Don Schlesinger: Just what is "Basic Strategy"?

[ET Fan]

> I don't think we can define BS as a
> "generic" strategy. I think that
> what we are discussing here is about which
> definition fits best.

Whatever you decide is "best" is what we must all abide by. :-)

ETF

[Don Schlesinger]

What you're describing is the famous "down logic" that John Imming made famous several years ago.

I wish he were still around to be discussing it with us!

Don

[Don Schlesinger]

> Whatever you decide is "best" is
> what we must all abide by. :-)

And you make the crucial point above. It seems somewhat illogical to compute precise EVs to ten decimal places and that take into account every card that has fallen, if we aren't going to define BS by using the identical algorithm that generated the expectations.

Hence, we come full circle to my original question: what should we define as the "standard" for "basic" strategy?

Don

[Cacarulo]

> As I understand it, the "zero
> memory" pair splitting you, and many
> experts, embrace is zero memory for the
> strategy employed, but NOT for the EV --
> which takes all card removals into account.

That's correct. A CA does the combinatorial of ALL the posible hands that might arise from the top of the deck and determines the best strategy (max EV). This strategy takes into account the player's two cards and the dealer's upcard as the departing point.
Using this optimal strategy anywhere in the deck will give you the best EV. No other "fixed" strategy will do better.

> It just occurred to me (maybe not new to
> you) that the process of determining
> strategy (and hence, EV) could theoretically
> be just about IMPOSSIBLE, for some rule sets
> and # of decks.

Yes.

> The problem is that the decision to hit or
> stand on any group of cards is based on EV,
> and that EV should include EVs on that same
> group of cards while splitting under
> "zero memory." Eg. Suppose the CA
> program decides 7-2-3 v 4, for some # decks
> and some rule set, should be HIT, but then
> LATER, while analysing splitting 7s it turns
> out that the cumulative EV, after you
> include all those cases, favors STAND. But
> still LATER, while analysing splitting 2s,
> EV swings in favor of HIT again. And then
> STILL LATER, while splitting 3s. EV swings
> in favor of STAND.

What you're describing here is optimal play which is "dynamical" and not "fixed". Of course, if I knew the deck composition at the moment of playing I would determine the optimal play for that instance.

> So for EVERY c-d hit/stand decision, you
> must first fully analyse all splits which
> could result in those decisions! Or so it
> seems to me.

Don't need to. On average would be the same decision I found off-the-top. Remember we are playing a fixed strategy.

> But, BEFORE YOU DECIDE WHETHER A SPLIT IS
> BS, don't you need all the EVs of all the
> resulting hit/stand decisions? So you
> determine these EVs, then decide to split or
> not FOR EACH CARD in the c-d group, then
> recalculate the EVs, then maybe reverse your
> hit/stand decision, then re-decide whether
> to split, and on and on ... recursive times
> three for 3 card groups, recursive times 4
> for four card groups, etc. Just about
> UNIMAGINABLE. And this for the SIMPLEST
> model we have -- the zero memory model.

For doing this you need a brute-force algorithm. Normally we use approximations for pair splittings. Now, there are good and bad approximations.
Lately, I've been working on the best approximation algorithm ever devised. If it is not exact it is so close to the exact value that we can avoid the brute-force algorithm. Still working on that.

> I remember you discussed
> "recursive" pair splitting
> algorithms with Steve on bjmath, but is this
> what you meant?

No, the "recursive" algorithm is an approximation which I devised a long time ago. It's exact in some cases and pretty close in others. The other method around which is not so good is the one described by Griffin's in TOB.

Sincerely,
Cacarulo

[Richard Reid]

Don:

Thanks very much for the warm welcome. This new launch is an absolutely marvelous idea and I see it is already showing to be a success. Congratulations!

Sincerely,
Richard Reid

[ET Fan]

It seems somewhat illogical to compute precise EVs to ten decimal places and that take into account every card that has fallen, if we aren't going to define BS by using the identical algorithm that generated the expectations.

Well, I'm glad you said "somewhat" illogical. What you seem to be missing is that i-d basic doesn't need to take every card that has fallen into account. All EORs are zero. Thus, in i-d land, BS is indeed defined by the identical algorithm that generates the expectations. And the expectations are SO VERY SIMPLE to generate!

But, as I said, I'm content to go along with the architect's definition. The only problem remaining is: WHAT do we do when the architects disagree? There may well be BS architects out there who share your misgivings about the limitations of "zero memory".

ETF

[ET Fan]

[ETF] So for EVERY c-d hit/stand decision, you must first fully analyse all splits which could result in those decisions! Or so it seems to me.

[Cac] Don't need to. On average would be the same decision I found off-the-top.

If this is true, then I can see that BS is tractable, though some recursion may be necessary. But I'm not sure. I will try to come up with some examples (perhaps with a simpler game than BJ) where relying on this does not result in a fixed strategy "that than which greater can not be conceived."

Thank you for the explanation.
ETF

[MathProf]

I ma sorry I have missed most of his discussion, but I had to be off-line most of the weekend. I have read some, but not all, the posts in this thread, so forgive me if I am being redundant.

From what I can tell, the term "Basic Strategy" was coined by Thorp in Beat The Dealer. It was used as the first strategy one would learn, before proceeding to learn counting strategy. That is, it was simply the "Basic" strategy, what you would learn in BJ 101, before going on to advanced stuff.

