll, this corresponds to the spread which
> minimises the ratio of VAR/EV^2=NO for the entire
> system, with the growth rate given by G = 1 +
> 1/(2*NO).

> I don't quite follow the second equation:
> G = 1+1/(2*N0)

> Is this the growth rate when betting optimally
> (resizing)?

Yes. I believe that all of Brett's studies were done with the assumption of optimal Kelly wagering.

> Can you give an example using the formula with a NO of
> 14,000?

Just plug in the number: Growth rate (logarithmic) is
1 + 1/28,000 = 1.0000357.

But, we really can't relate to such a number. That's why SCORE is easier to follow.

Don

> N0 can be applied to any form of wagering; you just
> have to stipulate your terms. For all of my Chapter 10
> charts, the bets are fixed, and the N0s that are
> provided assume such fixed-bet wagering.

> Yes. I believe that all of Brett's studies were done
> with the assumption of optimal Kelly wagering.

> Just plug in the number: Growth rate (logarithmic) is
> 1 + 1/28,000 = 1.0000357.

> But, we really can't relate to such a number. That's
> why SCORE is easier to follow.

> Don

So one can have a fixed bet NO and a continuous resizing NO. I did not know this!

What does the answer 1.0000357 mean?

I have bja2 and bja3, is there an easy way to convert the fixed SCORE to a continuous resizing SCORE?

Thank you again for your time.

4. Don Schlesinger: Re: Follow Up ?

> So one can have a fixed bet NO and a continuous
> resizing NO. I did not know this!

It's just a number. Maybe Brett would be unhappy using anything other than a continuous resizing scheme for a "pure" N0, but what's the point? It's not as if anyone can play that way. Continuous resizing is a somewhat useless concept in the real world, no?

> What does the answer 1.0000357 mean?

Nothing that anyone would care about. It's the logarithmic growth rate of the bankroll, under the conditions you gave me. If your response is a big "so what," then you're understanding that, this, too, is a somewhat useless concept.

> I have bja2 and bja3, is there an easy way to convert
> the fixed SCORE to a continuous resizing SCORE?

Not that I know of. What do you want the continuous resizing SCORE for? It's a completely useless number.

> Thank you again for your time.

My pleasure.

Don

> It's just a number. Maybe Brett would be unhappy using
> anything other than a continuous resizing scheme for a
> "pure" N0, but what's the point? It's not as
> if anyone can play that way. Continuous resizing is a
> somewhat useless concept in the real world, no?

If continuous resizing is the fastest way to grow wealth with the least risk? Then wouldn't the goal be to play as close to continuous resizing as possible?
Ex.
Playing .75 to .9 Kelly and resizing when 5% - 20% is won or lost. I put these numbers at less then full Kelly to account for real world considerations. I have experience playing this way, it can be done. Even if the improvement is just a couple % points doesn't the value increase because it is compounded?

> Nothing that anyone would care about. It's the
> logarithmic growth rate of the bankroll, under the
> conditions you gave me. If your response is a big
> "so what," then you're understanding that,
> this, too, is a somewhat useless concept.

> Not that I know of. What do you want the continuous
> resizing SCORE for? It's a completely useless number.

If one plays closer to optimal resizing then shouldn't a resizing SCORE be closer to reality then fixed SCORE?

I know how to figure the long run for fixed and continuous resizing. My long run is probably closer to the continuous numbers.
I know how to figure the EV or SCORE (I look at your book) for fixed bets. I do not know a simple way to figure the EV for continuous resizing?

Hmmmmm
Perhaps an easy way though inprecise?
Every time I reset my bets I know what the SCORE is and I know because I am resizing frequently it is cut roughly in half.

> My pleasure.

> Don

6. Don Schlesinger: Re: Follow Up ?

> If continuous resizing is the fastest way to grow
> wealth with the least risk? Then wouldn't the goal be
> to play as close to continuous resizing as possible?

It's a noble goal, but it's ridiculous in practice. You can't possibly know your precise advantage at every hand, you can't possibly bet the correct amount, even if you did know it, and you can't even remotely be bothered with all that when you're playing.

> Ex.
> Playing .75 to .9 Kelly and resizing when 5% - 20% is
> won or lost.

That's not continuous, now, is it? :-) So, now that we've got that silly notion out of our heads, it's just a question of how frequently, or infrequently, we choose to resize and make adjustments. We strike a compromise between optimality and practicality. For most players, practicality is more important.

> I put these numbers at less then full
> Kelly to account for real world considerations. I have
> experience playing this way, it can be done. Even if
> the improvement is just a couple % points doesn't the
> value increase because it is compounded?

With all due respect, you're probably deluding yourself into thinking that you're doing it precisely. The effort FAR outweighs any potential minuscule gain.

> If one plays closer to optimal resizing then shouldn't
> a resizing SCORE be closer to reality then fixed
> SCORE?

I don't know what you mean by "reality." To me, "reality" is how 99.9% of players play in the real world. Reality is not betting \$112.37 a hand, nor restructuring my entire bet ramp next shoe, because this shoe has been a disaster. Have been playing for 33 years, and have never met one person who thinks that way

> I know how to figure the long run for fixed and
> continuous resizing. My long run is probably closer to
> the continuous numbers.

Congratulations.

> I know how to figure the EV or SCORE (I look at your
> book) for fixed bets. I do not know a simple way to
> figure the EV for continuous resizing?

There are dozens of articles on win rates for perfect Kelly wagering. Just look anywhere around the Web. But, I repeat: you're deluding yourself. No matter what you do, your real-world win rate will be much closer to fixed-betting than to continuous resizing. I'm certain of it.

> Hmmmmm
> Perhaps an easy way though inprecise?
> Every time I reset my bets I know what the SCORE is
> and I know because I am resizing frequently it is cut
> roughly in half.

You're greatly overthinking this.

Don

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