Standard Deviation

[Sonny]

To sagefrog

I think Kasi answered these questions already, but I’ll add my input even though it probably just repeats what he said.

would it make sense if you had a simulation that gives the standard deviations at those corresponding true counts to figue the variance from those standard deviations and then plug those variance numbers into your spread sheet instead of the number you use.

Yes, absolutely. The 1.33 number is just a generic estimate. The actual variance at different TCs will usually be somewhere between 1.2 and 1.5 but I just used 1.33 to simplify things. Using numbers from a simulation should give more accurate results.

also was wondering why you use a variance = 1 for the negative tc's.

That must have been a mistake, maybe on an earlier version of the spreadsheet. They should all be 1.33.

also what is this variance in column D anyway.
is it variance of the TC or variance of the frequency of the TC or is it variance of EV at a TC ?

It is the variance of your bet. You will, on average, win or lose about 1.15 units on each hand because of doubles, splits, BJs, etc.

-Sonny-

 

[Kasi]

yeah so i guess the variance or standard deviation a sim gives us is an average, i'm just still wondering just what the standard deviation refers to or like in Sonny's spreadsheet what the variance refers to.
ie. standard deviation of what or variance of what?
like in the sim image below, i think standard deviation in the upper field refers to standard deviation of the winrate per hand and winrate per hour.
but i'm lost on what the standard deviation refers to in the column where there is a standard deviation associated with each TC.
i'm guessing it must be for either TC frequency or EV, or maybe both?

edit: ===>>> oh ok i think this post shows what the variance refers to. EV i believe from the sound of it:
http://www.blackjackinfo.com/bb/showpost.php?p=102358&postcount=12

This may or not help lol. But even I had trouble understanding what I said yesterday.

Go to the Wiz BJ App 4. He defined his game, rules etc. He ran 1.7 billion rounds like that. When he was done all he really knew was how many times he won or lost x units always betting 1 unit.

So take the 2nd column and multiply it by net win squared (1079*8 squared, or *64) for the first line, etc.) Do for each row and sum that total. Divide that total by the total rounds played. Hopefully you get 1.3037 (2,222,204,704/1,704,507,420) or so. Square root of that, SD, is 1.1418 like he said.

For this particular game the 1.3037 is the same as Sonny's 1.33.

You can also see how easy it was to get house edge from only that same info.

Hopefully you can also see how the variance would change with different rules - if you can't split to 4 hands, you can never have a net win of 8 units, etc.

Hopefully you can see how SD and EV are inextricably linked and it's tough to change one without effecting the other - if his next 1.7BB round sim had gotten 1 more win at 8 units and one less at -8 units, both EV and SD would slightly change.

Hopefully you can also see how betting more units than 1 at different times would change things too.

So, the way I imagine it, a sim just does something like that broken out by TC, etc and calcs it edge and SD at that TC in the same way. All a sim really knows is how many rounds its played and how often it won or lost x units with a 1 unit bet. Given game, pen system etc.

The more rounds it runs, the more accurate it is, kind of thing. Ultimately, it's more like a "guess" rather than an average. I guess when every possible combination of cards has been run, it would no longer be a guess at all lol.

Broadly speaking, I hope that gives you the main idea anyway that SD and EV are only figured out, and it's not "exact" even then, after the fact so to speak.

 

[sagefr0g]

This may or not help lol. But even I had trouble understanding what I said yesterday.

Go to the Wiz BJ App 4. He defined his game, rules etc. He ran 1.7 billion rounds like that. When he was done all he really knew was how many times he won or lost x units always betting 1 unit.

So take the 2nd column and multiply it by net win squared (1079*8 squared, or *64) for the first line, etc.) Do for each row and sum that total. Divide that total by the total rounds played. Hopefully you get 1.3037 (2,222,204,704/1,704,507,420) or so. Square root of that, SD, is 1.1418 like he said.

For this particular game the 1.3037 is the same as Sonny's 1.33.

You can also see how easy it was to get house edge from only that same info.

Hopefully you can also see how the variance would change with different rules - if you can't split to 4 hands, you can never have a net win of 8 units, etc.

Hopefully you can see how SD and EV are inextricably linked and it's tough to change one without effecting the other - if his next 1.7BB round sim had gotten 1 more win at 8 units and one less at -8 units, both EV and SD would slightly change.

Hopefully you can also see how betting more units than 1 at different times would change things too.

So, the way I imagine it, a sim just does something like that broken out by TC, etc and calcs it edge and SD at that TC in the same way. All a sim really knows is how many rounds its played and how often it won or lost x units with a 1 unit bet. Given game, pen system etc.

The more rounds it runs, the more accurate it is, kind of thing. Ultimately, it's more like a "guess" rather than an average. I guess when every possible combination of cards has been run, it would no longer be a guess at all lol.

Broadly speaking, I hope that gives you the main idea anyway that SD and EV are only figured out, and it's not "exact" even then, after the fact so to speak.

shwew ok. well thank you for going into such depth. sorry i have probably i dunno how many questions that would probably lead to more questions. but at least i follow what your saying for the most part. i never realized how darned complicated all that stuff is.
i was thinkin i was gonna next year when i'm 60 cause the local university lets 60 year olds take free courses, that i'd take a probability 101 course, lol now i'm not so sure. i mean i was trying to get a little back ground about some of the terminology and all of what your writing about and was browsing through bjmath.com's stuff an Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. ....... omg it's mind boggling! and worse than that it's even got the dreaded trigonometry stuff in it.
so but anyway (gosh i hope i'm right) i think i know what it is that this standard deviation and variance stuff is comming from in those true count columns of the cvcx simulation. it's for a given tc different categories (like a normal hand, double down, snapper, split, double after split, maybe insurance bet) of results (in terms of win or loss) of a flat bet over lots and lots of rounds of simulated play that the standard deviation is computed from. ...... right? :cat:

 

[Kasi]

it's for a given tc different categories (like a normal hand, double down, snapper, split, double after split, maybe insurance bet)

I think

Except for maybe insurance - I have no idea what sims do with that? Maybe just a separate side bet for variance purposes? Maybe the adv gained from using it as an index play is included in the adv at that TC? Maybe not either since it's flat-betting and you'd never make it anyway with BS?

Darn it - now you got me all confused to