16 v 10

Thanks everybody for taking the time to respond.

But, with all due respect, I'm not satisfied with any of the answers, and I simply don't agree with some of the points raised in the responses. I understand that this may be just a silly *mathematical* question and it may not affect the BS players' bottom line one bit, but I think this is an interesting problem (which I'm sure/I hope has already been studied) and I hope some of the participants on this board would feel the same. (BTW, I don't have to be told that the BS has been studied over and over and over again and *therefore* it must be right. All I need is a simple answer (if possible) or a pointer to the previous stuidies. Thanks.)

Since I have slightly better understanding of the problem (thanks to all of you), let me rephrase the question here:

[1] Is the Basic Strategy, defined as the strategy which maximizes the player's gain, or expectation, playing one hand against a complete pack of cards (Peter A. Griffin. The Theory of Blackjack, 6th Ed., p.12), still the optimal strategy, say for the fifth round?

[2] Say, on the fifth round, just before the cards are dealt, open the discarded cards and measure the True Count in a certain balanced count system. Repeat this for millions of times and take the average, and you will get the average value TC==0. Now do the same, but this time deal the hands (say, again on the fifth round) and if the dealer's up card is NOT ten-value card or if the player's dealt hand is NOT 16, then discard the whole try. Try again and only when the dealer's upcard is ten or face and the player's hand is 16, open the discarded tray (excluding the dealt hands) and add its TC into the sampling pool. Repeat this millions of times. Is the average TC before X-16 has been dealt still zero or some other non-zero value?

I hope I stated the question clear enough. I would greatly appreciated it if anybody could point me to any relevant references.

~Black Jack in the Box.

Consider the case of tossing a coin 6 times. On average, you will get 3 heads, BUT:

1/64th of the time you will get 6 heads;
6/64ths of the time you will get 5 heads;
15/64ths of the time you will get 4 heads;
20/64ths of the time you will get 3 heads (the average);
15/64ths of the time you will get 2 heads;
6/64ths of the time you will get 1 head; and
1/64ths of the time you will get 0 heads.

Thus, if you're betting that there will be exactly 3 heads out of 6 coin tosses, you'll be wrong more than twice as often as you're right (44 vs 20).

Yes, by the 5th round the *average* TC will be zero, but it will SELDOM be EXACTLY zero. Usually, it won't be far enough off of zero to effect any but the "close call" plays (e.g., hitting 16 vs Ten or 12 vs 4). Still, basic strategy will be "wrong" more often on the 5th round than on the first; but since you're not counting you have no way of knowing (a) the degree of the error, if any; or (b) which side the error is on; so you have no practical choice but to assume the average and hope for the best.

If you do not utilize an accurate method of tracking the cards, B.S. is your best option anywhere in the pack. Even card-counting doesn't track the actual cards very well, which is why no popular counting system has a very high playing efficiency. 70% is about as good as it gets, and that is with multi-level, multi-parameter systems. Card counting is designed to tell you when to put out the money and strategy deviations are secondary. It does give you enough information to vary strategy from time to time, but it does not come close to approaching 100% accuracy.

In order to vary strategy, more knowledge is needed. That knowledge can be imperfectly obtained by card counting. There may be other methods of tracking cards that are even more accurate, but without some sure way of doing it, you have to stick to basic strategy.

Is the average TC before X-16 has been dealt still zero or some other non-zero value?

Already asked and answered. Average TC before that hand (or any hand) is dealt is exactly zero.

When you play your hand, you are no longer in the same place. It's no longer "before." Basic automatically "counts" the cards in your hand and the dealer's upcard, just as it should. In fact, it counts the effects of removal more accurately than counting can or should.

For example, basic strategy for single deck standard strip rules 7,7 v T is to STAND.

Got it?

ETF

You said: only when the dealer's upcard is ten or face and the player's hand is 16, open the discarded tray (excluding the dealt hands) and add its TC into the sampling pool

If you exclude the dealt hand this is different than asking Is the average TC before X-16 has been dealt still zero or some other non-zero value? When you exclude those cards, you get the TC after the cards are dealt. If you exclude those cards, the average hi-lo TC in the discards will be precisely -52 /(#cards in the initial shoe - 3).

This has no bearing on the validity of basic strategy. Bsic takes this all into account.

