Don Schlesinger: Just what is "Basic Strategy"?

[Don Schlesinger]

Sporadically, on other sites, I've engaged in conversations about a topic that people actually get very passionate over. So, I thought I'd bring it to our pages here. What should be the definition of "basic strategy "? Now, before you react: "What a silly question; everyone knows what basic strategy is," permit me to point out that, technically, that simply isn't true.

As a start, we observe that the "classic" definition of BS is the decision, off the top of the pack, that maximizes the expectation (EV) of the hand we are playing, given knowledge of only our holding and the dealer's upcard. This, of course, is the "zero-memory" nature of BS. We aren't permitted to note any other cards in anyone else's hand. I'll return to this a little later.

Now, the above seems simple enough, until we realize that total-dependent BS is different from composition-dependent BS. Already, a new wrinkle! We all know that we're supposed to stand with 12 v. 4, however that rule assumes that we're blind to the nature of that 12. Is it 7,5; 8,4; 9,3; or 10-2 (not to mention 6,6, which is an entirely different can of worms!). So, as the name implies, total-dependent BS does not take into account the actual two cards that comprise the hand, but rather just the total that they add to.

If, instead, we treat those two cards as separate entities, to be differentiated, one from the other, we learn that not all 12s are created equally! Indeed, in a single-deck game, we note that a holding of 10,2 v. 4 should be hit, the EV being -0.19396 in an s17 game, compared to -0.21184 for standing (thanks to Cacarulo for these!). And, of course, there are many such composition-dependent plays.

But, where do we draw the line? If we're "permitted" to distinguish both cards in our initial holding, for the purposes of "basic" strategy, are we also permitted to observe a third, hit card? A fourth? Where does it end? Purists might say, "never," but this seems quite absurd to me. The dictionary defines "basic" as: "fundamental; serving as a starting point; an essential element or basis." Is it possible that learning a couple of hundred (thousand?!) different incarantions of 3-, 4-, 5-, 6-or-more-card combinations versus various dealer upcards could ever remotely qualify as "basic" in any sane person's mind? I think not!

So, where do we draw the line? How "basic" does composition-dependent BS have to be to remain basic strategy? That's my first question. The second is even thornier.

What do we do about pairs? I think we need to accept that, for pairs, we shouldn't consider 6,6; 8,8; or 3,3 as "composition" of the hand. We need to specify, right at the outset, that these simply are not 12, or 16, or 6. So, pairs get a kind of exemption; they're "excused" from being "composition-dependent," in the strict sense of the term. They get their own section of the color-coded BS charts we all cut our teeth on, and they are learned separately, as are the soft totals, such as A,6. (As a quick aside, I have always been violently opposed to calling this "soft seventeen," as the hand has nothing whatever to do with "17," and should never be considered as such. But, I digress.)

So, now, we move on to the following: If pairs get an "exemption" from being considered as composition-dependent, it's because we just want to consider, for any holding, if the cards should be split or not split. If the answer is don't split, then we revert back to the total (12, 16, 6) and play the hand according to total-dependent BS, right? Well, almost. What about 7,7 v. 10, in SD? Once we decide that we're not splitting this pair, what gives us the right to no longer consider this a "regular" 14 and stand? Just because this apparently c-d play happens to fall in the pairs section of the chart, why does it become "standard fare," in the t-d repertoire of every SD player? So, question number two is: Do you consider standing on 7,7 v. 10 in SD to be a composition-dependent play or not? If you're wondering what difference it makes how we consider it, my question is whether to include the play in the EV for SD only when invoking c-d plays, or for "normal," t-d EV.

Finally, and here's where things get out of control, how should we treat the hit cards we see after we split pairs? Suppose I know that it's correct c-d BS to stand on most multi-card holdings of 16 v.10. Suppose I split a pair of 8s against the dealer's 10 and hit the first 8 with a 4 and then a 5. On the second 8, I draw another 8, but I may not resplit. Does BS say to hit or stand on my 16? Well, t-d BS says to hit. So does c-d BS if I put on blinders and look squarely at my second hand, without regard to the cards to my right! But, those are MY cards, in MY hand, so why can't I look at them? If I do, then I stand on my 8,8 v. 10, because I also see another 8, a 4, and a 5.

So, how many cards in split hands am I allowed to reckon before "basic" turns hopelessly complicated? Again, the purists say "all of them"! So, if I'm allowed splits to four hands, and, after playing the first three hands there are, say, 13 cards lying on the table, and I now am playing my fourth hand, I'm supposed to include knowledge of all of those previous cards in the play of the current hand and still invoke "basic" strategy? Gimme a break! Permit me to claim how utterly ridiculous that concept is to me.

