questions

Kasi · Feb 25, 2009

White Guy said:

Well, just to be transparent, all I did was use Table 10.43, a 4.5/6 S17 DAS game from Don's book.
So it was a 6D game compared to Kolan's 4D game, it assumed indexes and who knows what Kolan's guy did, it used Hi-Lo instead of Zen, it assumed 75% pen instead of unstated for Kolan's guy, it assumed 100.hds.hr as opposed to unstated in Kolan's post, it assumed betting those amounts at certain TC's as opposed to unstated by Kolan as to when the amounts were bet, it assumed he played all hands dealt as opposed to some kind of back-counting/wonging-out scenario, etc.

So, I guess at least based on some sim lol. I just said simless because of so many assumptions compared to Kolan's orig Q.

So, who knows what Flash may be assuming. He seems to go by his general rules of thumb alot. Sometimes it makes general sense to me, sometimes not lol. Losing 33 max bets in 800 hands seems here. Having a $6K roll and not playing with $2K is probably good advice. Having a $7200 roll in a 6/8 with same rules would be nothing close to the same ROR to me.

Here's the sheet I used based on that Table 10.43.

Newb99 - I didn't know if this was similar to what you do in your sheet except for maybe you can plug in any unit spread (always in units as a spread) and the results should be valid given the freq, advs and SD's from the orig sim. Sounds like we're in the same ballpark anyway with any differences perhaps due to different underlying assumptions.

You can change the numbers in red for $roll, $unit size and put in any unit spread you want. So down in the Trip ROR, I just put in 400 (units) and 8 (hours) and got the small risk lol. Farther down, I put in 800 hands and saw losing $2K was getting close to -4 SD. Plug in the N0 number of hands here and the low of 1 SD should be zero.

Plugging in larger $rolls won't change much except lifetime ROR.

Plug in a $10K roll, change $unit to $10 and change spread to 1,1, 2.5, 10, 12 and results should equal the 1-12 practical spread from Don's table.

Change the TC freq, the W/L% and SD from any of his play-all tables and one should get what he gets.

The main thing is, even for a guy like you White Guy who maybe plays a fair amount, wants to win a little money, counts when he does play, with/without indexes, even for small stakes maybe or maybe not, I mean why not blow $100 on a sim that will answer all this nonsense and at least put you in the ballpark anyway as to risk and what to expect assuming you play a reasonably consistent game? I don't mean you personally but maybe a guy like that anyway.

Now a guy like FLASH, a 40 year vet, playing with the roll and stakes he does, I can't even imagine relying on rules of thumb nonsense and playing without a sim.

I know, I'm no dam* fun. I'm sure you guys have fun when you play without all this sim bullcr*p. The only time I have fun playing is when I know I won't even try to compare EV to results :grin:

Well, OK, I get back to the room, add back-in waitress and dealer tips, add in full-retail for the Coronas, count and mostly bet $5 with $5K in my pocket so, if things get desparate and I have to employ my voodoo "chance of finishing at least a half-unit ahead in the next 20 rounds with an x-unit roll" cr*p, and, If I'm even with starting roll, I figure I'm actually ahead.

But I still enjoy trying to figure what people do and why with how much, why they think what they might, etc, what "AP" means to them, etc.

So, like you maybe, I figure pretty much everyone who plays this game regularly in real life can teach me something lol.

sagefr0g · Feb 25, 2009

Kasi said:

yeah, well i may be a wild and crazy guy but that file you just posted is a treasure trove.

http://www.blackjackinfo.com/bb/attachment.php?attachmentid=2084&d=1235532506

:1st:

Kasi · Feb 25, 2009

sagefr0g said:

MAY??!!

Oh no, in my universe, you ARE a wild and crazy guy :grin:

Steve Martin - eat your heart out.

But thanks. As you know, same BS sheet I've posted before and you and Weekend Warriors are already familiar with.

BS does not mean Basic Strategy lmao.

It's just meant to show the math from a sim's results after the sim gives you the basics of freq, adv and var (or SD) in case anyone is interested. I threw in the calculators I could understand like Trip ROR and Achieving Goal assuming no time limit. And Long-term ROR solving for Units or Rate which is pretty much the same thing. Plugin rounds played and measure results from EV. Very simple stuff but OK stuff.

It has its uses but it cannot replace a sim. It cannot generate the raw data sims use.

It does not figure out optimal betting although I think I could make it do so if I wanted.

It does not figure out co-variance at various TC's.

It cannot figure out Goal vs Time. I often get close with that privately but I usually think it was an accident. I can't find an "infinite sum series" formula in Excel lol.

