Simulator results update

Earlier, I posted your simulation result of these words: 

“You need to play 733,993 hands for an 84% chance of being in the black.”

However, I believe this is a calculation result, strictly not a simulation one. I guess you probably used your simulated EV and SD to calculate this N0 number. 
 

I’m not so sure though. Maybe I’ll look up Don’s book on pp. 147-148 of BJA3 to understand this better.

You may need to run more hands (multiple simulation runs) for the “hands you need to play for an 84% chance of being in the black” number to converge to value indicative of your strategy.
 

The number you got could be indicative of your strategy but it could be an outlier for the first few runs. An outlier can be much higher or much lower than what it will ultimately converge to.

I’ve studied online about N0, the number of hands needed to play so that EV = SD. The definition is

N0 = Variance / (Expected Value per hand)^2.

This value estimates how many hands are needed to smooth out the random fluctuations and approach the expected average value. 
 

So, after N0 hands of playing, player has an about 84% probability of making a profit of one standard deviation, not “in the black” (EV > 0) though. Right?

"So, after N0 hands of playing, player has an about 84% probability of making a profit of one standard deviation, not “in the black” (EV > 0) though. Right?"

No, not right! It means that you've played a sufficiently large number of hands such that, even if you were to experience a one-SD loss, your EV would now be equal to that loss, and you'd break even.

So, yes, EV > 0, and "in the black," meaning not losing anything.

Don

I see. SD cannot be negative. To be more accurate, it should be SD = | EV |.

However, confusing are "Expected Value per hand" and "Variance per hand."  When betting with a spread, there are no such things. 

* Gronbog bangs his forehead against his keyboard *

That probably is not the main point of this discussion though. What I want to say is this

“You need to play 733,993 hands for an 84% chance of being in the black.”

Should be 

“You need to play 733,993 hands for an 84% chance of making a profit of $160,000.” Based on the result figure I posted earlier. 

The 84% chance is just the chance of being above 0.

I’ve tried the stimulator to better understand the N0 number. It looks like you updated something, because the result of N0 now is one order of magnitude smaller than before.  The sim result now is

“You need to play 69,216 hands for an 84% chance of being in the black (this is the N0 number of hands)”

Using your simulated EV and SD numbers:

"Average Won per 100 hands" = $17.24

“Standard Deviation per 100 hands” = $453.62.

We have 

N0 = Variance / EV^2 = (453.62/10)^2 / (17.24/100)^2 =69,232.

I guess I figured this out myself. However, regarding the meaning of N0, both Don and you converge on the same "in the black" interpretation, but I'm still not very confident about it. I'd like to hear a third opinion from Gronbog. 

You're not going to hear a third opinion from Gronbog, because it's like being told that 2 + 2 = 4, and you're arrogant enough to write, Thanks a lot, but I'd like to hear a few more opinions before I accept what you're telling me. 

So, sit down and take as long as you have to to get what I've written through your head. But, you can ask 10 more times, and the answer I've given you isn't going to change.

Don

I did do an update or fix, I had a problem where the N0 number could be thrown off if you changed the number of hands per visit during different simulation runs without resetting the numbers or changing the name of the output, I fixed that.

(changing the number of hands per visit without resetting or renaming will still affect average visit numbers, percentage visits won and things like that but that basically makes sense so doesn't need a fix)

Are all these computer runs putting any $$ in Aceside's pocket? I think not.

Perhaps the fear of the unknown yields timidity subconsciously to him and others for not playing..

As I've said previously, having feedback from Don is a luxury they fail to recognize.

Let me just say this. Trust yourself, not simulations. People have different math and definitions. As far as I know, Phil’s Blackjack simulator is the most scientific one in the world! 

It's mind boggling how you guys continue to feed the troll.

After a very long history with aceside, I've concluded he's not a troll. First, it's why I asked how old he was, but he won't answer. I think he's very, very young, may still live at home, has a moderate to weak background in math, and has no filter, which leads me to believe that there are further personality issues or disorders. So, while he's extremely annoying most of the time, I don't think he's just yanking our chain. You won't of course, get a straight answer from him on any of the above, but if he were willing to be more forthcoming about his background, maybe a) he wouldn't have been barred permanently from Norm's site, and b) he might be tolerated more by others. He clearly doesn't know how to interact with adults, so that's a major concern.

I would give you further personal opinions as to what I believe to be his problem, but won't post on an open board.

Don 

Regarding my math skills, I am in the moderate to advanced level. However, I don’t know programming very much, so I heavily rely on Phil now.

Several years ago, I started this BJ adventure on another forum but eventually was banned there.  That was probably because 21forme was annoying. We lived in the same region, after all.

I do take credit for convincing NOrm to ban him.  It only took 5 years of putting up with his idiocy there.  But the reason for being banned is strictly YOU.

My theory - aceside started his trolling at age 12.  Now he's 17 and still has never been to a casino.

Part of it is that I find it difficult to let misinformation stand uncorrected. New players come to these forums to learn and they often don't yet have the knowledge to separate fact from fiction

That makes sense, Gronbog.

Don - I sent you a PM on blackjackinfo.com.

Let me get back to Phil. I’ve carefully studied this part and come up with a few more revisions on this simulator.

First, to be more accurate, 1-SD corresponds to 84.1%; 2-SD to 97.7%.

Second, it’s possible to simulate the 1-SD to 84.1% correspondence.  All you need to do is break the total hands in a sim run into equal segments each N0 long and then record the probability of winning segments.

Third, I find it’s redundant to use these things, N0 and SCORE.  I have invented two new terminologies for Blackjack, defined as follows:

1. Root_0 ==  SD / EV;

2. Root_s == 1000 EV / SD, 

where both EV and SD are positive.