Gabi: advantage

[Steve Jacobs]

> (1) Strategy itself.
> When using BS, a player by definition only
> employs handtotals in making his play
> decisions (handtotal vs. dealer upcard given
> some RC/TC; I really doubt Steve Jacobs
> disagrees).

I choose to use Griffin's definition of basic strategy, which is based on the composition of the hand rather than only on hand total. TC/RC has nothing to do with basic strategy, so on that point I definitely disagree. Keep in mind however that I do not suggest that the definition I use for basic strategy is the only reasonable definition. Multiple definitions exist quite independent of any statement I have ever made on the subject, and it simply isn't rational for anyone to imply that I'm responsible in any way for this ambiguity.

> Even when that player is a 100% accurate
> counter (i.e. he counts 10's, with nine
> sidecounts for 2 upto ACE, and has memorized
> the full set of handtotal indices :-), he is
> still playing Basic.

As far as I know, all definitions of basic strategy include the concept that it is derived from a freshly shuffled, random shoe. One can employ basic strategy while counting, but card counting generally encouters deck states which are unreachable by basic strategy. I believe the concept of "strategy variations" widely viewed as an addition to basic strategy, and not included within the definition.

> However, the moment he
> starts to use a rule like "hit 10,2 vs
> 4", he is no longer playing Basic.

Well, now you have a problem. Don's definition of basic strategy permits the player to account for the specific two card combination that makes up the player's original cards. This is a long standing tradition from "zero memory" basic strategy.

> He's
> then playing Hybrid. And the moment he has
> advanced to the stage where ALL of the play
> is covered by handcomposition rules (2-card
> hands, 3-card hands, 4-card hands, ...) and
> this superman at no time has to rely on a
> handtotal rule, then and only then is he
> playing Optimal.

This is perhaps where I would have the most difficulty with your definitions. The word "optimal" applies to virtually all definitions of basic strategy, and to try to confine it to a single strategy is even less practical than retroactively declaring that "basic strategy" has only one meaning.

The strategy which you call "optimal" is probably the one that I refer to as a "perfect memory" strategy. This is the strategy that results when a player makes optimal use of the exact deck composition at all times.

A purely "total dependent basic strategy" is the strategy achieved when the player is constrained to only use hand totals. Note that there are a large number of different playing strategies that can be created by restricting the player in this way. The basic strategy associated with this constraint is the strategy which is optimal in the sense that it maximizes the player's EV when played off the top of a freshly shuffled shoe.

The "zero memory" version of basic strategy is slightly less constrained, and allows the player to use hands totals along with the 2-card composition originally dealt to the player. The "basic strategy" phrase includes the idea that optimal play is used, within the specified constraints, to maximize EV off the top of the deck.

> And if he quits his perfect
> counting and indices, but keeps playing
> according to JUST handcomposition rules,
> he's still playing Optimal.

Any player who is guided by a mathematical model which measure performance an maximizes their outcome accordingly can be said to be "playing optimally." This covers a very broad range of things, of which "various definitions of basic strategy" is perhaps a small subset. Log optimal strategy is another example.

> (2) Strategy derivation.
> The human-friendly BS rules should obviously
> be an as close as possible approximation of
> Optimal Strategy (OS). The only way then to
> figure BS out FROM SCRATCH is to do a full
> combinatorial so-called backtracking
> analysis for OS play!

That is one way to compute a basic strategy, but it certainly isn't the only way. In fact, I think it would be fair to state the nobody has ever actually computed any strategy this way, because nobody has every computed a "perfect memory" strategy. Pair splitting makes this computationally difficult.

> This leads to optimal
> stand/hit ev's for all n-card hands (so also
> for all 2-card hands). Subsequently that
> result has to be somehow mapped to
> (soft/hard) totals, and for that there are 3
> approaches.
> #1: For every total, construct a
> handprobability-weighted average for hit-ev
> and for stand-ev from the hit- resp.
> stand-ev's of the 2-card hands that make up
> the total. (The hit or stand decision for a
> total then simply follows by comparing the
> two average ev's.) I think this is what
> Cacarulo does.

Cacarulo's tables on the bjmath site are absolutely not computed this way, and he has said so himself. Don thought that this is what he was doing, but he misunderstood Cacarulo's method of computation. See Cacarulo's post on the bjmath site for further clarification on this point. His method was to compute composition dependent strategy numbers, then publish the numbers for the 2-card cases. For example, if you look at the "hitting" number of 3,2 vs. A in Cacarulo's single deck charts, the value is -0.32259. If I run my CA program for EV of hitting 3,2 vs. A, using full composition dependence for subsequent decisions, the EV is -0.3225918210. I have zero doubt in my mind that if Cacarulo's charts were given to more decimal places, the extra digits would match.

