Using common, easy to learn blackjack strategies, the std dev of X is around a=26 times the mean of X, X being the change of one’s balance over the course of 100 hands.

If n = a^2, then the mean of the total = the std dev of the total.

This means that after about n=676 hands, the expected value of total change in balance is n X = 676 X, and std dev of value of total change is also 676 X. You’ve got a 68% chance of being above water at that point.

When n = 4 a^2, the expected value is twice the std dev of the value, so you have a 95% chance of being above water at that point etc.

However, also of interest is the risk. Almost certainly at some point you will be underwater. The statistics of the universal minimum will be of interest. There’s about a 50% chance that the UM will be worse than -230 X. There’s about a 10% chance that it will be worse than -830 X. There’s a 1% chance it will be worse than -1600 X.

To be continued:

Yeah if I can just cut you short…

Probably easier to just count the cards…

It’s not hard.

Some call it luck…

Multiple decks of cards are used these days.

Multiple decks of cards are used these days.
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Doesn’t matter.

All decks have the same value.

100 hands is about what you can expect in an hour at a casino. It will vary but it will be of that order.

There will be only a limited range of people, then, to whom blackjack will be an appealing prospect as a means of a living (as distinct to an entertainment option.)

Someone who is capable of playing sufficiently advanced strategy to have this a 100 hand std dev to mean ratio of 26 will probably have other employment options.

Consider someone who would be willing to do this for an expected benefit of $60 per hour (This has to cover the accommodation and travel expenses associated with being a professional blackjack player.)

If they were self-financing, and they were willing to accept a 1% chance of a complete wipeout, they would want a bank of $100000.

Let’s assume the person can flog themselves and play 8 hours a day for 300 days a year without getting barred or going batshit. 2400 hours, 240000 hands per annum. $144000 minus expenses and taxes. But that’s the expected value. After a year there would be a 2% chance that they would be in the negative. The std dev = $76000. So basically it would require a commitment for years. Given the money they are risking and the alternative lines of business they could be in, it may not appeal to a lot of people. Obviously someone who has millions of dollars can except the risk but someone who has millions of dollars probably doesn’t want to be playing fkn blackjack for a living, which basically involves concentrating all the time for hours on end. They can make a good living just on ordinary investments.

So perhaps professional blackjack is best suited to a) those who have a steady outside income so that they can ameliorate the variance in the blackjack earnings (hence, I suppose, being semi-professional blackjack players), or b) cases where the people playing are not the people risking the money. Someone with a bank of tens of millions of dollars can bankroll dozens of players and have no significant risk over the course of a year, while the people playing can be guaranteed a respectable wage.

Probably easier to just count the cards…
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It should think it is obvious that card counting is part of any strategy with a positive expected return…

http://filmbalaya.com/2011/10/10/sf-docfest-2011-holy-rollers-the-true-story-of-card-counting-christians-review-and-trailer/

Jesus approves of card couting.

+n

It should think it is obvious that card counting is part of any strategy with a positive expected return…
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Thats why it is illegal…

No, card counting is not illegal anywhere.

Really. Anywhere.

No, card counting is not illegal anywhere.

Really. Anywhere.
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And the Mafia are a myth…

The mafia’s for real.

Though apparently they ain’t what they used to be.

dv said:

No, card counting is not illegal anywhere.

Really. Anywhere.

But betting on the results of your computations is…

But betting on the results of your computations is…
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No it isn’t.

dv said:

But betting on the results of your computations is…
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No it isn’t.

Tis my impression from reading about card counters who go to get lengths to disguise themselves and their activities if caught beating the odds by card counting then you are kicked out of the casino and they ring all their mates to tell them. But I may be wrong.

OK legal or not, you will get your arse kicked out of the casino…

The three components to successful advantage play are

a) keeping count (duh)

b) keeping your betting and decision strategy straight in your head

c) evading detection

I’ve had people sneak up behind me and put their money on my cards. I left.

c) evading detection
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Yeah but no but, but yeah…

How do you avoid detection by winning…

How do you avoid detection by winning…
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Sometime people win without counting. They don’t kick out everyone who has a few wins.

They don’t kick out everyone who has a few wins.
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OK my bad, I thought you were working on a system of 8 hours a day for 300 days…

OK my bad, I thought you were working on a system of 8 hours a day for 300 days…’
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Certainly you’d want to be doing it in a town with numerous casinos…

It seems we need an estimate of the frequency of activating the casinos’ card-counter alarms.

I’ll leave dv to do the numbers.

The Rev Dodgson said:

It seems we need an estimate of the frequency of activating the casinos’ card-counter alarms.

I’ll leave dv to do the numbers.

Which i think are, for the most part, based mostly on identification of the spread of bets relative to which cards have already been played. Not an easy thing to do…

Basically you’ve got to mix it up, don’t just have a high-bet and a low-bet, occasionally make “mistakes” etc.

This means that after about n=676 hands, the expected value of total change in balance is n X = 676 X, and std dev of value of total change is also 676 X. You’ve got a 68% chance of being above water at that point.

When n = 4 a^2, the expected value is twice the std dev of the value, so you have a 95% chance of being above water at that point etc.
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I’m somewhat disappointed that none of you spotted my deliberate error. The standards are slipping.

Obviously I meant 84% in the first paragraph, and 97.5 % in the second, as these would be one-tailed tests.