OBO different from Peek

[NotEnoughHeat]

I believe those sims in the OP were full index but to double check I updated CVCX to 5.0132 and ran new sims. I used the canned strategy under Stanford Wong 'Old Complete High-Low' and made sure to uncheck 'European no hole card' which is automatically checked under 'affecting options' on the page that you attach the strategy. The sims came back with similar numbers but I finally figured out what was happening when I was playing around with the configuration. It seems that if you have 'no dealer hole card dealt' checked then the 'ENHC' will stay on even if you uncheck it. I unchecked it. Opened up the attached strategy page and sure enough it had automatically rechecked that option. I ran sims with my own indices and they were as you would expect: OBO with similar numbers to hole card games.

Mystery solved. Thanks for the attention to this issue Norm.

[NotEnoughHeat]

For anyone wondering, the difference in dealing a hole card with and without peek appears to be negligible. 4 billion round sims with my indices turn out 47.60, 47.55, 47.20 for HC-Peek10/A, OBO, HC-NoPeek respectively. The card eating rationale seemed to make sense but these results might suggest that you don't lose too many rounds at an advantage when weighed against rounds with a disadvantage. Perhaps wonging would produce a noticeable difference. I'll report back when I look into it.

[Skyler62]

If someone spent their entire life playing Blackjack, do you know the maximum number of hands they could expect to play? The following is just a rough calculation and should be much greater than the actual result:

Suppose someone starts playing casino BJ when they are 21 and plays every day until they die at age 100. Furthermore, suppose they play 18 hours per day and they find a game in which there are very few players so they can play one hand every minute. How many hands will they play over a lifetime? The answer is ...

60 hands every hour x 18 hours per day x 365 days per year x 79 years = 31,141,800

Why is this important? And what is the relevance to playing billions of simulations? There are several excellent discussions of the "Law of Large Numbers" in several books that show why this is important.

In my copy of The World's Greatest Blackjack book, there is a discussion on page 199 regarding the Law of Large Numbers. It is very brief although there are several other more detailed discussions in other books that are more concerned with the theory of gambling. These include:

. Blackjack Strategy Ebook
. Math of Gambling
. Science of Casino Blackjack
. Blackjack Secrets

In any case, the following is an extract from TWGBJB on page 199:

Law of Large Numbers

While a statistical percentage will converge on the theoretical, the absolute difference is likely to get larger.

It is perfectly possible, and very likely, that your losses could keep increasing in an even game. This in no way violates the statistical theory, but it does show the fallacy in waiting for a trend to reverse. The next table shows how your net losses could be getting larger and larger even though you are getting closer to the expected theoretical percentages in an even fifty-fifty game.

LAW OF LARGE NUMBERS IN EVEN GAME

Hands...Hands..Hands....%.....Net
Played...Won....Lost....Won...Loss

...10.......4.......6..........40.....2
..100......43......57........43....14
.1000.....460.....540......46....80
10000....4900....5100....49...200

I added all the "dots" into the above table in an attempt to make the colums "line up". It was difficult to do that with the forum software. So I will just try to specify all the rows and colums again using text.

In the above table there are four rows.

The 1st column is "Hands" (meaning "Hands Played"). The four rows correspond to: 10 100 1,000 10,000.
The 2nd column is "Hands Won". The four rows correspond to: 4 43 460 4900.
The 3rd column is "Hands Lost". The four rows correspond to: 6 57 540 5100.
The 4th column is "% Won". The four rows correspond to: 40 43 46 49.
The 5th column is "Net Loss". The four rows correspond to: 2 14 80 200.

Even more startling are the calculations that are shown in the following table. In an even game, you would think that each side should be ahead for about half the time (which is consistent with the idea that "things even up"). Surprisingly, this is the least likely result.

The point I'm trying to make is that we have to be very careful when assuming that running large numbers of simulations (in the billions and trillions) mean the results carry more authority. It seems like a very powerful conclusion. But the truth (according to the Law of Large Numbers) is something very different.

The example I calculated showing that someone who devoted their entire life to playing Blackjack could expect to play a maximum of about 30 million hands (the actual result figures to be seriously lower - maybe just a few million hands) and so it's dangerous to draw any conclusiong and place your money at risk by running billions of simulations because in a lifetime of playing Blackjack, the max number of hands one can expect to play is not really related to the maximum number of simulations one can run and you will likely just be left with huge errors and the results will be unreliable.

I don't know what the answer is. It is much easier to find flaws with existing ideas than it is to correct them. All I'm trying to say is, "Be careful with your money."

[Norm]

The example I calculated showing that someone who devoted their entire life to playing Blackjack could expect to play a maximum of about 30 million hands (the actual result figures to be seriously lower - maybe just a few million hands) and so it's dangerous to draw any conclusiong and place your money at risk by running billions of simulations because in a lifetime of playing Blackjack, the max number of hands one can expect to play is not really related to the maximum number of simulations one can run and you will likely just be left with huge errors and the results will be unreliable.

