#### shiznites

##### Well-Known Member
I've been enjoying You've Got Heat by Barfarkel. In a later chapter the author mentions not being close to his 'N0' number. This got me to thinking, "What's mine?"

How do you get the calculation of the time to "get into the mathematical 'long run' in which your per-hour expectation would accumulate enough to equal one standard deviation? In other words, how do you calculate the average number of hands, or hours to reach that 'N0' number where the Law of Large Numbers manifests itself"? (part of quote taken from You've Got Heat)

EDIT: NEVERMIND JUST FOUND THE ANSWER

#### StandardDeviant

##### Well-Known Member
shiznites said:
I've been enjoying You've Got Heat by Barfarkel. In a later chapter the author mentions not being close to his 'N0' number. This got me to thinking, "What's mine?"

How do you get the calculation of the time to "get into the mathematical 'long run' in which your per-hour expectation would accumulate enough to equal one standard deviation? In other words, how do you calculate the average number of hands, or hours to reach that 'N0' number where the Law of Large Numbers manifests itself"? (part of quote taken from You've Got Heat)

EDIT: NEVERMIND JUST FOUND THE ANSWER
What is the definition of "long run?" I'm thinking that N0 and "long run" are related by not equivalent concepts.

#### SleightOfHand

##### Well-Known Member
StandardDeviant said:
What is the definition of "long run?" I'm thinking that N0 and "long run" are related by not equivalent concepts.
I think that the "long run" is more of a theoretical concept saying that after a huge amount of trials, your EV is X. However, N0 is related in the sense that it says how "far" the long run is. Its kind of like saying how guarunteed the money is. The bigger the N0, the more variance there is, which makes it take longer for the EV to push the variance to a more comfortable range. The smaller the N0, the more likely you are to be close to your EV.

#### Kasi

##### Well-Known Member
StandardDeviant said:
What is the definition of "long run?" I'm thinking that N0 and "long run" are related by not equivalent concepts.
Well, here's my jibberish on the subject.

"Long-run", I suppose in theory, means "infinite".

We are mortal.

Define it as you want.

I'm 21. I initially play "full-Kelly" and continue to do so for 30 years.

Flash Forward.

Now I'm 51. Still playing the exact same game the exact same way for the last 30 years. My initial 2000 unit roll is now 64000 units. My orig 13.5% risk to my orig roll is now really, really small, trillions to one. It would take a huge neg SD event to lose my orig 2000 units between now and 30 years from now when I'd be 81. Maybe it'd happen once in a billion billion 30-year time frames.

Have I reached the "long-run" yet - I still could lose it all in the next 30 years?

Yes, I COUlD lose it all in the next 30 years but it would take a neg SD event to actually occur that would not be expected to occur but once in trillions.

I'd say, at age 51, I have reached the "long-run" even though some might say I haven't becasue there was still a chance of losing it all before I died.

N0 says, traditionally, after so long, my EV and 1 SD are equal. The implication is that, after that length of time, the fact that I am still not losing means the lilkihood is that my results are due to "skill" and not "luck" - my "skill" has overcome 1 SD of "luck".

It's a pretty conservative defintion of "long-run" if you ask me but no one asks me. If one wants to define N0 as when EV=2SD or EV=3SD, or more, why not? I happen to prefer the "EV=2 SD" or "EV=3SD" alot more than the "EV=1SD" definition which I have never figured out why it seems to be such a standard since any JoBlow can overcome "EV=1SD" fairly often simply by being reasonably "lucky".

For N0 to have EV equal 2SD, N0 is 4 times as many hands as N0=1SD. For 3 SD, 9 times as long etc.

Whatever, if you achieve traditional N0, even starting out as a full-Kelly bettor, you have doubled your roll (same thing) and your orig risk is now "orig risk*orig risk". You started at 13.53%. Now it's .1353*.1353=.0183.

Have you reached "long-run" at that point? Depends on how you choose to define "long-run".

Regardless, things are greatly looking up at that point, for you anyway, aren't they?

Especially, from your point of view, if you are already 75 years old and will only play 100,000 more hands in your lifetime.

Not so much if you are 21 and will expect to play 1,000,000 more hands in your lifetime.

Kind of thing lol.

God, what jibberish.

Apologies.

#### blackjack avenger

##### Well-Known Member

Don't call Kelly betting 13.53% ror:joker::whip:

Kelly equivalent 13.53%
or
Fixed kelly I would think works!

Kelly betting requires constant resizing and in theory a 0% ror!

