bfbagain: To SSR:Answers, answers.

[bfbagain]

OK SRR. For you. :-)

But when a beginner asks a question, is it out of bounds to assume he is asking a "simple question" paraphrased like this: "I walk into a casino, looking for a $5 table, and I find 3. A SD, a DD and a 6D game. Which should I play to provide the least fluctuation in my bankroll?"

In (our?) my haste to provide a constructive way at understanding the term volatility, it appears that a couple of points have been overlooked. If so, and you are right, then please accept my apology.

Obviously, the term ?beginner?, in your posts have elicited responses that have emotional overtones. It may be best, in the future, to let ?the beginners? themselves pose the questions, as it is apparent, by your own hand, that you really wouldn?t come under this heading. But this is just a matter of style, and it takes more than one party to communicate successfully, i.e., to have constructive dialogues.

But to re-evaluate your question, as stated above, requires what players who play the game to win, ASSUME, and that simply is that we are there to WIN! This is, what I think, was what really was assumed by us, and not by your question. You see, blackjack, as you know, has built-in, an inherent fluctuation. So to play the game with the ?least? fluctuation, by default, is to play a LOSING game, and that?s not our purpose. So the logical answer if fluctuation reduction is the goal, is simply to not play at all. But that?s not your goal, and I understand that. So let?s go to the bankroll aspect of your question. To have the least amount of fluctuation in a bankroll, again, by default, is to play with little to no SPREAD. So maybe the question might be better framed as, ?what is the best game, that will allow a beginner to play and WIN, while keeping the fluctuation of bankrolls to a minimum??

And clearly, the answer to this question is to play the Single Deck game. The reason being, that a spread of 1-2 units, or 1-3 units, depending on the rules, will BEAT this game, while utilizing the smallest bankroll, and with the least amount of overall fluctuation. In some single deck games, a flat bet can get the money. But in NO multiple deck game (including double decks) will a flat bet get the money. Nor will a spread of 1-2 units. And it?s a close call with some double deck games where the most you could expect is to play a break-even game, requiring an even greater spread.

I think this is what you?re looking for, and I?m not clear as to why it appears that you are trying to pull people?s chains, as yes, you know this is the correct answer to this question.

You appear indignant when confronted, but methinks you protest a little to much, as unlike classrooms, you?re not the teacher here, nor are we the students. We ALL are merely trying to learn more about this game. And some of your examples, in other posts, are not valid as it pertains to blackjack, e.g., your physical citations, i.e.,

In the 1950's, aeronautical engineers were saying "we can't exceed the speed of sound, the turbulence will destroy any airframe light enough to go that fast." Thank goodness the engineers working on the Bell X series didn't listen, thank goodness Chuck Yaeger had the intestinal fortitude to believe the non-believers and give it a go.

And yes, these are all true, however, it has now been proved, within the realm of mathematics, that given a specific game, with a specific rule set, that the mathematical assumptions are immutable. A single deck game is not all of sudden going to contain 55 cards as opposed to 52. They may call it something else, but it won?t be single deck blackjack. I hope you understand that I?m not attempting to engage in conflict here with you, it?s that there are certain aspects of the game that are not going to change, no matter how much research you may want to do, or questions you may want to ask. We are not re-inventing the wheel here.

At this time, and it?s only in my non-expert capacity, that you are not furthering the development of ?beginners? by engaging in the verbal gymnastics that seem to exist in your posts. You are clearly an intelligent man. And I have no doubt that there are contributions that you can make overall to the bj community. And though I?m sure it has been somewhat amusing to those watching from a distance, I really have no doubt that if your posts, were they on other sites, that the ?experts? on those sites would provide similar answers, albeit in a different style (certainly after observing these exchanges) and manner, but essentially the same nonetheless.

I?ll finish with the following statement: Sites like this one, i.e., who cater to blackjack players attempting either to learn , share, or both, the knowledge that will further their success in extracting the money from casinos, make an inherent assumption that all the players here are trying to WIN. Nothing more, and nothing less.

cheers
bfb

[stainless steel rat]

> OK SRR. For you. :-)

> But when a beginner asks a question, is
> it out of bounds to assume he is asking a
> "simple question" paraphrased like
> this: "I walk into a casino, looking
> for a $5 table, and I find 3. A SD, a DD and
> a 6D game. Which should I play to provide
> the least fluctuation in my bankroll
> ?" In (our?) my haste to provide a
> constructive way at understanding the term
> volatility, it appears that a couple of
> points have been overlooked. If so, and you
> are right, then please accept my apology.

