sd screenshot.jpg
1. I'm working with BJA3 and trying to get a basic grasp of how SD is calculated.
2. The rough and dirty formula on pg 16 is SD = 1.1 * (sq root of # of rounds of play).
3. So if I want to find the SD for 1 round of play then is it just :
SD = 1.1 * (sq root of 1) = 1.1 * 1 = 1.1 units
1 unit = $8.04
1.1 unit =$8.84
4. CVCX tells me SD per round is $25.09 so obviously I'm not even in the ballpark.
Help.
A standard deviation of 1.1 is a very rough estimate for the standard deviation if one round of blackjack in units. This is not the same as the global standard deviation of your system, which considers the frequency of each true count, the standard deviation at each true count, and how much you bet at each true count.
CVCX does not display the standard deviation of your system in units, so you have no way of verifying the $25.09 manually. However, if you believe the $25.09 figure (and you should!), the standard deviation of your system in units is 25.09 / 8.04 = 3.12
Actually, if you export you CVCX sim to excel it will provide the SD for each true count giving you the information need to calculate the same SD.Originally Posted by Gronbog
Luck is nothing more than probability taken personally!
Covariance. About 0.50 for two blackjack hands played simultaneously. See the bottom of page 24. But, you bring up an interesting point. This explanation comes AFTER the chart I referred you to, and perhaps some allusion should be made to the explanation at the earlier point.
Don
I am trying to calculate the total standard deviation using the method on page 20 of BJA3.
I'm doing something wrong because my math shows SD is 1.16 units but CVCX shows SD is 2.53 units.
The sim is a simplified bet ramp just for the purpose of learning how to calculate SD.
Any advice is appreciated.
SD total CVCX Screenshot1.jpg
SD total CVCX Screenshot.jpg
When you are backcounting the total frequency is not 1. You have to count rounds observed but not played as rounds. You may notice Don's charts on page 20 of BJA3 all divide the product of variance times frequency by frequency. Notice the frequency being divided is around 25 to 30 percent. You need the frequency of the counts you just watch and that plus the frequency of the hands you play is 1. The sim data implies you are playing 46% of the total rounds.
Last edited by Three; 05-22-2018 at 12:47 PM.
I ran the formula once on a calculator and got the right answer. Thanks for catching the frequency mistake. Perhaps I made a mistake when I did it but I don't think so.
Total Variance = (($5^2*0.8005*1.161^2) + ($60^2*0.0807*1.153^2) + ($200^2*.1188*1.160^2))/($32.6^2*1.00)
= ($$25*1.0790107+ $$3600*0.1072833 + $$40000*0.1598572)/$$1062.76
=($$26.975267 + $$386.21988 + $$6,394.288)/$$1,062.76 = 6,807.4831/1,062.76
= 6.4054754
Total SD = SQRT(Total Variance) = SQRT(6.4054754) = 2.530904
Now double checked on a calculator with the math to be reviewed by all.
I don't see how not dividing by the SQRT(1062.76) would be right, unless you used bets expressed as a multiple of average bet instead of dollars. If you did the latter the division by average bet squared would be dividing by 1, which would drop out of the equation. Of course expressing a bet in any unit would do the same thing. Without adjusting for monetary units of average bet variance would be in dollars and need to be divided by average bet squared or divide the SD calculated by average bet to get the variance that would produce the SD of 2.53 units that the OP is looking for.
Last edited by Three; 05-23-2018 at 08:33 AM.
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