CVCX Standard Deviation Calculation

**MercySakesAlive** · 01-16-2017, 02:08 PM

I'd like to know how the standard deviation calculation is made in CVCX for the two or three highlighted areas in the screenshot that is attached.

I'd like to know just for my own amusement more than any other reason.

CVCX has helped me have a fun hobby where I seem to consistently win for the past two years! Thanks!

**Norm** · 01-16-2017, 05:40 PM

It's the normal standard deviation calculation, assuming a full population: https://en.wikipedia.org/wiki/Standard_deviation

**MercySakesAlive** · 01-17-2017, 01:05 PM

For instance, to find the SD in the big box up top I need to know the "mean" and the "data points". Its probably very obvious to a math wiz like yourself, but I would like to know which are the "data points" that I add up to calculate "the mean". I can't seem to figure out which column of data I should be looking at. Thanks for taking the time to help me!

**Norm** · 01-17-2017, 01:22 PM

The mean is assumed to be zero, which is the norm with blackjack. There are hundreds of millions of data points.

**DSchles** · 01-17-2017, 02:13 PM

Originally Posted by MercySakesAlive

For instance, to find the SD in the big box up top I need to know the "mean" and the "data points". Its probably very obvious to a math wiz like yourself, but I would like to know which are the "data points" that I add up to calculate "the mean". I can't seem to figure out which column of data I should be looking at. Thanks for taking the time to help me!

The s.d. is the square root of variance. When the mean is assumed to be zero, the variance is the same thing as the average squared result of a hand of blackjack <i>at that particular count.</i> So, you simply catalog the results of the hands played at that count (win 1, lose 2, win 4, lose 0.5, etc.), square them, weight them by frequency, to get the variance, and then take the square root, to get the s.d.

To see how this would work out globally, without respect to count, go here: http://wizardofodds.com/games/blackjack/appendix/4/

Don

**MercySakesAlive** · 01-17-2017, 11:28 PM

Thanks, Don. Thanks, Norm.

I'm specifically confused about, in the example in the attachment, my win rate per hour is $60.73 but my SD per hour is $758.42.

What can infer about this game by looking at SD? I don't know how to look at SD in a meaningful way. Can I look at SD and say "wow, that SD is way too big!" ?

**bigplayer** · 01-18-2017, 06:11 AM

Looks to me like your Variance is sky high because your bet ramp is so sub-optimal. You're betting 2x$15 with a 1.3% edge but 2x$250 with a 3.8% edge. Your 1% to 2% edge bets are not big enough to get you into the long run very quickly. Notice your top bet is 2.5x higher but your win rate is only 50% higher. Your SCORE is only marginally better and your Certainty Equivalent is negative when ideally it should be around 50% of your win rate.

**seriousplayer** · 01-18-2017, 07:55 AM

Originally Posted by bigplayer

Looks to me like your Variance is sky high because your bet ramp is so sub-optimal. You're betting 2x$15 with a 1.3% edge but 2x$250 with a 3.8% edge. Your 1% to 2% edge bets are not big enough to get you into the long run very quickly. Notice your top bet is 2.5x higher but your win rate is only 50% higher. Your SCORE is only marginally better and your Certainty Equivalent is negative when ideally it should be around 50% of your win rate.

Please elaborate more on you post. Why is the variance sky high when it is 15597. The edge on the sim for the custom bet is 2.259% but you have it as 3.8%

**MercySakesAlive** · 01-18-2017, 11:56 AM

Blackjack CVCX 0 top bet.jpg

Thank you for the reply, bigplayer. That screenshot was a somewhat arbitrary set up just to use an example to try to learn some more about how to read SD values in a meaningful way. Here's a betting ramp I was thinking about though. Any comments are appreciated. I'm a hobbyist who has played a $5 - $125 spread for a couple years with success and thought I'd up my bets to this schedule here if the heat was low. (The only difference with this betting schedule is that my bankroll is $25,000 instead of $10,000)

**seriousplayer** · 01-18-2017, 01:06 PM

Originally Posted by MercySakesAlive

Blackjack CVCX 0 top bet.jpg

Thank you for the reply, bigplayer. That screenshot was a somewhat arbitrary set up just to use an example to try to learn some more about how to read SD values in a meaningful way. Here's a betting ramp I was thinking about though. Any comments are appreciated. I'm a hobbyist who has played a $5 - $125 spread for a couple years with success and thought I'd up my bets to this schedule here if the heat was low. (The only difference with this betting schedule is that my bankroll is $25,000 instead of $10,000)

How many rounds of simulation did you run? Because the "Standard Error" is high .017 for optimal and .010 for custom. I would run more round to get the "Standard Error" for both optimal and custom down to between .001 - .004. Also, just a question what did you do to make the B5, B7, B9 blanks and what does it mean?

**bigplayer** · 01-18-2017, 01:29 PM

At each 0.5% of advantage you should be betting around 2x$25 for a roughly optimal ramp. At a 1% edge you should be wagering around 2x$50, not 2x$10 for your $25,000 bankroll and a 1/3 Kelly Betting Fraction. Your edge is indeed higher using your strategy but your are giving up a ton of EV. You'd probably make more money spreading 2x$5 to 2x$100 optimally than you are making spreading 2x$3 to 2x$250 sub-optimally. The second bet approach above is much closer to optimal, although I don't know whether a casino would take it for very long.

**MercySakesAlive** · 01-18-2017, 02:51 PM

Serious player, thanks for the heads up on the standard error value. I ran a lower simulation number (1000 million) so yeah I'll take your advice.

The B5, B7, B9 etc boxes are blank. These bets were set in the "depth bets" section on the "sim page" (the page right before you run the sim).

The boxes 5,7,9 etc are empty because I didn't assign a number in the depth bets to 5,7, or 9 etc because I adjust my bets every on even counts.

I probably over explained that but there you go.

**MercySakesAlive** · 01-18-2017, 02:54 PM

bigplayer, thanks, I am going to play around with those ideas. I'd love to get a little insight on how to interpret the standard deviation numbers in a meaningful way. even if I have to convert them to variance values. can one look at a variance or SD value and say "wow, that betting schedule or game or playing strategy has way too much variance." ?