This is not why we run billions of hands. When we run a billion hands, we are really running 50,000 hands 20,000 times to get a more accurate result of what happens in 50,000 hands. Or, 1,000 hands one million times. The more hands we sim, the lower the standard error. But, you don't have to play anything like a million hands, much less a billion, to have a high probability of being on the right side of the curve.

[Norm]

There is a huge difference between an advantage and a threshold.

A sim will tell you the N0.

[Skyler62]

Thank you for your replies. I am so happy to have discovered this forum.

I have been working by myself for many years to create my own simulation. I am a software engineer and although I am now retired, I have been creating software for many years and my interest lies mostly in my BJ simulation.

I would love to know two things:

First, is there some simulation that is available to the public that most of you use and if so, is it open source? The reason I ask if it is open source is because I can't imagine ever running a simulation that I did not create or that I could not examine to understand exactly how it works. I will be happy to explain why that is the case later on.

Secondly, I would guess that some of the members here have likely created their own simulations. Why? Because even though it can take many hours (or days or weeks or months) to write a comprehensive BJ simulation, the work required is not very difficult. Most anyone who has been trained to write software could likely do it. There are only a few interesting problems that require unique solutions. For example, shuffling a shoe containing a large number of decks has to be able to be done with an amount of time that I describe as "proportionately linear". In other words, the time taken is proportionate to the number of cards. If it is proportionate to the square of the number of cards, that will create a problem if you want to run a large number of simulations. (and there are several reasons why people want to run a large number of simulations).

Shuffling a shoe and doing it in an amount of time proportionate to the number of cards in the shoe was a very interesting problem. When I first started, the time required to shuffle the shoe was not linear. It was not terrible. But after working with my simulation for a number of months, I finally discovered a very nice way to shuffle the cards that is directly proportional to the number of cards in the shoe. I would be happy to share that method with any of you who are interested in it.

So, I'd like to know if anyone here has written their own simulation. Do you all run an existing simulation that was created by someone else? Or has one or more of you created your own simulation and do you run that one?

The reason I feel it is so important to run a simulation that you have created or at least, that is open source so that you can read it all and understand exactly what it is doing and how it works is as follows:

By creating my own simulation, I have discovered some terrible flaws in the way that many of the world's greatest experts - like Thorpe, Braun, Einstein, etc. - do not seem to have discovered. Now, I'm probably mistaken about this. But I will be glad to tell you all exactly what I'm talking about. If I'm correct, and I have to assume the odds are low that all these geniuses actually missed a very serious flaw in their approach to counting, I will be very embarassed. But, I'd like to find out for certain - one way or another.

Has anyone here ever stated there are some serious flaws in the traditional approach to the way all these "experts" count cards and base their systems on those results? If so, it will require a serious reassessment of the way people count cards and the way it affects their strategy and wagers.

Oh Hell! I'm probably all wrong about this. But it's hard to swallow that since I have created my own simulations and it bears out what I'm saying.

If any of you could tell me the name of the simulation that you prefer to run, I'd certainly appreciate that - especially if it's open source.

[Norm]

By creating my own simulation, I have discovered some terrible flaws in the way that many of the world's greatest experts - like Thorpe, Braun, Einstein, etc. - do not seem to have discovered. Now, I'm probably mistaken about this.

Yep, probably mistaken. Download the CVData/CVCX demo to see what sims can do: www.qfit.com/downloads.htm.

[Skyler62]

Thank you very much for the link Norm. I will definitely take a detailed look at this software.

[Gronbog]

Yes, several, if not many here have written their own simulators and combinatorial analysers. Some do share their code. Eric Farmer, who posts here under that name is one such person. You can find a link to his latest work by searching his recent threads.

If your results are contradicting those of some of those you have mentioned, then the problem likely lies in your code. You mention shuffling algorithms. You must be very careful about handling random numbers and using them to manipulate cards. It is extremely easy to introduce unwanted biases. These issues have all been solved. No need to re-invent the wheel. Google can be your friend.

[Three]

I don't know what the answer is. It is much easier to find flaws with existing ideas than it is to correct them. All I'm trying to say is, "Be careful with your money."

With the law of large numbers the results seem to converge on the expected because the denominator in the fraction makes the likely distance from expectation insignificant not that it ever reduces it. Like you get 50 straight heads to start a series of coin flips. That puts an initial bias in the sample of 50 heads. After 100 total flips that is half the flips, 50%. After 1000 the bias is reduced to 1/20th or 5%. After 10000 the bias is 1/200th or .5%. After 1,000,000 flips the bias is .005%. This is because expectation increases linearly as trials continue to accumulate while the SD increases by the square root of number of trials.