Please help blackjack newbie.

Thank you to all of vegas of wizard users. I was got lots of useful information from this forum.
And sorry about my wreck of English. I'm not native.

Anyway. As I know, I can measure range of profit and loss using variance.

Assume below condition.

Bet same amount of money = unit
number of play hands = hands
ignore house edge
No side bet.
Follow basic rule

At a rough level. Sqrt (hands)*1.21*unit is range of profit and loss.

So if I play 100 hands. I will suffer 12.1 units up and down.

And standard Normal Distribution chart show over 20 units of profit and loss probability under 10%.

But, my game result history show. Over 20 units volatility about 20~25%.

Sample size, about 20k played hands.
Additionally, I play 5 hands against one dealer's hand.

I mean, 1unit $20 is mean my bet $4 each hole.

That makes me confuse.

So, question Is my volatility formula is right? Or something wrong.

If I'm misses anything to measure risk. Please let me know.

Thank you.

SD for blackjack is more like 1.15

Assuming house edge of 0.5% you’d expect a win or loss above 11.5 units about one in three sessions. Session length 100 hands

Quote: daypay

Thank you to all of vegas of wizard users. I was got lots of useful information from this forum.
And sorry about my wreck of English. I'm not native.

Anyway. As I know, I can measure range of profit and loss using variance.

Assume below condition.

Bet same amount of money = unit
number of play hands = hands
ignore house edge
No side bet.
Follow basic rule

At a rough level. Sqrt (hands)*1.21*unit is range of profit and loss.

So if I play 100 hands. I will suffer 12.1 units up and down.

And standard Normal Distribution chart show over 20 units of profit and loss probability under 10%.

But, my game result history show. Over 20 units volatility about 20~25%.

Sample size, about 20k played hands.
Additionally, I play 5 hands against one dealer's hand.

I mean, 1unit $20 is mean my bet $4 each hole.

That makes me confuse.

So, question Is my volatility formula is right? Or something wrong.

If I'm misses anything to measure risk. Please let me know.

Thank you.
link to original post

First, Blackjack is not really my strong suit.

Second, it's very possible that I misunderstood your post.

That said, I don't know what basis you are using to calculate what you're doing, in terms of variance/SD. 1,000 initial deals playing five-handed at $4/hand is going to have more variance than 5,000 initial deals playing one-handed at $4/hand because so much of it comes down to the dealer's final hand.

Anyway, perhaps I did misunderstand what you're asking. If I didn't, then it seems like you're using the SD on $20 as if you were betting $20 playing one-handed, possibly.

Thank you.
There was a slight error in the SD I used, but I am glad that the calculation formula itself is not wrong.
Then, let's think that the sample size is small, so the variability is measured larger than the theory

My English is not good enough.
There was a lack of accurate explanation. Nevertheless, thank you for your consideration to give me the best answer.

My question was whether the expected profit and loss calculation that I used to play blackjack was correct.

Thanks to Ace2 who replied above, I could see that the calculation method was not very different.

Thank you for taking the time to answer me again.

Quote: daypay

Thank you.
There was a slight error in the SD I used, but I am glad that the calculation formula itself is not wrong.
Then, let's think that the sample size is small, so the variability is measured larger than the theory
link to original post

Nope. If you played 3000 sessions (100 hands per session), about 1000 of them would fall outside of one SD

daypay, welcome to the forums! As mentioned by others the variance is "around" 1.15... I say "around" because the exact rules of the game effect the basic strategy (yes there is different basic strategy pending the rules of the game) which in turn effect the variance.

Also, you mentioned you're playing 5 hands against the dealer 1 hand, thus you're introducing co-variance of each of the hands... because while they're independently played and payed from one another, the cards drawn on each effect the your hands at the table. An obviously easy example of this would be if you played 5 hands in a single deck game and your first 4 hands got aces (lucky you)... so what's the odds of getting a blackjack on your last hand? I believe Wong discusses co-variance in enough detail in his book Professional Blackjack.