The purists rebel: Where do we draw the line? May you have knowledge, at the very least, of the card you originally split away from the beginning hand? Yes, I concede. It was one of the first two cards you received. What about one hit card to that new hand? Hmm. Problem. If I allow one, why not two? If two, why not three? Do you see where we're going? Why not 13?! Why not, indeed? And, if you permit the 13, then I ask, when I'm at the table with one other player, and he plays his hand and I see the cards in it, how ridiculous is it to claim that I absolutely may not use knowledge of those cards in the play of my own hand and still invoke "basic" strategy, but, alternatively, if I happen to split pairs three times and have 15 or 16 cards lying around, it's fine and dandy for me to reckon them all in the play of my hands, because, er, they belong to me?!

Your answers to any or all of the above questions are eagerly solicited. In short, just what would you want us researchers and authors to call "basic strategy"?

[Cacarulo]

Yes, I agree that this t-d vs c-d discussion make things very confusing.
In my opinion, BS should be composition-dependent (knowledge of player's 2 cards and dealer's up-card). This way we avoid the problem of pairs and soft-doublings. After splitting I would again consider only the first two cards for each pair independently of other cards seen. There is where I would draw the line.
BS is defined as the best strategy off the top but this only serves to the purpose of fixing the strategy (always stand on 10,2 vs 4, etc.). So BS is a FIXED strategy that you will use at any round.
Suppose the EV of a game is "x%" and this value was calculated off the top. What would be the EV of this game at round "n"? Well, if we use the FIXED strategy or BS I mentioned above this number should be exactly "x%".
The more knowledge you have of the cards the better will be this "x%". A mix between t-d and c-d is not better that c-d alone.

Hope this helps.

Sincerely,
Cacarulo

[98%]

What does the term 'basic' imply when used in the context of blackjack analysis? I think that the most basic concept of blackjack is that you are given two cards, the dealer shows an up card and, based on that information, you must make a decision. To those with some degree of mathematical sophistication, this decision becomes one of maximizing the EV for the hand. So the basic question which must be answered is "How do I play my two cards against the dealer's upcard to best maximize my EV?" This, of course, implies a composition-dependent basic strategy, which I think is the correct definition, at least in the case of the first two cards dealt.

Now, when more cards start to hit the table if you start splitting and what not, then things can get complicated. I think the basic question should remain the same and should not be altered to the form of "How do I play my two cards against the dealer's up card given that I have just split 8s and that my last hand received a 4 and a 5?" I liken this thought process to card counting and I think it is a more advanced form of analysis than is implied by the name "basic strategy".

Now, I think that 3 and 4 card totals should also be examined in terms of their composition. The question still remains of how to maximize your EV given the cards in your hand, but it should not extend to other hands and, technically speaking, a split is multiple hands, not just pieces of one hand.

This is, of course, all very theoretical and not of much use to the real world player. I personally stick to total dependent strategies with an occasional composition-based departure and I'd wager that most people do the same. I think that, for purposes of edge calculation and discussion of games, it is best to speak in terms of a generic, total-dependent strategy. Even this can get confusing, though, as there are different basic strategies for different sets of rules or numbers of decks in play. These parameters can be specified easily, though, with no worry of causing confusion. For purposes of discussion, I would like to see people call the conditions-specific, generic, total-dependent basic strategy "basic strategy". That way everyone can be on the same page.

[Cacarulo]

In part you're right and I forgot something important in my definition. The part is that after playing your initial 2-cards or after splitting a pair a t-d strategy is required. So, first BS should be c-d and when all that info has gone you are left with t-d.
Since the idea is to maximize EV it's better to play this way (c-d/t-d) than to play all the time a t-d strategy.

Sincerely,
Cacarulo

[Don Schlesinger]

Very interesting post, and one with which I agree completely.

But, I'm wondering about the very first pair-split I make, and whether the classical textbook method for determining BS actually ignores the twinned card, since it is now in a different hand. I think that may NOT be the case.

Cac??

Don

[Don Schlesinger]

> After splitting I would
> again consider only the first two cards for
> each pair independently of other cards seen.

Does that mean that, when playing each hand, I am NOT allowed to "remember" the other card that it was originally paired with?

Don

[Cacarulo]

> Does that mean that, when playing each hand,
> I am NOT allowed to "remember" the
> other card that it was originally paired
> with?

Correct. Say you get 10,2 vs 6 on your first round and you STAND. Next round you receive 10,2 against a dealer's 4. Would you consider the cards dealt on the previous round? BS says NO!
Let's look at the above example: 1D,H17

10,2 vs 6 you STAND.
Dealer gets two 9s and busts.
Now you get 10,2 vs 4
What would be the optimal play? The optimal play would be to STAND!
What would be the correct BS? The correct BS would be to HIT!

