bfbagain: Misinterpreting terms, e.g., volatility

[bfbagain]

Before this becomes a thread that ends off the page, I'd thought I clarify something, in a more common sense way, so new players get a more realistic understanding, i.e., in laymen?s terms, what volatility, variance, and standard deviation essentially means.

Let's get some of the math terms out of the way. Standard Deviation is the square root of variance. Understand variance, and you'll understand standard deviation, e.g., "SD."

The non-mathematical, read: statistical definition of variance is a difference between what is expected and what actually occurs. Basically, we call this luck

Contrast this with the pure mathematical definition, i.e., The square of the standard deviation. In other words, adding a statistical measure of the variability of measured datum from the average value of the set of data.

Now SD's mathematical definition is simply a formula, but that doesn't really define it. A better definition is The higher the standard deviation of an expected return, the greater the relative riskiness because of uncertainty in the amount of return.

The key word here is uncertainty. So in an attempt to quantify (measure), RISK, we use SD to define a range of values, and within these values, i.e., the variation of these values, lies VOLATILITY.

Volatility is defined, in laymen?s terms as, being easily excited, that is, it is the relative rate at which the numbers in a specified range are moving up and down.

So, if a player wanted to understand the term of volatility, they would NOT look at the RESULT of the range of numbers, which we know is the SD of, or the variance, which is the spread of these numbers within this range, but at the FREQUENCY that these numbers change.

Essentially, in the game of blackjack, it breaks down like this: The advantage shifts back and forth between the player and house as the cards are dealt. We identify this advantage and either raise or lower our bets as a result of our identifying the change of this advantage prior to the shuffle. We know that there is risk associated with the change in bet sizes, and we try to quantify this risk through statistical measurements, i.e., we use the mathematical terms SD and variance.

BUT...... the RATE that these numbers change is known as VOLATILTY!

So we have to ask, which of the possible blackjack games offered, will have the RATE of ADVANTAGE change more quickly? The Single Deck game of Blackjack? The Double Deck game of Blackjack? Or the 6/8 Deck games of Blackjack?

If you look, you'll see that long term results, statistically, will favor the Single Deck game.

But if you look at the short term results, you'll see that it is actually the Single Deck Game that MUST have greater VOLATILITY due to the rate of change of advantage that takes place. Just look at TC frequencies, and you'll have your answer. So there clearly is greater volatility, or FLUCTUATION in the Single Deck Game of Blackjack

And to continue with why Single Deck Blackjack scares the bejesus out of the casinos, is that card counters can identify the changes in advantage, and choose to bet the minimums, i.e., make waiting bets, when the house has the advantage, and bet maximums, when we (the player) have the advantage. This change happens rapidly in Single Deck games, as in an ?excited state?, whereas these changes do not occur at the same rate when you add multiple decks. Multiple decks tend to smooth the frequency of advantage changes out, thus there are more ?waiting bets? made, and requiring a larger ?spread? to overcome this lack of advantage change.

cheers
bfb

[Don Schlesinger]

Thank you for a lovely effort. I enjoyed your post, not only because it supports my point of view (:-)), but because it was well-written, and attempted to explain some difficult concepts in layman's terms.

And, even though your distinction between "volatility" and "standard deviation" is not the classical one for finance or investments (more in a moment), it was important to make that point.

Just before reading your post, I had gone to the Chapter 10 charts to do something similar. I had looked at the frequencies of, say, true counts >=+4 in SD and in 6-deck, and, of course, it's no contest. I think it was about 17% for SD and 5-6% for SD, depending, of course, on pen. So, the dispersion of true counts around the mean of zero is considerably wider for SD than for 6-deck, which might be some people's definition of "volatility."

Note, also, that if we look at games with identical rules, the actual line-by-line standard deviations, at each true count, are greater for single deck (by about 0.01 or so) than they are for 6-deck. Again, the game is inherently "more volatile," by its very nature.

Finally, my only quibble is that, in the world of finance, "standard deviation" and "volatility" (of a stock's returns, for example) are, indeed, interchangeable concepts; they mean the same thing. And the traditional definition for "volatility" is: The annualized standard deviation of the continuously compounded returns (log-returns) of the stock.

Thanks again for an excellent post. I think most of us (can't speak for SSR!) will be quite satisfied with the explanations.

Don

[bfbagain]

And yes, it becomes a little cloudy for many people to differentiate between these terms, (as you rightly point out the investment community not being one of them), but it is precisely for that reason I tried to draw a more "layman" like difference between these terms.

The assumptions, and the vernacular used, in specific environments, e.g., Wall Street, tend to make many people's eyes glaze over. So, and I know you saw that, it is with that in mind behind the slight difference in defined terms. :-)

cheers
bfb

[Wolverine]

Thanks for the primer on "statistical terms the newbies screw up." It was very helpful to read, thank you.