> Obviously, the term ?beginner?, in your
> posts have elicited responses that have
> emotional overtones. It may be best, in the
> future, to let ?the beginners? themselves
> pose the questions, as it is apparent, by
> your own hand, that you really wouldn?t come
> under this heading. But this is just a
> matter of style, and it takes more than one
> party to communicate successfully, i.e., to
> have constructive dialogues.

> But to re-evaluate your question, as stated
> above, requires what players who play the
> game to win, ASSUME , and that simply is
> that we are there to WIN! This is, what I
> think, was what really was assumed by us,
> and not by your question. You see,
> blackjack, as you know, has built-in, an
> inherent fluctuation. So to play the game
> with the ?least? fluctuation, by default, is
> to play a LOSING game, and that?s not our
> purpose. So the logical answer if
> fluctuation reduction is the goal, is simply
> to not play at all. But that?s not your
> goal, and I understand that. So let?s go to
> the bankroll aspect of your question. To
> have the least amount of fluctuation in a
> bankroll, again, by default, is to play with
> little to no SPREAD. So maybe the question
> might be better framed as, ?what is the best
> game, that will allow a beginner to play and
> WIN , while keeping the fluctuation of
> bankrolls to a minimum??

OK. But the previous conversation took a turn south on this term "variance".

Before I go on, I use the normal definition of variance (sigma^2) and standard deviation (sigma), computed as follows:

add all the observations and divide by N, the number of observations. This is the mean. Now for each observation, compute "obs^2 / N" and sum them all up.

The purpose of the squaring, for those not into any kind of statistics, is to accomplish at least two goals. Some observations will be below the mean, some above. Squaring them makes them all positive so +/- observations don't cancel each other out and make us believe there is no variance at all. Squaring them (and this is more important) highlights the _big_ differences over the small differences. For example a difference of 3 is 9 when you square it, but a difference of 20 is 400. So bigger deviations produce larger squares, and eventually affect the variance more than the smaller differences.

Now there is where I seem to have a disagreement. variance is not about how many times my observations (my bankroll) fluctuates up and down, it is more a measure of how _much_ it is going up and down.

Perhaps you can find a flaw in this reasoning:

SD game, according to CVCX, I am going to see a + count in about 31% of the hands played. 6D game, again according to CVCX, I am going to see a + count in about 25% of the hands. Both games are dealt to 67% for equality.

If I play for (say) 1000 hands, in the 6D game, dealing 208 cards, that is going to be about 38.5 rounds per shoe, assuming heads-up. So to play that 1000 hands, I am going to go through 26 shoes. Any error that I overlooked there?

In the SD game, dealing 70 cards before shuffling, which is 13 rounds again assuming 2.7 cards per hand for me and the dealer, which will require my playing through 77 shuffles, or about 3x the "shoes" as in the 6d game. Again, any glaring error there?

Now for a bit of a leap of faith. So that my head doesn't explode, I'm going to assume that for any "shuffle" the TC either goes positive, or it goes negative, or it stays near zero. That is, a single shuffle will either be positive, negative or zero. You can comment on whether that is within bounds or not.

That means that for the 6D game, 25% of those 26 shoes are going to go positive, about 1/2 of what is left will be zero the rest negative. That is, I will get about 6-7 shoes that cause me to ramp my bet. For the SD game, the numbers are about 24 shuffles will see me with a + count.

Now, for variance. If you want to say that the more your bankroll fluctuates up and down, ignoring how much it fluctuates, then there is more fluctuation in the SD game. But in the 6D game, there are longer periods of up and down, which makes the variance larger (add the sums of the squares of the changes in bankroll per hour or however often the sampling is done).

Now I won't claim to be a statistical genius. I ask a close friend of mine in biostatistics when something complex comes up as I certainly overlook important but not obvious details at times. But if someone asks me, based on the above, "which game is going to produce the wildest swings in my BR?" I'm sticking with the 6D game, because the spreads are necessarily larger and the "swings" last longer. In the SD game my BR bounces around all over, to be sure, but the bounces are generally not huge swings, just producing a very irregularly shaped curve.

Now, feel free to point out mistakes, as I don't mind that at all. Heaven knows I make enough. Just ask my wife. But when someone jumps in and doesn't even understand that std dev is sqrt(variance) then I'm not sure that we are using the same language (and I am _not_ talking about you here...)