It's just intended for "math-challenged" people like me, if they have access to a sim's results.

Trust me, if I wanted to know what people ask here becasue I wanted to risk real money on it, I would just buy a sim and not even bother with sheets. Except for the fun of it.

rukus · Feb 25, 2009

answers

KOLAN said:

1,000,000 $.

i saw it in a movie so i dont need no stinkin sim.

FLASH1296 · Feb 25, 2009

Truth is that I didn't really play serious BJ before 1985.

That was just 24 yrs ago.

Probably about the time, give or take a few yrs., that the median poster here was conceived.

:laugh:

I frequently suggest "rules of thumbs" because they are good for casual, occassional, low-stakes players.

I privately tutor an entire coterie of novice card counters, but I run my mouth here a lot too.

Yes, I very certainly do consult sims, etc.

sagefr0g · Feb 26, 2009

hey Kasi

Kasi said:

is there maybe something amiss with E26 (std dev per round in units) in your sheet that you uploaded?
think maybe that sumproduct stuff shouldn't go all the way to B17?

:whip:
or maybe it doesn't make any differance cause it would be multiplying B17 times zero anyway?

so no big deal, but i'm young and easily confused.
still i get the same answer even when i change the columns going down to only B15 & E15 & D15 anyway, lmao.
how come that thing divides by B17 anyway? i mean heck it's always dividing by sqrt(1), which is one anyway.

:whip::whip:
i been tryin to figure this stuff out, lol.

edit: an i'm trying to figure out what's going on inside that sumproduct thing where its' SQRT(SUMPRODUCT(B4:B17,E4:E17,E4:E17,D4

17,D4

17))/SQRT(B17) .
what's it doing squaring the E4:E17 units bet & D4

17 std dev stuff? is that how come it's in their twice. geesh that array stuff is confusing.

White Guy · Feb 26, 2009

Thanks. I will definitely leave bookmark that table and info.

Kasi · Feb 26, 2009

sagefr0g said:

You're right in that it makes no difference including B17 because there is nothing in the other columns.

Maybe I did it so I could add anoter row in if I had to without having to change the formula again lol. Sounds good lol but I have no idea.

I divided by sqrt of B17 hoping it might be the right thing to do when one doesn't play all the hands and maybe only plays 27% of them and maybe the same formula would work in both cases lol.

Yes, those columns are in there twice and getting squared. I'm turning the stuff into variance firat and then take the sqrt at the end to get SD. Since his tables give SD in that column. That squaring stuff is just how you do variance I think lol. See Table 2.1 where he squares the bet units but uses variance in a column instead of SD. One can add variance. In the sheet variance is $394 per ROUnD lol. Aren't you glad we don't talk variance - SD per round of $20 sounds alot better lol.

The sumproduct stuff just let me do it all in one cell rather than using a whole bunch of columns up top.

But to prove it to yourself, you could make a colum and squre your bet units. Another column and square the SD. Multiply those 2 columns and the freq column together.. Sum that column. Take the sqrt of it. Should get same answer lol.

Thanks for looking it over.

sagefr0g · Feb 26, 2009

Kasi said:

so i guess i'm understanding what your doing is turning the sim standard deviations from D4 thru D15 into variance by squaring, then it's ok to add since it's variance. so your squaring the bets also, is that part of getting the variance as well? or why square the bets? sorry, i'm just trying to figure it out, lol. i'll get it, geesh maybe i should just look in Blackjack Attack.

:whip:
ok i see the bets squared in table 2.1 . gotta read that stuff, i might catch on, might figure out why, lol. thanks for explaining.

edit: so i tryed one thing, i sumproduct'd the B collumns (tc freq) and the C collumns (advantage) and i got what i think is the games advantage over the player if he's flat betting and playing perfect basic strategy & (maybe with indices if the sim used them)

sagefr0g · Feb 27, 2009

part one simulations

Kasi said:

i looked it over some more. when i want to understand something, sometimes it helps me to write about it. lmao, that's why most of the time i don't know what i'm writing about.

Incredible how you can be using all this stuff, simulations, spreadsheets and whatever and maybe not really have a clue. So I thought maybe I’ll try and define some of it, try and explain some of it in my own words or whatever, borrow from other sources when I can’t explain something. However wrongheaded that may be.
It’s really all gonna start with something like Norm’s simulator, say cvcx. Just guessing but what I think a simulator does is play blackjack for lots and lots of rounds. Plays blackjack the same optimal way for some particular game for if you’re a perfect card counter, sort of thing. Then the simulator takes all the data from all those billions and billions of rounds, correlates it in certain ways and makes certain calculations. This perfect card counter uses perfect basic strategy; and basic strategy departures according to the true count and bets a certain way according to the true count for a given game.
Then the simulator spits out certain calculated data, like in the image below.