See what I mean? The same goes for splitting pairs.

I think the confusion is on the name "Basic". I would call it "Non-Counter Strategy or Non-Memory Strategy". Among all these NCS or NMS we need the one that gives us the best EV and at the same time it has to be something easy to remember.

Sincerely,
Cacarulo

[Don Schlesinger]

I'm actually surprised to learn this. The difference with the pairs, in your analogy, is that the other card, which is now split away, is, nonetheless, a card from my ORIGINAL hand!

And, some describe BS as the EV-maximizing play, given knowledge of nothing more than the dealer's upcard and the cards in your original hand!

See the problem?

Don

[Cacarulo]

> I'm actually surprised to learn this. The
> difference with the pairs, in your analogy,
> is that the other card, which is now split
> away, is, nonetheless, a card from my
> ORIGINAL hand!

BS does not care about the other card. Once you have split (according to BS) you're left with two NEW hands which "must" be considered independent.
After getting the first card for the first pair you may choose between c-d or t-d. C-d is more precise.
The same goes with the second pair.

> And, some describe BS as the EV-maximizing
> play, given knowledge of nothing more than
> the dealer's upcard and the cards in your
> original hand !

> See the problem?

I would change that a little: "given knowledge of nothing more than the dealer's upcard and the first two cards!. After splitting you play each hand split as a new hand comprised of two cards against the same dealer's upcard" (I know it can be worded better )

Sincerely,
Cacarulo

[Don Schlesinger]

> BS does not care about the other card. Once
> you have split (according to BS) you're left
> with two NEW hands which "must" be
> considered independent.
> After getting the first card for the first
> pair you may choose between c-d or t-d. C-d
> is more precise.
> The same goes with the second pair.

OK. If that's the way it's done.

> I would change that a little: "given
> knowledge of nothing more than the dealer's
> upcard and the first two cards!. After
> splitting you play each hand split as a new
> hand comprised of two cards against the same
> dealer's upcard" (I know it can be
> worded better )

Perfectly clear.

Don

[Cyrus]

> I would change that a little: "given
> knowledge of nothing more than the dealer's
> upcard and the first two cards!. After
> splitting you play each hand split as a new
> hand comprised of two cards against the same
> dealer's upcard" (I know it can be
> worded better.)

I'll try to word it just a little better, if I may.

Every hand played in Basic Strategy assumes that it is played after a shuffle, ie off the top of the pack.

Suppose we get a pair and we split it, by following BS, then we play out the first split hand. To play the second split hand, if we want to follow Basic Strategy instead of something else, we must assume that the second split hand is actually the first hand dealt off the top.

[Don Schlesinger]

> Suppose we get a pair and we split it, by
> following BS, then we play out the first
> split hand. To play the second split hand,
> if we want to follow Basic Strategy instead
> of something else, we must assume that the
> second split hand is actually the first hand
> dealt off the top.

Understood. But, apparently, when playing the first hand, we must also assume that we don't know that the other half of the split is lying to the left of us, and that bothers me a little bit, because that card belongs to my original hand (which, I understand, doesn't exist anymore)!

Don

[Richard Reid]

> I'll try to word it just a little better, if
> I may.

> Every hand played in Basic Strategy assumes
> that it is played after a shuffle, ie off
> the top of the pack.

> Suppose we get a pair and we split it, by
> following BS, then we play out the first
> split hand. To play the second split hand,
> if we want to follow Basic Strategy instead
> of something else, we must assume that the
> second split hand is actually the first hand
> dealt off the top.

I like your definition, Cyrus. This allows us to look at the cards we have in our current hand and to make a decision based on only these cards.

When dealing with splits, we look at the orginal hand first and decide to make a play based on it being played off the top of the deck. If we decide to split, then we look at the first of the split hands in isolation as if it now is being played off the top of the deck, and we make our play. Then we look at the next hand of the split hands in isolation as if it too were being played off the top of the deck, with no knowledge of the previous split hand that was just played. In other words, we treat each hand of a split hand individually with no knowledge of the other split hand(s).

I do like your definition. It allows for us to treat 7,7 vs 10 in single deck in isolation from the other 14's should we go as far as two card composition basic.

So, that being said, with your definition, the decision to go with total-dependant or composition-dependant basic is still an option.

In other words, "Do we treat 9,3 vs 4 different than T,2 vs 4, and different than 5,2,5 vs 4, etc. or do we treat them all as 12 vs 4?

Sincerely,
Richard Reid