> And clearly, the answer to this question is
> to play the Single Deck game. The reason
> being, that a spread of 1-2 units, or 1-3
> units, depending on the rules, will BEAT
> this game, while utilizing the smallest
> bankroll, and with the least amount of
> overall fluctuation. In some single deck
> games, a flat bet can get the money. But in
> NO multiple deck game (including double
> decks) will a flat bet get the money. Nor
> will a spread of 1-2 units. And it?s a close
> call with some double deck games where the
> most you could expect is to play a
> break-even game, requiring an even greater
> spread.

I agree perfectly there.

> I think this is what you?re looking for, and
> I?m not clear as to why it appears that
> you are trying to pull people?s chains, as
> yes, you know this is the correct answer to
> this question.

I'm not sure either. As I said, I based my comments on two things. Measured Std Dev (I can compute the variance from that, unlike some) and then "observed variance" by simply playing the game an awful lot, and now having to put up with my brother/son/uncle/cousins/etc nagging me to play those damned 6D shoes and not understanding why I prefer the DD which is often too "rich" for their blood. I sat at a 6D shoe at the MGM this past summer, $10 minimum, and I went through a $1000 faster than my wife in a jewelry store. The count was ridiculous, I was spreading 1-12, betting $120 over and over and getting blistered by 15/16's where all I could do was surrender and watch my BR collapse. I've not had such a horrendous streak at DD games, although I have had some horrible things happen, along with some wonderful things of course...

> You appear indignant when confronted, but
> methinks you protest a little to much, as
> unlike classrooms, you?re not the teacher
> here, nor are we the students.

Note that "appear" != "are".

> We ALL are
> merely trying to learn more about this game.
> And some of your examples, in other posts,
> are not valid as it pertains to blackjack,
> e.g., your physical citations, i.e., In
> the 1950's, aeronautical engineers were
> saying "we can't exceed the speed of
> sound, the turbulence will destroy any
> airframe light enough to go that fast."
> Thank goodness the engineers working on the
> Bell X series didn't listen, thank goodness
> Chuck Yaeger had the intestinal fortitude to
> believe the non-believers and give it a go.
> And yes, these are all true, however, it
> has now been proved, within the realm of
> mathematics, that given a specific game,
> with a specific rule set, that the
> mathematical assumptions are immutable. A
> single deck game is not all of sudden going
> to contain 55 cards as opposed to 52. They
> may call it something else, but it won?t be
> single deck blackjack. I hope you understand
> that I?m not attempting to engage in
> conflict here with you, it?s that there are
> certain aspects of the game that are not
> going to change, no matter how much research
> you may want to do, or questions you may
> want to ask. We are not re-inventing the
> wheel here.

Here is a problem more realistic. The SCORE for a good SD game is 120. The SCORE for a good DD game is 100. Which do you play? My answer? Not enough information. Can I even _play_ the SD game with anything beyond flat-betting, without getting tossed? So, practically, SCORE is not the only measure of a game that is important. If I can spread 1-20 in a DD game with poor rules but good penetration, while you can only spread 1-2 in a good SD game with equal penetration and better rules, I'm taking the DD game...

So SCORE might be a starting point. But there are practical considerations as well..

> At this time, and it?s only in my non-expert
> capacity, that you are not furthering the
> development of ?beginners? by engaging in
> the verbal gymnastics that seem to exist in
> your posts. You are clearly an intelligent
> man. And I have no doubt that there are
> contributions that you can make overall to
> the bj community. And though I?m sure it has
> been somewhat amusing to those watching from
> a distance, I really have no doubt that if
> your posts, were they on other sites, that
> the ?experts? on those sites would provide
> similar answers, albeit in a different style
> (certainly after observing these exchanges)
> and manner, but essentially the same
> nonetheless.

> I?ll finish with the following statement:
> Sites like this one, i.e., who cater to
> blackjack players attempting either to learn
> , share, or both, the knowledge that will
> further their success in extracting the
> money from casinos, make an inherent
> assumption that all the players here are
> trying to WIN . Nothing more, and nothing
> less.

> cheers
> bfb

And then again, don't forget that some also have a propensity to "needle" "heckle" and do other non-productive things (again, absolutely not directed at yourself). However, I really intend to keep a far lower profile as these discussions almost always take tangents away from the original point, which doesn't accomplish a thing except to waste time.

Thanks for civil comments and discussion, and particularly your analysis of my analysis above. Perhaps we can get a sane definition of variance once and for all, rather than something that is not up to statistical/probabilistic rigor.

The concept of squaring things is so critical... And "typical" definitions of commonly accepted terms like variance and standard deviation would make life so much nicer. And it was why I didn't touch the "volatility" word at all. variance in the statistical sense has nothing to do with dollars, it has to do with the variability of the game outcome, and then we often factor in dollars and cents to understand the number a bit better. But variance is variance, and somehow that can't quite be coped with...