Average bet, what that is, is I think take the sum of all your initial bets in units and divide it by the number of all the rounds. According to cvcx help it’s Bet Average - Average initial bet in units. This is the bet before double downs, splits, surrender or insurance.

Then you have W/L% . cvcx defines it as “Win/Loss - Also called EV or IBA (Initial Bet Advantage.) This is the amount won or lost divided by the initial bet.” So you make some initial bet, you win or lose some amount, then divide the amount won or lost by the initial bet and express it as a percentage of the initial bet. This can be done for all initial bets made for the entire simulation. So you can end up with an overall W/L%.

Then you have win rate, Win Rates - Units and dollars won per hour. So you have some number of rounds played per hour and win rate is the number of units or dollars won in an hour or that many rounds.

Then you have standard deviation which is provided by hand and hour. I believe that’s expressed in terms of units per hand and units per hour. I think how the simulator gets standard deviation is that it takes the differences of all the resultant win and losses in units measured against the mean result in units then squares that obtaining variance and takes the square root of that variance. Below is how it’s described in bjmath.com:
The Definition of Standard Deviation:
Variance tells us the dispersion (ie Is it a fat or skinny bell shape?) of our Normal Distribution (bell curve). The "Standard Deviation is referred to as the square root of the Variance. Without any doubt, the "Standard Deviation" is the best measure of dispersion around the arithmetic mean. In a phrase, it is the "root mean squared deviation."
Equation for the Standard Deviation: (for ungrouped data)
SD = sqrt { sum(x - mu)^2 / (n-1) },
where x is the data value,
mu is the arithmetic mean of the data items, and
n is the number of data items.
Variance The Variance (which is the square of the standard deviation, ie: σ2) is defined as: The average of the squared differences from the Mean.

Then we have risk of ruin. (ROR) The probability of losing your bankroll. Can be expressed as a trip risk of ruin or total bank risk of ruin. One heck of a lot more can be said about risk of ruin but we’ll just leave it at this for now.

Same for Di and c-Score. I don’t understand those yet so it’s just be said those values are calculated as well.

The smaller image shows that N0 is also presented by the simulation. N0 is the number of rounds played that should put your expected value equal to standard deviation. N0 = Var / EV^2 is given by the Blackjack Book Encyclopedia, but I don’t understand it.
From cvcx help we have:
“Optimal Kelly Bank - This is the bankroll in units required for a risk of ruin of 13.5%. This is also the risk level used in SCORE calculations.
Optimal Kelly Bank - This is the optimal unit size in dollars for maximization of growth.
N0 - N0 is another strategy scoring technique developed by Brett Harris. It is defined as "the number of rounds that must be played, with a fixed betting spread, such that the accumulated expectation equals the accumulated standard deviation As such, it is a measure of how many rounds must be played to overcome a negative fluctuation of one standard deviation with such a fixed spread." See the article The Theory of Optimal Betting Spreads on http://www.bjmath.com (Archive copy) for more information”. http://www.bjmath.com/bjmath/Betsize/theory.htm (Archive copy)

Now we come up with true count frequencies, expected values and standard deviation for a given true count.

The true count frequencies I just think is the percentage value for how often a given true count presented for the simulation. More or less how often a given true count presents, it tends to be normalized over time.

The expected values or win/loss percentage figures are presented for each given true count. I think this is essentially the percent advantage for a given initial bet that one would realize if that true count was to present.

Standard deviation figures are given in terms of (I think) units for each given true count. I believe that would be a measure of how much dispersion your results would present from the expected value for that given true count for a given initial bet.

Standard error , hmm well I’m not sure how the term is used for cvcx.

so that's most what i can say about simulations....... part two, i rant on about Kasi's spread sheet.

sagefr0g · Feb 27, 2009

part two, the spread sheet

Kasi said:

So now I wanna try and see if I can say something about what’s going on with Kasi’s spread sheet, maybe come to a better understanding of it all.
So the first image is very similar to the rows and columns of cvcx where the true count frequency, expected value at a given true count and standard deviation at a given true count are presented. So this is where you need a simulator such as cvcx to get that information so as to update the spreadsheet.
The figures in red under the bet column are in terms of units bet and can be changed without messing things up.