Should this be archived for future "newbies" to read through or be directed to? Just my 2 cents.

[Parker]

This looks like as good a time as any to revive the long-dormant "Parker's Picks." Also please archive Don's reply, so that everything is perfectly clear.

I might add (even though it means very little) that this squares with my own experience. I'm not sure if I coined the phrase, "Single deck is a wild roller coaster ride," but I know that I have repeated it many times -- sometime with a few expletives added.

[Norm Wattenberger]

Great post.

"One refuge remaineth, that is patiently to suffer what so euer lucke allotteth."

- Fleming

[Norm Wattenberger]

Even casinos have trouble getting into the long run sometimes. Last fiscal year, the Mohegun Sun payback on $500 slots was 103.63%.

[stainless steel rat]

> Before this becomes a thread that ends off
> the page, I'd thought I clarify something,
> in a more common sense way, so new players
> get a more realistic understanding, i.e., in
> laymen?s terms, what volatility, variance,
> and standard deviation essentially means.

> Let's get some of the math terms out of the
> way. Standard Deviation is the square root
> of variance. Understand variance, and you'll
> understand standard deviation, e.g.,
> "SD."

> The non-mathematical, read: statistical
> definition of variance is a difference
> between what is expected and what actually
> occurs. Basically, we call this luck
> Contrast this with the pure mathematical
> definition, i.e., The square of the
> standard deviation. In other words, adding
> a statistical measure of the variability of
> measured datum from the average value of the
> set of data. Now SD's mathematical
> definition is simply a formula, but that
> doesn't really define it. A better
> definition is The higher the standard
> deviation of an expected return, the greater
> the relative riskiness because of
> uncertainty in the amount of return. The
> key word here is uncertainty . So in an
> attempt to quantify (measure), RISK , we
> use SD to define a range of values, and
> within these values, i.e., the variation of
> these values, lies VOLATILITY. Volatility
> is defined, in laymen?s terms as, being
> easily excited , that is, it is the relative
> rate at which the numbers in a specified
> range are moving up and down .

> So, if a player wanted to understand the
> term of volatility, they would NOT look at
> the RESULT of the range of numbers, which
> we know is the SD of, or the variance ,
> which is the spread of these numbers within
> this range, but at the FREQUENCY that
> these numbers change.

> Essentially, in the game of blackjack, it
> breaks down like this: The advantage shifts
> back and forth between the player and house
> as the cards are dealt. We identify this
> advantage and either raise or lower our bets
> as a result of our identifying the change
> of this advantage prior to the shuffle. We
> know that there is risk associated with
> the change in bet sizes, and we try to
> quantify this risk through statistical
> measurements, i.e., we use the mathematical
> terms SD and variance.

> BUT...... the RATE that these numbers
> change is known as VOLATILTY! So we have
> to ask, which of the possible blackjack
> games offered, will have the RATE of
> ADVANTAGE change more quickly? The Single
> Deck game of Blackjack? The Double Deck game
> of Blackjack? Or the 6/8 Deck games of
> Blackjack?

> If you look, you'll see that long term
> results, statistically, will favor the
> Single Deck game.

> But if you look at the short term results ,
> you'll see that it is actually the Single
> Deck Game that MUST have greater VOLATILITY
> due to the rate of change of advantage that
> takes place. Just look at TC frequencies,
> and you'll have your answer. So there
> clearly is greater volatility, or
> FLUCTUATION in the Single Deck Game of
> Blackjack

> And to continue with why Single Deck
> Blackjack scares the bejesus out of the
> casinos, is that card counters can identify
> the changes in advantage, and choose to bet
> the minimums, i.e., make waiting bets, when
> the house has the advantage, and bet
> maximums, when we (the player) have the
> advantage. This change happens rapidly in
> Single Deck games, as in an ?excited state?,
> whereas these changes do not occur at the
> same rate when you add multiple decks.
> Multiple decks tend to smooth the frequency
> of advantage changes out, thus there are
> more ?waiting bets? made, and requiring a
> larger ?spread? to overcome this lack of
> advantage change.

> cheers
> bfb

I don't disagree with a single thing you wrote.

But the argument starts here:

If a student turned in a report to me, where the assignment was to answer the question "in the game of BJ, which game has greater variance in your bankroll, SD, DD or 6D?" And he answered "OK Doc, here's the nitty gritty. The SD game has higher variance because it uses 52 cards, and I am going to bet a larger amount on it than the 6D game which has 312 cards and where I will bet a smaller unit."

I then ask, "OK, you changed two things. You changed the number of cards you are playing with, _and_ you changed the betting unit. Now prove that the change from 52 to 312 cards is reducing your variance, rather than the change from betting $25 to $5 units."