[G Man]

"Here is a problem more realistic. The SCORE for a good SD game is 120. The SCORE for a good DD game is 100. Which do you play? My answer? Not enough information. Can I even _play_ the SD game with anything beyond flat-betting, without getting tossed? So, practically, SCORE is not the only measure of a game that is important. If I can spread 1-20 in a DD game with poor rules but good penetration, while you can only spread 1-2 in a good SD game with equal penetration and better rules, I'm taking the DD game..."

Don`t you think that the DD game you are referring to will also have a better SCORE ? Honestly, it`s about time you put an end to this and as we say in chess, resign since your position is hopeless.

[bfbagain]

I think I understand why you are having a problem with this. Now to be sure, and again it?s only my opinion, my belief is that you think that everyone else has the problem, and you?re the only one who has the courage to frame the questions, i.e., ask the questions and expect the answers to your questions, thus, providing a service to all of us.

I don?t like attributing motives when the dialogue is about advantage play, as that normally is a slippery slope. However, we all know (and this is NOT being applied to you----) that there ARE such creatures as internet trolls, and for those types, I have no problem with identifying their agendas, and other than malicious agendas (gee, do they exist in the advantage play community?), only political debate creates the kind of agendizing (is that a word? I don?t think so, but I?ll use it nonetheless) that I might respond to.

So, what is the exact problem? Again, sometimes we overlook the simplest of things, and that is your attempt to equate, by whatever measure you choose (as none is appropriate in reality) the Single Deck Game, to the (and the Double Deck Game) 6 Deck Game of Blackjack.

Your comment: SD game, according to CVCX, I am going to see a + count in about 31% of the hands played. 6D game, again according to CVCX, I am going to see a + count in about 25% of the hands. both games are dealt to 67% for equality.

You see, they are NOT EQUAL. You can?t compare 67% pen on a single deck game, with 67% pen on a 6 deck game. Do you understand? I?m sure you do. Thus, any other comparisons are flawed as well. You really compare SCORES of single deck games with those of 6 deck games. They are totally different animals.

I?m going to provide some numbers here for your perusal. Please note, that it should become abundantly clear why you can?t compare these games. You have to use a different criteria to determine what game you?ll play, and why.

Here?s an example. The SCORE of a SD game, dealing 7 (using 67% pen, your example) rounds with H17 is 156.22, SD =2.266 per hand, NO=6400, RoR is full Kelly. This is using a 1-4 spread, and only requires $18,150 BR with your betting unit being $100. This is using AOII w/ace side count and full (mine) indices.

Now, look at the 6 Deck game. The SCORE of a 6 deck game, dealing 67% pen (again, using your example of 67% pen.) H17/DAS/ is 17.95, SD =8.156 per hand, NO=55,668, RoR is full Kelly. This is using a 1-12 spread, and only requires a $192,000 BR with your betting unit being $100. This is playing 2 hands. For one hand, the BR requirement is $136,500. SCORE is 12.33.

Which game would you play?

I would play the first game (SD) and I would not play the second (6D w/H17/DAS with 67% pen)

Now let?s look at a 6 deck game I would play.

The SCORE of a 6D game, dealing 75% pen. with S17/DAS/RSA/LS is 70.94, SD =7.572 per hand, NO=14,099, RoR is full Kelly. This is using a 1-12 spread, and requires a $90,000 BR with your betting unit being $100. again, playing 2 hands. The BR for one hand is $63,500. SCORE=48.73.

Which of the 6 deck games should you play?

Doesn?t it become crystal clear that these games are completely different? This goes back to understanding what strategy, i.e., overall plan of attack that you will use to WIN, i.e., to GET THE MONEY is!

If you look at bankroll requirements, and nothing else, you?ll see that your decisions, albeit that they may appear to be easy, are, in fact, complicated.

This is just one more ?extremely important? illustration, of why blackjack is a game of skill, and requires the use of a real brain.

You shouldn?t be wily nilly in playing any game, just because it?s ?there.? It?s one of the reasons that I accumulate the frequent flier miles I do. And keep in mind, I didn?t even include the DD games I would play. And then, there is another really important issue that often goes by the board from most players, and that is every time you ?change? the game you play, i.e., you go from DD to 6D, etc., you are actually changing your NO (the long run).

Now that?s a study that I?d like seen done by the math heads. A formula that can determine precisely how much ?NO? changes by going from DD to 6D, SD to DD, and back again. It would be like how much does quitting smoking add back, in years, to your expected lifespan.