Below E19 bankroll in units, E20 lifetime bankroll & E21 unit size in dollars are fairly self explanatory.
E20 & E21 in read can be changed at will and E19 will update.
E23 the average bet in units is computed by multiplying the frequency a true count will present by the number of units bet where this product is computed and summed over the range of true counts in like manner. E24 average bet dollars per hand is pretty much self explanatory.
E25 win rate per round in units is computed by multiplying the frequency a true count will present by the win rate (or initial bet advantage) for that true count times the number of units bet for that true count where this product is computed and summed over the range of true counts in like manner.
E26 standard deviation in units per round is computed squaring the standard deviation per true count and bet per true count then multiplying the frequency times the squared std dev & squared bet, the same is done for each true count range and summed then the square root is taken.
E27 win rate per 100 hands in units is self explanatory.
E28 standard deviation per 100 hands in units is computed by taking square root of 100 and multiplying by E26 the standard deviation in units per round.
E29 win rate in dollars per round is computed by multiplying the true count frequency, the advantage at a given true count and the units bet at a given true count then summed over the range of true counts in like manner. That value is then divided by the unit dollar value.
E30 the standard deviation per round in dollars is just figured by multiplying the standard deviation in units per round by the unit dollar value.
E31 the win rate per 100 hands in dollars is just figured by multiplying the win rate per 100 hands in units by the unit dollar value.
E32 standard deviation per hour in dollars is just figured by multiplying the standard deviation per 100 hands in units by the unit dollar value.
E33 variance in dollars squared per round is just the standard deviation per round in dollars multiplied by itself.
E34 W/L% is computed by multiplying the true count frequency & the advantage for a given true count by the units bet for a given true count summed over the range of true counts and then divided by the sum of the products of the frequency of each given true count & the amount bet at each given true count.
E36 hours to double bank is computed by dividing bankroll by win rate per 100 hands in units.
E37 rounds to double bank is computed by dividing bankroll by win rate per round in units.
E38 number of average unit bets in bankroll is computed by dividing bankroll by average bet units.
E39 hours to N0 is computed by squaring standard deviation per 100 hands in units divided by win rate per 100 hands in units.
E40 rounds played to N0 is computed by multiplying hours to N0 by 100.
E42 risk of ruin is computed by taking [one minus (win rate per round in units divided by standard deviation per round in units)] divided by [one plus (win rate per round in units divided by standard deviation per round in units)] where all that is taken to the power of the bankroll in units divided by standard deviation per round in units.
E43 the risk of halving the bankroll is computed by taking the square root of the risk of ruin.
E44 the DI is computed by (dividing the win rate per 100 hands in dollars by 100) and then dividing that value by (the standard deviation per hour in dollars divided by 10) and then multiplying all of that by 1000.
E45 the score is the DI squared.
I’m going to skip over the goal with no time limit, the trip ror, long term ror and long term ror solved for rate stuff. Cause I totally don’t understand what’s going on with all that, lol.

E85 is the number of hands played and can be changed.
E86 the expected value for the number of hands played is computed by multiplying the number of hands played by the average bet in dollars per hand and the W/L% or the advantage the player has over the game.
E87 the total variance is computed by multiplying the number of hands played by the variance in dollars squared per round.
E88 which is one standard deviation for the number of hands played is computed by the standard deviation per round in dollars by the square root of the number of hands played.
E89 low one standard deviation is the expected value for the number of hands played minus one standard deviation for the number of hands played.
E90 high one standard deviation is the expected value for the number of hands played added to one standard deviation for the number of hands played.
E92 which is two standard deviations for the number of hands played is computed by multiplying the value for one standard deviation by two.
E96 which is three standard deviations for the number of hands played is computed by multiplying the value for one standard deviation by three.
E100 which is four standard deviations for the number of hands played is computed by multiplying the value for one standard deviation by four.
The low and high standard deviations for 2sd, 3sd & 4sd are computed by subtracting or adding the expected value to the standard deviation value in question.

Kasi · Feb 27, 2009

sagefr0g said:

Yes, that's what I'm doing with the SD column - turning it into variance so I can add it. With Powersim sims his column is already variance so I don't do it. (That took me a while to figure out one night lol.)
Likewise with the bets - it's turning the bets into the variance of the bets.

Since, say, if flat-betting, 1 SD in BJ is 1.15 units on average when betting 1 unit for one hand. But for 100 hands it's 1.15*sqrt of 100 since SD=1.15X*sqrt of y where x is flat-betting x units per hand and y is number of hands.

So, basically, it's just making them the same animal so they can be added up and square-rooted later lol.