With your specific situation in mind, I would actually point you towards software like CVCX. With this software you can input your exact game conditions (or any other game you come across) and it will give you more information than you'll know what to do with up front... as well as the variance/etc.

If you check some of my blackjack posts from probably 5+ years ago you'll see I talk a lot about EV's, SD's, etc, etc.

Lastly, there are 3 articles on this website that go pretty in depth ("A to Z") with blackjack in reference to card counting. You did not specify much interest in counting with your problem above, but this goes in to a bit more of the frequencies and math behind so maybe it can give you some direction with your current situation. =)

https://wizardofvegas.com/articles/A-to-Z-Counting-Cards-in-Blackjack/

SD is around 1.15. Variance is around 1.32

As long as you’re playing basic strategy in a 3:2 game, rule variants will have a negligible effect on that

Assume 1/2 percent edge, don’t fuss over tiny playing adjustments for rule variations, and this will be accurate within $5 per hour of play as a $100 bettor on the strip. No need to split hairs over a few bucks

Quote: Ace2

SD is around 1.15. Variance is around 1.32

As long as you’re playing basic strategy in a 3:2 game, rule variants will have a negligible effect on that

Assume 1/2 percent edge, don’t fuss over tiny playing adjustments for rule variations, and this will be accurate within $5 per hour of play as a $100 bettor on the strip. No need to split hairs over a few bucks
link to original post

You didn’t address Covariance on playing five hands.

Quote: unJon

Quote: Ace2

SD is around 1.15. Variance is around 1.32

As long as you’re playing basic strategy in a 3:2 game, rule variants will have a negligible effect on that

Assume 1/2 percent edge, don’t fuss over tiny playing adjustments for rule variations, and this will be accurate within $5 per hour of play as a $100 bettor on the strip. No need to split hairs over a few bucks
link to original post

You didn’t address Covariance on playing five hands.
link to original post

The covariance problem in blackjack is actually a dealer-blackjack problem, mostly I believe. When the dealer has a blackjack hand, you will lose both two-hand hands simultaneously. If it is a 3:2 blackjack game, this covariance value will be significant; however, if it is a 6:5, the covariance will be negligible. I think.

Quote: aceside

Quote: unJon

Quote: Ace2

SD is around 1.15. Variance is around 1.32

As long as you’re playing basic strategy in a 3:2 game, rule variants will have a negligible effect on that

Assume 1/2 percent edge, don’t fuss over tiny playing adjustments for rule variations, and this will be accurate within $5 per hour of play as a $100 bettor on the strip. No need to split hairs over a few bucks
link to original post

You didn’t address Covariance on playing five hands.
link to original post

The covariance problem in blackjack is actually a dealer-blackjack problem, mostly I believe. When the dealer has a blackjack hand, you will lose both two-hand hands simultaneously. If it is a 3:2 blackjack game, this covariance value will be significant; however, if it is a 6:5, the covariance will be negligible. I think.
link to original post

No, lots of co variance when dealer busts, or draws to 21 from a 6, or…. lots of dealer hands…. Certainly NOT just against blackjacks

Quote: SOOPOO

Quote: aceside

Quote: unJon

Quote: Ace2

SD is around 1.15. Variance is around 1.32

As long as you’re playing basic strategy in a 3:2 game, rule variants will have a negligible effect on that

Assume 1/2 percent edge, don’t fuss over tiny playing adjustments for rule variations, and this will be accurate within $5 per hour of play as a $100 bettor on the strip. No need to split hairs over a few bucks
link to original post

You didn’t address Covariance on playing five hands.
link to original post

The covariance problem in blackjack is actually a dealer-blackjack problem, mostly I believe. When the dealer has a blackjack hand, you will lose both two-hand hands simultaneously. If it is a 3:2 blackjack game, this covariance value will be significant; however, if it is a 6:5, the covariance will be negligible. I think.
link to original post

No, lots of co variance when dealer busts, or draws to 21 from a 6, or…. lots of dealer hands…. Certainly NOT just against blackjacks
link to original post

Maybe you are right, but I posted this specifically to seek comparison of the covariance values between a 3:2 and a 6:5 blackjack games.