So your question regarding variance, although an interesting one (to some, and not to others) really pales, IMO, to one of bankroll requirements to play a winning game, which requires first, the ability to actually ?select? the game that best gives a winning opportunity.

And FWIW, we are really off the reservation here, in that this discussion should not be on a beginners page.

Cheers
bfb

[Brick]

[bfbagain]

Several of your sims seem to be way out of line.

Sorry, I don't think so.

" Now, look at the 6 Deck game. The SCORE of a 6 deck game, dealing 67% pen (again, using your example of 67% pen.) H17/DAS/ is 17.95, SD =8.156 per hand, NO=55,668, RoR is full Kelly. This is using a 1-12 spread, and only requires a $192,00 BR with your betting unit being $100. This is playing 2 hands. For one hand, the BR requirement is $136,500. SCORE is 12.33."

This is incorrect. A bankroll of about only $18,000 will yield a score of 18.00 playing 2 hands, give or take a few cents. The unit needed is about a $5 unit not $100 unit. It appears several other of your sims are also incorrect.

Actually, the unit amount is irrelevant. For a $5 unit, the required BR that provides a SCORE of 17.95 playing 2 hands with 67% pen with the given rules is $10,500.

You may be confused. This is using AOII with "my" indices. They are not from the Carlson's book.

Anybody guess which ones!?

But nice try. :-)

cheers
bfb

[Brick]

I re-read your post and think what you were saying is $192,000 BR for 6 deck is needed to achieve the comparative win-rate of single deck with a 1-4 spread betting black,is this correct?If so, then I understand and will delete my previous post. However I'm getting a SCORE of about 200.00 with that bank.

The SCORE im getting for hi-lo($10,000 bank)is about 10 bucks an hour(2 hands),I dont understand why your count system is showing such a high win rate,it surely cant be the index numbers.

Keep in mind that I'm not ,up to' or trying' anything,just wondering why your count system is smoking hi-lo.

Brick

[bfbagain]

to compare anything to single deck blackjack is flawed on it's face from the beginning.

So no, it was not my attempt to compare win rates between a (lousy) 6 deck game with the rule set of H17/DAS with terrible pen. to a single deck game with H17 and 7 rounds dealt. They are so different it's not even funny.

The most important conclusion that someone could draw from looking at those numbers (besides the one that says they should almost never play a 6 deck game with H17/DAS only) is the huge amount of bank required to even play that lousy 6 deck game, and how small of a bank is needed to play a very good single deck game. And this all started when SSR was trying to compare different games with the same pen.

67% penetration on a single deck game and 67% penetration on a H17/DAS 6 deck game is similar to the automobile and the horse and buggy.

cheers
bfb

[Don Schlesinger]

If you all have the patience, reread "More on SCORE," BJA3, pp.177-83. Part of the confusion as to how you can get a $192,000 bankroll requirement for a supposed "SCORE," is that, using my definition of SCORE, you can't -- because "classical" SCORE mandates a bank of $10,000.

Use "hourly win rate," in your explanation, and Brick won't have a right to be confused! :-)

Don

[bfbagain]

I understand. But the "c-SCORE", in my illustrations do not change based on the "bank."

And this is also the case for unit size.

Although SCORE, which included risk and bank ($10,000) as defined by you would/should have eliminated any confusion -- and I stand corrected in that I "could have", not necessarily that I "should have" used win rate -- CVCX was the app (original) of choice, therefore I was trying to keep the apples to apples analogy intact, as difficult as that seems to have become. Thus, the use of c-SCORE.

But all of that really belies the essence of "my" point, which is if you're going to play a winning game, and you found yourself playing that horrendous game (6 deck H17/DAS 67% pen.), a player needs to be prepared to have a large bankroll to unit size, at full kelly, to even make the attempt at winning in that game.

Now I use as my basis for my game comparisons, a $100 unit, thus the $192,000 BR, as you know. But even a $5 (red chip) player, playing 2 hands in most casinos in America today, where they have to double their minimum bet, i.e., 2 hands of $10 each, would need a $19,000 BR to play that game. Contrast that to playing a nickle SD game - H17 - and that nickle player only needs a BR of $820! for 1 hand.

To me, this what a beginner should be learning, no?

And if I did use win rate, it wouldn't have had, IMO, the same impact that seeing what kind of bank is really required to play that game, as I emphasized above.

But, other than that, I am guilty, nonetheless. :-)

cheers
bfb

[Brick]

Using your examples and comparasins of "win rate" has ironically expressed SSR's findings of variance to be true.

[bfbagain]

[Brick]

than single deck.