That is the flaw here. If you change two things, you can not attribute the change in variance to just the number of cards. A statistician knows how to address this test. And there are statistical methods that will attribute part of the variance to each of the two changes, pretty accurately. Or, you can do as I prefer, and just change exactly one thing. In this case the number of cards in the deck we are playing with. No changes in betting units. No changes in anything, other than to make the games somewhat equivalent the spread has to be tweaked or the SD game will kill the 6D game on win rate.

Now if someone asks you to answer the question, "I am going to a casino, I am new and have just started counting, and I see three tables side by side, one SD, one DD and one 6D, which one will produce the smallest bankroll fluctuation?" And before you answer, I already get the idea that if I double my unit size, I am going to greatly change my bankroll fluctuation and ROR, but that's not what I am asking. My question is simply "which game produces the least variance?" I'm a new counter. I've not memorized BJA3 or any other book. I don't have any sim software. So most likely I am going to sit down at one of those three $5 tables and play. I've read about "spreads" and know that 1-4, 1-8 and 1-20 are well-regarded.

Which game do I play? I'm not asking you to tell me how much to bet. Just which game should I choose?

As the title of the last BeeGees album goes, "this is where I came in..."

Sometimes a simple question deserves a simple answer. I did my best to provide one... And I carefully explained all conditions in my assumptions as well (same betting unit, same penetration, same rules, etc...)

[Don Schlesinger]

> So most likely
> I am going to sit down at one of those three
> $5 tables and play. I've read about
> "spreads" and know that 1-4, 1-8
> and 1-20 are well-regarded.

Oh, I get it now. It's "cheating" to "inflate" the SD variance by using a larger unit size than the one for 6-deck; that isn't playing fair. But, it's perfectly all right to spread 1-4 in SD and then 1-20 (!) in 6-deck, because, after all, the infinitely larger spread does nothing to inflate the size of the 6-deck variance! :-)

Thanks for explaining that. :-)

Don

[Magician]

> Which game do I play? I'm not asking you to
> tell me how much to bet. Just which game
> should I choose?

[raises hand from back of class]

The game with the highest SCORE?

[bfbagain]

but that's beside the point. And to your statement..

I don't disagree with a single thing you wrote.

Of course you do. :-) Otherwise you wouldn't have framed your statement, the parameters of your question, and the question itself in the manner who have.

So I'm not going to get into a debate with you on whether or not which game had greater volatility. You have already, in your mind, answered the question, and are simply attempting to....what exactly are you attempting?

Instead of asking, as it is apparent that you have thought this through, have the necessary software to view your own parameters, and I'll assume enough blackjack literature to form your own opinion, why not just tell us what you think is right, the reasons behind it, and that'll be that.

I thought my post was specific. Volatility is what happens on the way to arriving at standard deviation. How much volatility exists is based on the parameters that mathematicians have already researched ad nauseum.

I will point you in the direction I think you need to go in, and that simply is SPREAD.

Here's a question for you: Why, in order to BEAT, i.e., to WIN at the 6-8 deck game of blackjack, do you spread your bets?

cheers
bfb

[Parker]

> Which game do I play? I'm not asking you to
> tell me how much to bet. Just which game
> should I choose?

> As the title of the last BeeGees album goes,
> "this is where I came in..."

No it wasn't. The original question was, "Which game, SD, DD, or 6D, has the lowest volatility?" It was not "Which game should I play?"

Obviously, with rules, pen, heat, etc., being equal, we choose the single deck game. However, we do not choose it because it is less volatile.

We choose it because we will, in the long run, make the most money.

Or to put it another way, as Magician pointed out, because it has the highest SCORE.

[stainless steel rat]

> Oh, I get it now. It's "cheating"
> to "inflate" the SD variance by
> using a larger unit size than the one for
> 6-deck; that isn't playing fair. But, it's
> perfectly all right to spread 1-4 in SD and
> then 1-20 (!) in 6-deck, because, after
> all, the infinitely larger spread does
> nothing to inflate the size of the 6-deck
> variance! :-)

> Thanks for explaining that. :-)

> Don

"To the man who has a hammer, everything looks like a nail."

Every now and then you might think a bit beyond "BJA3" and into the real-world of beginners playing BJ and counting for the first few times. The questions they ask, the issues they have, are _far_ from the questions and issues a pro or long-term player might have. And the answers they need are different as well.

It is easy to overlook that...

For the last time, most beginners walk into a casino looking for a $5 table because that is what they want to play for starters. If they have a choice of SD, DD or 6D (I can think of a casino where that is normal) games with a $5 min, which should they play?

I think the answer is obvious, given _their_ context and _their_ intentions. Forget about a pro trying to contain ROR at 13.5% or less, trying to develop the optimal spread/bet unit to achieve that.

But don't let me divert the conversation toward the question that I believe was originally asked. By all means let's stick to the current discussion that doesn't apply to most beginners at all...