Also, I don't know, but I think this squaring stuff has to do also do with just making life easier when things are left of the curve and have negative values. So squaring them makes them all positive and easier to deal with.

Yeah - I think doing that would give you a flat-bet BS advantage for the game. Not only indexes would have an effect but also the cut-card. Maybe you could even do it with freq and SD column to get avg SD for the game?

I guess it should end up something close to what it,they are at TC0 anyway lol.

As Henry Higgins? would say in that musical when she could say the rain in Spain stays mainly in the plain "By George I think he's got it!" lol.

And keep in mind, quite often I don't understand the why behind most of this stuff. So for heaven's sake don't start asking me about why a hyperbolic sine function is used in the Goal Reach stuff or logarithms or log growth, binomial whatever, etc lol.

I'm a lazy guy - spend an hour to get a formula I copy from somewhere working and then never think about the why again. OK, sometimes I do, sort of lol. Glad you are.

Kasi · Feb 27, 2009

sagefr0g said:

Great post.

I say move to include in "Sticky Stuff".

N0 is easy - it's just intended to show that by that time when your EV=the range of 1 SD, there's a good chance your results are not due to random fluctuations but likely due to the fact you actually are playing a winning game.

What don't you understand about it - the "why" of the formula?, how to calc it? What it means? It's an arbitrary notion.

From just the top row of your picture, you ought to be able to calculate that 60000 or so hands as N0. ANd then verify that after that many hands, your EV will equal the spread of 1 SD.

Kasi · Feb 27, 2009

sagefr0g said:

I forgot how complicated I made it lol. At some point I wanted all the formulas to be based and use nothing but what's "on top".

But of course alot of it can obviously be greatly simplified - like win rate per round could just be W/L%*avg bet.

I just mention that becasue it may not always be obvious from some cvcx sims when one is not playing 100 hands per hour becasue the table is full or whatever.

And this sheet is not set up for back-counting when one only plays 25% of all hands seen etc. That's another one lol. But you could tweek it do that.

I see the usefulness of hourly win rates - maybe comparing one game to another, etc but if, over time, all you know is how many hours you played, if you played at fulltables, half-full tables, heads-up etc a stated hourly win rate may not be that realistic as EV.

I mean if I did this stuff, when I got back to my room, I'd estimate the number of hands I actually played rather than just write down how many hours I played.

If this sheet doesn't convince someone to just buy the sim, I don't know what will lol.

sagefr0g · Feb 27, 2009

Kasi said:

well i guess if you try and get something to conform to excel's stuff then sometimes it's gonna get complicated.
so but for me just starting to deconstruct or what ever, look at the formula's in your spread sheet it's a lot of stuff Schlesinger talks about that's hard to get a handle on. lol, i can kind of work backwards from your spreadsheet and sort of have a leg up when i reread Blackjack Attack. i get kind of lost what Schelsinger's talking about sometimes when he tells the stories behind stuff and then it's like when he goes back to the maths, i'm like, wtf, i forgot what the heck it was even about. lmao.
so but getting a handle on the spreadsheet even helps understand cvcx and other blackjack stuff, for me anyway.
but i guess, eventually i'll take those formula's i tried to summarize and maybe write them out in more simpler mathematical form and maybe learn something from that.

Kasi · Feb 27, 2009

sagefr0g said:

Hey the main thing is, like you said, all a sim does is generate TC freq and the adv and SD at each TC. I think lol.

All else can be figured out from that. No doubt QFIT will tell me I'm full of it.
In which case, and there would be no doubt, I'm full of it

But so what, even if not. Just buy the sim and have it do the rest of the figuring out for you. You need it anyway to generate the raw data.

I guess it did come in handy using Walker's SP21 book when all she gave were tables of freq and adv and variance at each TC. And covariance too - handy for spreading to more than 1 hand. CVCX doesn't give covariance by TC as near as I can tell. I think, when spreading to multiple hands, it's just incorporated into the total variance and expressed as one number that way. All at diff pen levels using various number of indexes or not and for the different basic SP21 games - H17, S17, redoubling or not etc. So, basically, all I had were the first 3 columns under various assumptions.

But no optimal ramps per se, no win rates, no avg bet, no SD per round, no ROR, no N0, no SCORE, no trip roll calculator, no goal calculator etc. But I generated similar tables just for fun for SP21 like Don's tables in CH 10 using the same formulae. Sort of a "manual sim" lol.

sagefr0g · Feb 27, 2009

Kasi said:

lol pay no attention to the man behind the curtain.

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