Wolverine: "n0" term

[Wolverine]

On the beginners page bfbagain used the term "N0" or "n0" to indicate the 'long run.' I assume this is the 'n' (number of hands) that constitutes when the game being tested via simulation will equate to the long run?

What does this mean in terms of bankroll? Anything? What does it mean in terms of RoR? If you reach the magic n0 number of hands, does it mean that RoR has essentially been expunged?

bfb indicated a SD game with an n0 of 6400 (if memory serves me correctly). Is this a good number (which it seems) or an average number? At 100 hands per hour (straight up), it would seem that 6400 hands could be played by a casual counter over a half dozen weekends in a year.

Thanks for the explanation to a newbie. :-)

[bfbagain]

Yes, it is N0. I think I used "O", but it should be "0."

For your reference, Brett Harris defined this term, and therefore I respectfully point you to his article at bjmath on optimal betting spreads. http://www.bjmath.com/bjmath/Betsize/theory.htm

There is also a neat calculator on bjmath here..
http://www.bjmath.com/bjmath/refer/N0.htm

I hope this helps.

cheers
bfb

[Cacarulo]

> On the beginners page bfbagain used the term
> "N0" or "n0" to indicate
> the 'long run.' I assume this is the 'n'
> (number of hands) that constitutes when the
> game being tested via simulation will equate
> to the long run?

> What does this mean in terms of bankroll?
> Anything? What does it mean in terms of RoR?
> If you reach the magic n0 number of hands,
> does it mean that RoR has essentially been
> expunged?

> bfb indicated a SD game with an n0 of 6400
> (if memory serves me correctly). Is this a
> good number (which it seems) or an average
> number? At 100 hands per hour (straight up),
> it would seem that 6400 hands could be
> played by a casual counter over a half dozen
> weekends in a year.

> Thanks for the explanation to a newbie. :-)

As bfbagain has said it's well explained in Brett's paper but I will add a few things.

Don's SCORE is equal to the win rate per 100 rounds using a fixed betting scheme with an Equivalent Kelly Bankroll of $10000, that is SD^2/EV = $10000. A fixed bettor with a bankroll equal to the EKB will have a Risk of Ruin of 13.53%.
DI is the square root of SCORE and it's an equivalent measure.
Both quantities are related to N0 (N-nought) which is called the Long Run Index. N0 is equal to SD^2/EV^2, and since it is dimensionless, it is the same for the corresponding unit spread. N0 is the number of rounds (watched and played) such that the expectation (EV) is equal to the standard deviation (SD). As such it is a measure of how long a player needs to play in order to be confident of being ahead. In other words, N0 is, for a fixed bettor, the number of rounds needed to double the Equvalent Kelly Bankroll (EKB).

It can be easily shown that:

SCORE = ($10000/N0) x 100

Hope this helps.

Sincerely,
Cacarulo

[bfbagain]

said it quite as well!

FWIW, I hope this is both archived on DD, as well as on Parker's pages.

Maybe post this on the beginner's page, although that's a scary thought. :-)

Thanks Cac, for a terrific explanation.

bfb

[Don Schlesinger]

See p. 203 of BJA3 for an explanation of DI, and pp. 211-12 (#11) for N0.

Note that the "zero" part of "N-zero" comes from the fact that when you play the requisite N0 number of hands, EV - SD = 0.

Don

[Cacarulo]

> See p. 203 of BJA3 for an explanation of DI,
> and pp. 211-12 (#11) for N0.

> Note that the "zero" part of
> "N-zero" comes from the fact that
> when you play the requisite N0 number of
> hands, EV - SD = 0.

Note that "N-nought" was the original "British" term coined by Brett. "N-zero" is the "American" form but he always talked of N0 as N-nought.

Cac

[Cacarulo]

> Maybe post this on the beginner's page,
> although that's a scary thought. :-)

Let's leave something for the DD' subscribers

> Thanks Cac, for a terrific explanation.

You're welcome.

Cac

[Wolverine]

Thanks for all the help! I think I understand n0 a little better now (and I even read the 20 page mathematical proof bfb pointed me to--a little dry though). I liked the "simple explanation" above, much easier to understand!

I like that it is in DD only, a good perk for those that pony up the extra money for the personal touch DD provides. Just my 2 cents.