In your example for fixed bets one can get to the point where they can't lose all their bank because the bank can be larger then the number of bets one has in their finite life!:joker::whip:

Not going broke, an advantage in death!:joker::whip:

#### StandardDeviant

##### Well-Known Member
Kasi said:
It's a pretty conservative defintion of "long-run" if you ask me but no one asks me. If one wants to define N0 as when EV=2SD or EV=3SD, or more, why not? I happen to prefer the "EV=2 SD" or "EV=3SD" alot more than the "EV=1SD" definition which I have never figured out why it seems to be such a standard since any JoBlow can overcome "EV=1SD" fairly often simply by being reasonably "lucky".
I'm with you on that one. The 1SD and even the 2SD cases occur so frequently as to be uninteresting. A 3SD event can reasonably be called "rare."

#### Kasi

##### Well-Known Member
blackjack avenger said:
Don't call Kelly betting 13.53% ror:joker::whip:

Kelly equivalent 13.53%
or
Fixed kelly I would think works!

Kelly betting requires constant resizing and in theory a 0% ror!

In your example for fixed bets one can get to the point where they can't lose all their bank because the bank can be larger then the number of bets one has in their finite life!:joker::whip:

Not going broke, an advantage in death!:joker::whip:
Here we go again lmao.

But thanks for the virtual "whipping" lol.

So, if "Kelly" betting means constant re-sizing, down to fractions of a cent, never playing a minus EV hand with a 0% ROR and who lives forever, would you say a Kelly better has reached the "long-run" even after he has played only 1 hand just because his ultimate ROR is 0%?

Even though he might have a 1% chance of losing 99% of his starting roll while constantly re-sizing and being able to bet fractions of a cent?

What IS the N0 for such a bettor anyway lol?

Yes, in my example, I guess just me, my definition, but if I'm so old I can't play enough remaining hands to lose enough of my current roll to finish a lifetime loser, guaranteed to die a lifetime winner, loosely speaking, I'd say I had reached the "long-run" lol. At least "my" long-run to me.

It's like, if I was allowed to resume internet gambling tomorrow and was allowed to flat-bet the \$2 BEA-utiful Micro SD game, I could play 100/hds/hr for 2000 hrs/yr for the next 40 years (8,000,000 hands) before I could lose what I have won with odds of not losing it of over 11,000,000 to 1 even if I did.

It doesn't matter - I'd hope every bettor knows the likllihood of his results after each session and cumulatively to now, the lilihood of losing x% of current roll over how long in the future and his ROR going forward etc after each session he has played and takes it from there as to when to re-size or not or know everything is A-OK lol.

#### blackjack avenger

##### Well-Known Member
Who is Whom?

No, I am not flogging you. I just like the symbols. I think of them as a casino and a player
but which is which? :joker::whip:

As soon as the name kelly is used one should be meaning optimal resizing. As far as it being only a theory and not being applicable in the real world.:joker::whip:

Given a 10g bankroll two betting styles one could choose from are:

fixed 13.53% ror of total bank
or
bet kelly and have a 13.53% chance of losing 86.47% of your bankroll

One does not have to bet perfect kelly in the real world to get much of it's power. All one needs to do is bet 75% to 90% and resize at the end of a session or during a large bankroll move as needed. If you bet less as you lose you can hang around longer which is one of the purposes of kelly.:joker::whip:

As far as the long run and kelly, one cannot constantly bet higher so you eventually reach fixed betting.:joker::whip:

#### Kasi

##### Well-Known Member
Couldn't get that"quote" thing right so apologies in advance.

But thanks for the virtual "whipping" lol.

Hope you enjoy it as much as I do lmao.

So, if "Kelly" betting means constant re-sizing, down to fractions of a cent, never playing a minus EV hand with a 0% ROR and who lives forever, would you say a Kelly better has reached the "long-run" even after he has played only 1 hand just because his ultimate ROR is 0%?

I'd say....., just right now, yes. :laugh:

Even though he might have a 1% chance of losing 99% of his starting roll while constantly re-sizing and being able to bet fractions of a cent?

I'd say, yes.

What IS the N0 for such a bettor anyway lol?

Wondered myself lol. Would unit-EV and SD in units compared to remaining roll remain constant for every round played? Maybe it would seem N0 would have to re-stated after every round played?

A/K/A freakin clueless lol. Let some heavyweights join in lmao. Even in my ivory castle, I don't worry much about cr*p that's impossible anyway

It doesn't matter - I'd hope every bettor knows the likllihood of his results after each session and cumulatively to now, the lilihood of losing x% of current roll over how long in the future and his ROR going forward etc after each session he has played and takes it from there as to when to re-size or not or know everything is A-OK lol.