> #2: Like #1, but not just 2-card hands that
> make up the total but all n-card hands that
> make up the total. I think this is what
> Steve Jacobs does.

I'm not quite sure what you mean here. I compute a composition dependent strategy, and my EV numbers come from that computation. Then, I use those numbers to generate an approximate total-dependent strategy, but my simplified strategies only consist of hit/stand/etc. and I have never published average numbers associated with any of those plays. The overall game EV numbers that I quote are based on the full composition dependent strategy.

Cacarulo and I use virtually identical models for computing basic strategy, and there is nothing "total dependent" involved. I'm not really sure which of your three methods best describes how our CA programs work. Our method for handling pair splitting doesn't fall neatly into any of the "usual" definitions of basic strategy. The pair splitting model can be described roughly as "allow the player to remember all the cards seen during the current hand (or current branch of a split), and also allow the player to remember the number of splits that have been made so far." This falls well short of "perfect memory" but goes well beyond "zero memory." This model also goes slightly beyond the model that Griffin used for his pair splitting algorithm.

I hope this helps clarify my position.

[Steve Jacobs]

> Absolutely not. Either you reckon all the
> crads in your hand(s) or you don't.

See chapter 11. The algorithm he uses for pair splitting absolutely does not reckon all cards in all hands. I think Griffin might have liked to do that, for the sake of mathematical precision, but it was never feasible for the computers that Griffin had access to. Such a thing might be within reach of today's computers for single deck games, but I know of no attempts to perform the computation.

> You
> don't get to pick for which hands you do and
> which you don't. Show me where Griffin
> authorizes that. On the contrary -- see
> below -- I'll show you where he DOESN'T
> authorize thst.

He "authorizes it" by virtue of providing a pair splitting algorithm which specifically ignores cards from the "other" splits. One quote from one paragraph simply isn't enough to negate an entire chapter.

> Here's what Griffin says, verbatim: "By
> defintion, the description of the basic
> strategy is 'composition' dependent rather
> than 'total' dependent in that some card
> combinations which ahve the same total, but
> unlike compositions, require a different
> action to optimize expectation." That's
> clear enough. He then continues:

> "Notwithstanding these many
> 'composition' dependent exceptions (which
> tax the memory and can be ignored at a total
> cost to the player of at most 0.04%) we'll
> define a 'total' dependent basic strategy,
> recognizing all the while that it is a
> simplification for convenince of
> reference."

> Bottom line: Despite Steve's protestations,
> I do, indeed, know of no one who would
> define "basic" strategy according
> to strict compostion-dependent guidelines,

Sigh. You conveniently ignore the part above where Griffin says "recognizing all the while that it is a SIMPLIFICATION FOR CONVENIENCE OF REFERENCE."

> especially since Griffin also mentions that
> (and this is crucial to my argument):

> "It is even conceivable, if not
> probable, that nobody, experts included,
> knows precisely what the basic strategy is
> [seems silly, no?!] if we pursue the
> definition to include instructions on how to
> play the second and subsequent cards of a
> split depending on what cards were used on
> the earlier parts."

The key phrase here is "...if we pursue...". He clearly holds this out as a valid definition. He certainly doesn't insist that this definition be strictly adhered to, nor does he insist that this definition be avoided. It seems pretty clear that he mentions it here for the sake of completeness, then moves on (in virtually the entire remainder of the book) to apply a minor simplification for pair splitting, for the sake of making it possible to perform the computations.

> So, again, quote Griffin, that's fine with
> me. I don't agree with him here.

That's fine, I'm not asking you to, never did. Thank you for (at long last) acknowledging that your definition of basic strategy differs from Griffin's.

[Viktor Nacht]

[Parker]

I have a mental picture of some poor newbie reading this thread while thinking, "All I wanna know is if I should learn KO or Hi-lo . . . "

[StrayFrog]

> Absolutely not. Either you reckon all the
> crads in your hand(s) or you don't.

i don't think i can keep track of ALL the crads.

:^)

[humble]

What's wrong with giving newbies a glimpse of the universe? :-)
You don't need to understand something to appreciate it (I don't understand most abstract art).

[humble]

Thanks Steve Jacobs for reading my post and for the extensive answer.
I am preparing a little reaction that includes some novel suggestions. I will post it as a new thread on the appropriate bjmath.com page: some (well 2) people have probably rightly pointed out that Blackjack Beginners isn't really the place to continue things.

Cheers,
humble.