ETF

"Is basic strategy the best move half way thru a deck, when I get 20 and the dealer has a 10 up? Has the probability of this situation occurring say something about the composition of the deck and how I should play my hand?"

Consider geting the above hand at the top of the deck? Can you say anything about the remaining composition of the deck, other than it is light the 3 tens you see? No.

Now re-shuffle and cut the cards, except take the top half of the cards you have just cut and throw them across the room. There. You have just played thru half the deck.

Deal out the cards. If you get 20 and the dealer has a 10 up, can you say the probability of this occuring was any different than that first hand off the top of the deck? Which half of the deck has more tens in it, the one you threw across the room or the one on the table? I think all you can say is the deck on the table is NOW light 3 tens.

Suppose you get a 16 instead. Now which half of the deck had more 10s? The key card you need is a 5. Basic strategy says that with a 16 vs a 10 up with four 5s remaining in the deck, hit is the best thing to do. Can you say which half of the deck has the most 5s in it, the one across the room or the one on the table?

I think you better hit, the correct assumption would be both halves of the deck have two 5s in them, the appearance of the 10 dealer's up card had the 4/13ths of a chance, the same as if it came off the top of the deck.

If you think otherwise, than when you play insist that the cards not be cut, that way you will always be playing with the magical 10 rich half of the deck that normally you throw away. Don't follow basic strategy if you get dealt some hand off the top of the deck, because obviously you are playing with some count-screwed remaining half, in oder for that hand to have occured.

70% is about as good as it gets, and that is with multi-level, multi-parameter systems

My understanding is that 70% PE is about the limit for single-parameter counting systems but multi-parameter systems can exceed 70%, and approach 90%.

You may be right. I was going from memory. Do you know which systems can approach 90% playing efficiency?

will only get you about 70% at best.

the game, whereas counting is a statistical approach to betting the game with some strategy variations because of additinal info as you proceed through the deck.

Thanks, everybody.
I still have some lingering/unexplainable "uneasy feeling", but I guess I should move on. Before I do, here's a small story:

I was a long time (pseudo-) Basic Strategy player, and I started learning counting about half a year ago. I think I'm pretty good at keeping counts and I use (or just memorize) almost one hundred indices (I use a few different one-level systems). Once in a while I make mistakes (of some significance) and almost always that happens on one particular hand. Can you guess what hand? Yes. 16 vs. 10! When the (running) count is equal to or greater than 0, I know I'm supposed to stand according to the strategy table (in all counting methods I use). But, my Basic Strategy action, HIT, is sooooooo deeply ingrained in my brain, it just comes out when I'm tired or talking to other people or otherwise distracted. I think it's possibly because I erroneously (and probably subconciously) thought that "BS table == Strategy Table at TC==0" when I studied counting. Am I the only one who's having this kind of problem while transitioning from BS to Counting? BTW, 16v10 is incidentally the only hand where the BS differs from the Strategy at TC==0.

OK, signing off for now.
~Blue Jack in the Box.

I guess out of those 100 indexes you never looked at 12 vs 4 very closely.

Thank you for the references. I'll have to take a look at Chapter 5 again.

BS says to hit 16 vs. 10. The count is assumed by BS to be 0 BEFORE THE DEAL. The composition of the hand though makes the count change, and so BS alters the count as well. If you look at a 10,6 vs 10, and start with a count of 0, then adjust for the 3 known cards, your RC is now -1, not 0. You are assuming the count is 0 after the cards are dealt, but the count is now offset by those 3 cards now. In other words, BS tells you to hit 16 vs. 10 at RCs of -1 not 0.

If you want to be certain about BS, take into consideration the count for each play contained within it. Look at every play, and adjust the count for each one, you will see that many of them are not RCs of 0. In other words, BS was the original set of indices, it told you what to do with a hand at the count most likely to occur after those cards are dealt. You can add more indices as you obtain a greater knowledge of the count beyond knowing just the 3 cards in play.

just standing on 16 vs 10 all the time since you are spreading your bets with the count, you'll have more money on the table when the count is positive and standing is required...and less money (or none) on the table when the right play is to hit.

Stanford Wong's Professional Blackjack book says to stand at a count of +1 or more and to hit at count of less than +1, if your not a counter then the play would be to hit.

I meant to say it says stand at count of 0 or more and hit at count of less than 0.