Standard Deviation

[jaredmt]

how can I figure out my standard deviation based on the counting system I use, what count I play at, and what betting system I use?

is there a formula based on your edge and betting system?

I use wong halves. minimum is $10. @ +2 i bet $20 and add an extra $20 for every true count after that. I truncate the count rather than rounding. Im not entirely sure what my max will be. somewhere between $30 and $100 (probably doesnt help much). I only play when count is at +1 or better. I bet insurance at +3 but i might wait till +3.5 or +4 to lower the SD

all this assuming a regular game where BS player gets .5% disadvantage.

p.s. i did see the SD chart for BS flat betting, but I would think SD is a lot bigger for some one who plays with an advantage and raises bets

[FLASH1296]

The S.D. for HALVES is listed in Professional Blackjack by Stanford Wong.

Note that it is for the 6 deck S17 game with NDAS so your SD is actually slightly larger, as is your e.v.

As to your assumption re: increased SD due to betting more money, I think that you are correct because the Standard Deviation is the Square of the Varainace.

[Sonny]

Originally Posted by jaredmt

how can I figure out my standard deviation based on the counting system I use, what count I play at, and what betting system I use?

The most accurate way is with a simulator. Blackjack Attack has an entire chapter filled with results from just about any game you'll find, but it's for HiLo.

-Sonny-

[jaredmt]

ok it says win rate is $17 and SD is $426

but benchmark raises bets faster than me. they raise $25 at a time, starting at 0 or +1. i do $20 at a time starting at +2. so I will always have less money on the table until the tc reaches +6, when i hit my max of $100. do you think this will lower the SD a lot? or would it even out to the same since I will probably be playing 8d mostly?

[Kasi]

Originally Posted by jaredmt

how can I figure out my standard deviation based on the counting system I use, what count I play at, and what betting system I use?

is there a formula based on your edge and betting system?

I don't think edge would matter.

But once you know the frequency the TC's will occur, the advantage associated with each RC and the variance or SD associated with each TC, then yes you can calculate your Stan Dev from that if you want.

And, basically, that's what a sim will do for you and why you need one, like Sonny says, because all those things will change with different games, different pens, different counting systems, use of indexes, etc. There is no formula that will figure freq, adv and sd at each TC. They are what they are once you told the sim everything it needs to know.

But once you have the freq, adv, and sd at each TC, you can pretty much calculate the effect of changing spreads and rolls from there if you want, how SD, risk,N0, and EV etc changes with each different spread without running additional sims for each new spread.

But, really, so what if one can, easy enough to just run another sim if you have one. Plus sims are good at figuring an optimal spread for you giving you the best risk/reward ratio. A good starting point.

But, I sometimes get a little vague on how sims handle multiple hands - covariance issues, wonging out - frequency issues, and maybe even insurance - variance issues lol. Don't worry about it - go with the sim!

[Sonny]

Originally Posted by jaredmt

so I will always have less money on the table until the tc reaches +6, when i hit my max of $100. do you think this will lower the SD a lot?

It might lower your SD a bit, but it will probably lower your advantage even more. Your short-term swings will be smaller since you're getting less action, but your long-term risk will be greater because your advantage is smaller compared to your variance. That means a higher risk of ruin.

As Kasi said, once you get all the numbers from a sim you can play around with them and see how things change with different bet spreads. This spreadsheet will get you started:

http://www.blackjackinfo.com/bb/showthread.php?p=15578

-Sonny-

[jaredmt]

o sweet thanks! i was actually wondering what the frequencies of each TC were too. and I think with this info, I can attempt to write my own program for my own spread, br, and unit size when/if I have the time or the patience lol.

i guess with the 1.33 variance, that means on average you win/lose 1 unit 2/3 of the time and win/lose 2 units 1/3 of the time right? I have basic programming skills so it would be easier for me to calculate everything with %s rather than running through each card and each play.

[callipygian]

Originally Posted by Kasi

I don't think edge would matter.

EV does matter because SD uses (actual-expected) as a term in its calculation. For any system, you need to calculate the EV first before you can calculate SD.

Originally Posted by Kasi

But once you know the frequency the TC's will occur, the advantage associated with each RC and the variance or SD associated with each TC, then yes you can calculate your Stan Dev from that if you want ... I sometimes get a little vague on how sims handle multiple hands - covariance issues, wonging out - frequency issues, and maybe even insurance - variance issues lol. Don't worry about it - go with the sim!

SD's can be calculated from the win-loss percentages for every combination of player cards vs. dealer cards. It's just sqrt[ Sum {P(i,j)*((%win(i,j)*Bet(i,j) - EV(i,j))^2-(%lose(i,j)*Bet(i,j)-EV(i,j)))}].

[callipygian]

Originally Posted by jaredmt

i was actually wondering what the frequencies of each TC were too.

That depends on the number of decks and the penetration.

Originally Posted by jaredmt

i guess with the 1.33 variance, that means on average you win/lose 1 unit 2/3 of the time and win/lose 2 units 1/3 of the time right?

No, it would mean that 68% of the time, your actual result will fall within sqrt(1.33) units of your expected result, and 95% of the time, your actual result will fall within 2*sqrt(1.33) of your expected result. SD = sqrt(variance).

Note that a 1.33 variance is pretty low. Sonny gave me a ballpark figure of SD = 2.5 to 3 for most counters; I've found through my own calculations that SD's can go as low as 2 under some Wonging conditions. These would correspond with variances of 4 to 9 ... a variance of 1.33 corresponds to a SD of 1.15, which is flat betting.

[Sonny]

EDIT: See calliphygian's corrections to this post below

Originally Posted by callipygian

For any system, you need to calculate the EV first before you can calculate SD.

If you’re calculating the variance through simulation (instead of a population of known data points) you don’t necessarily need to calculate the mean (EV) first. In the case of most gambling games you can just take the average squared result. For example, the pseudo-code for calculating the variance of a coin toss might look something like this:

for (rounds = 0; rounds < N; rounds ++)
{
   Result = Random Number (0|1);
   If (Result == 0){
      Win = WinPayout;
}
   else {
      Win = LossPayout;
}
   Bankroll += Win
   Variance += Win^2;
}

VariancePerHand = Variance/N;
SDPerHand = Sqrt(VariancePerHand);

-Sonny-