Amen to that.

Couldn't agree more and then some.

But can we mutually just agree to never publicly bring up again such fundamental agreement by both of us on the important stuff?

I'd just hate to approach the future with the thought of maybe never being flagellated again :grin:

#### Kenneth

##### Member
Kasi said:
So, if "Kelly" betting means constant re-sizing, down to fractions of a cent, never playing a minus EV hand with a 0% ROR and who lives forever, would you say a Kelly better has reached the "long-run" even after he has played only 1 hand just because his ultimate ROR is 0%?

What IS the N0 for such a bettor anyway lol?
As I understand it, the phenomenon of data "entering" long-run in statistics refer to the mean of these data approaching closer to the estimated EV. In other words, he might have played one hand, but he might have had 5 initial units in front of him for the only round he played that ended up being doubled down, and the result was 10 units won.

It seems to me that what's confusing you is the way we learned about the long-run; long-run being the messiah with the shiny-holy grail to save us from malevolent standard deviations that could give us a fiery roll, but like any functioning hammer, could make or break just the same.

As for his N0, given that N0 is a number of rounds required in order for the EV to equal one SD, 0% ROR probably does not alter the N0 conceptually; meaning that he still has a concrete N0 to overcome-though he would be mad if he aspired to- in order to approach the EV.

#### Kasi

##### Well-Known Member
Kenneth said:
As for his N0, given that N0 is a number of rounds required in order for the EV to equal one SD, 0% ROR probably does not alter the N0 conceptually; meaning that he still has a concrete N0 to overcome-though he would be mad if he aspired to- in order to approach the EV.
Hi Kenneth - welcome - where u been hiding urself?

Anyway, agree with the above.

Probably also agree I could easily be confused lol.

I don't know what "long-run" means. Maybe, like "porn", I'll know it when I see it even if I can't define it.

Somewhere being between it would take a -10SD event to have me lose \$ from where I started, like after a 1MM hands or so, however many hands it takes, or taking a -4 SD event to lose from that point forward, I have reached "long-run". Just becasue, at some point, the liklihood of such things happening in my remaining lifetime can "safely enuf" be ignored.

So, to me, my lifetime is "long-run" enough to me, from a "practical" point-of-view, even though "long-run" might mean "infinite-time" in theory.

Really, in simplest, most practical terms, if one has quadrupled orig roll, survived that long to have achieved that, there's a really darn good chance he will never lose his roll from that point forward unless he is really one really, really sorry unlucky sunuvabitch and plays a long time.

There's always a chance you could lose all from any point forward (assuming you will live that long) - but if it's 1 in a trillion trillion chance would one say one has reached long-run? What if only 1 in 1 million? Or 1 in 100,000? Put another way, would it take a -!5 SD event to lose all, or a -8 SD event, or a -4 SD event? -15 SD events have never occurred since time began. -8 SD events, well, chances are, you've never seen one and never will. -4SD events, maybe, just maybe, you've actually been that unlucky.

It's all relative to me lol.

#### Kenneth

##### Member
I have been in and out of the forum.
I'm not 21 yet; I don't have any experience, and consequently lack any accurate information or even a single anecdotal datum to share with others aside from imagination - nobody would want that anyways! Besides, most questions in Card Counting could be answered by more knowledgeable sources, and I had nothing constructive to add on nor do I feel better about myself by finding fault with someone.
Besides, BJ is not my only interest.

As for the long-run, the concept really confused me and I've always thought the term is a fire waiting to sack Rome by sounding like it's related to time, but there is this Law of Large Numbers - which is commonly referred as the Law of Averages that doesn't actually exist. **According my Statistics textbook, it "states that the long-run *relative frequency of repeated independent events settles down to the *true relative frequency as the number of trials increases."

Defined in this sense, long-run would mean any # of independent trials - as in each round - required to equal to the *theoretical probability. Applied to BJ though, I think it would suffice to define long-run as the # of hands played required to be the "man left on the Rio Grande" despite the negative fluctuations, i.e., N0 or multiples of N0; accounting for the penetration down to a single card, mistakes, etc. would make the precise evaluation impractical if not impossible. After all, so long as one profits and manages money with discipline, this sort of thing is probably just for folks like me; I enjoy "this sort of thing".

Thanks for the warm welcome by the way!

*relative frequency - probability that certain event would occur relative to other outcomes in question.
*theoretical probability - "when the probability comes from a mathematical model."
**quotation marks mean it came straight out of my textbook.