Now the 101 course in any subject is necessarily going to be incomplete. It will not give the student a full grasp of all the complexities and subtleties of a subject. There is going to some difference of opinion as to what would be the most appropriate curriculum for any 101 course, and how much detail you will go into. So to some extent, we cannot expect there to be a "the" basic strategy.

If I were to define what I would consider as Basic Strategy, I would use total dependent strategy. I would treat two card compositions as "Fine Points" of Basic Strategy. I think I first picked up this term from Revere's book and I think it is a good one. So in one sense, we have tow form of Basic: the basic Basic, and the Fine Points.

There are, of course, multi-card exceptions ot BS. But if we try to list all of these, we have a strategy which is hardly basic. In fact, it would be more difficult to master, and less useful, than elementary counting strategies.

I do not treat any pairs as fine-points. We have to list to separate entry for pairs anyways. So in particular, I would have the 77v10 Stand in Single Deck as part of the BS.

I also treat 16v10 differently: "Surrender if possible, otherwise Stand. Fine-Points: Hit 10-6 and 9-7."

My motivation for this is partly political. Most of us do a lot of Standing on 16v10, and it sticks out like a sore thumb to civilians. It would be easier on us, if the "book" said to Stand rather than Hit. There are legitimate mathematical reasons for this approach as well, but I wouldn't push it so much if I didn't see this political gain.

Finally, I would use the optimal EV-maximizing strategy off the top of the deck as the criterion for the Basic Strategy, only because this is what is Basic.

[Cacarulo]

> [ETF] So for EVERY c-d hit/stand decision,
> you must first fully analyse all splits
> which could result in those decisions! Or so
> it seems to me.

Let's say you know that for 8,4 vs 6 BS is to STAND. Off-the-top you receive 8,4 and the dealer gets a 6. What would you do? Obviously, you'd STAND.
A couple of rounds later (n cards have been removed but you didn't care) you get again 8,4 and the dealer gets a 6. What would you do now? Again, you'd follow BS and STAND.
Since we're "not counting" we don't take care of the cards that have been dealt after the first round. The same would have happen if you split a pair of 8's against a dealer's 6 in round #5 and get a four in the first pair. The answer is STAND. This doesn't mean that you're making the optimal decision. Maybe the optimal is to HIT.

Hope this helps.

Sincerely,
Cacarulo

[Don Schlesinger]

> Don:

> Thanks very much for the warm welcome. This
> new launch is an absolutely marvelous idea
> and I see it is already showing to be a
> success. Congratulations!

Thanks for the kind and encouraging words. Coming from you, they mean a great deal.

Don

[Don Schlesinger]

> Well, I'm glad you said
> "somewhat" illogical. What you
> seem to be missing is that i-d basic
> doesn't need to take every card that has
> fallen into account. All EORs are zero.
> Thus, in i-d land, BS is indeed defined by
> the identical algorithm that generates the
> expectations. And the expectations are SO
> VERY SIMPLE to generate!

Yes, I understand all of this. To repeat, if I get a vote as an architect (and, clearly, we ALL do!), I vote to not call BS a strategy that isn't correct for any game we mortals play in a casino!

> But, as I said, I'm content to go along with
> the architect's definition. The only problem
> remaining is: WHAT do we do when the
> architects disagree? There may well be BS
> architects out there who share your
> misgivings about the limitations of
> "zero memory".

There are several questions here. The first is to set limitations for how far c-d BS can go, before, to many of us, it becomes absurd. Many seem to think that the original two cards should be it! That being the case, we attack pairs next. And, the consensus seems to be that, once the cards are split, "the other one" no longer exists! So be it.

From this, we can create BS matrices that are "correct" according to our definitions.

The next problem comes when we create EV tables that are NOT predicated on the above assumptions, but rather on perfect combinatorial analysis. In essence, we're claiming that the EVs are "correct," but they're not according to "our" BS. This may or may not be problematic for some.

Finally, I point out that, unfortunately, no real-world live game (Internet is different) is played with a shuffle after every round (not even the CSMs!), and, therefore, all real-world BS EVs are actually somewhat poorer than what we theoreticians like to write that they are.

Don

[Don Schlesinger]

And, I agree with virtually everything you've written.

One question: Do your "fine points" (actually c-d BS) go beyond two-card totals, or do you draw the line at what is "basic," even for fine points?

Don

[Cacarulo]

> From this, we can create BS matrices that
> are "correct" according to our
> definitions.

> The next problem comes when we create EV
> tables that are NOT predicated on the above
> assumptions, but rather on perfect
> combinatorial analysis. In essence, we're
> claiming that the EVs are
> "correct," but they're not
> according to "our" BS. This may or
> may not be problematic for some.

It turns out that using the matrix generated by CA (the architect) is better than using the matrix generated according to our definitions. The definitions mainly apply to the way of playing.

> Finally, I point out that, unfortunately, no
> real-world live game (Internet is different)
> is played with a shuffle after every round
> (not even the CSMs!), and, therefore, all
> real-world BS EVs are actually somewhat
> poorer than what we theoreticians like to
> write that they are.

I've found some slots which have a great advantage off-the-top and there I use c-d the way I explained before.

Sincerely,
Cacarulo