Hi,
What is the correct play (stand or hit) for 16 versus 10?
Here are the details:
- infinite deck;
- 16 consists of 3 or more cards, or is a split hand;
- resplits are not allowed.
Blackjack Rookie
Blackjack Rookie,
With an infinite deck, the removal a finite number of cards is negligible and thus basic strategy becomes the same as the correct strategy at a count of zero; which for 16 vs. 10 is to hit.
Dr 21
"and thus basic strategy becomes the same as the correct strategy at a count of zero; which for 16 vs. 10 is to hit."
You might want to check that. The Hi-Lo index for 16 v. 10 is zero. The interpretation of that is: STAND if the true count is greater than OR EQUAL TO zero.
So, your reasoning isn't very helpful here.
Don
Don,
While I did write the post based on memory, I took your advice to check it. Back in 1992, I wrote a spreadsheet for an infinite deck game in order to study the effect of card removal. According to my spreadsheet, for an infinite deck game the EV for 16 vs. 10 (before checking for dealer blackjack) is:
Hit -0.57522
Stand: -0.57578
So, if there is no error in my spreadsheet, the correct strategy (just barely) is to hit. As the difference doesn�t show up until the 4th significant figure, I can see why the actual index of approximately 0.1 was rounded to 0. Of course, there could be an error in my spreadsheet.
Even if my spreadsheet is in error, you are incorrect to say that my reasoning isn�t helpful, as my reasoning would still be correct. But, if the index is truly 0 (and not some small positive epsilon, then my conclusion would have been wrong. See the difference?
Dr 21
According to my spreadsheet, for an infinite deck game the EV for 16 vs. 10 (before checking for dealer blackjack) is:
Hit: -0.57522
Stand: -0.57578
Surrender: -.053846
The -0.50000 is for early surrender (which of course we would prefer).
Dr 21
"Even if my spreadsheet is in error,"
Don't know for dealer not checking for a natural. I'll assume you're right. Correct infinite-deck expectations for a "normal" game are: hit: -0.5398; stand: -0.5404. Hit is correct for generic 16.
"you are incorrect to say that my reasoning isn�t helpful, as my reasoning would still be correct."
No, it isn't.
"But, if the index is truly 0 (and not some small positive epsilon, then my conclusion would have been wrong. See the difference?"
No; YOU don't see the difference. Your premise, and therefore, your reasoning, is incorrect. Your premise is that the concept of correct basic strategy is based on a true count of zero. It isn't. Your premise is, further, that, if the index were zero for 16 v. 10, then having a true count of zero would imply that we should hit. It implies no such thing. With a TC of zero, we would stand. That's how the zero index would be interpreted, if it were the correct index.
So, again, I'm not questioning your spreadsheet; it's your reasoning that is wrong.
Don
Don wrote:
Your premise is that the concept of correct basic strategy is based on a true count of zero.
Don,
In general, basic strategy is not the same as the correct strategy based on a true count of zero due to the effect of card removal. For example, if you have a 14 vs. a 10 in single deck (if my memory serves me correctly) you should hit unless your 14 is composed of 2 sevens. In other words, the fact that there are only 2 sevens left in the deck change whether or not you should hit. You know this and I know this.
However, my reasoning as stated in my previous post is:
�With an infinite deck, the removal of a finite number of cards is negligible and thus basic strategy becomes the same as the correct strategy at a count of zero�
Both your numbers and mine show that you lose less money by hitting, so why wouldn�t you hit? If you still think I�m wrong, please explain the fallacy in the quoted statement above. Don�t put words in my mouth such as �Your premise is that the concept of correct basic strategy is based on a true count of zero.� Thanks.
Dr 21
"In general, basic strategy is not the same as the correct strategy based on a true count of zero due to the effect of card removal."
So far, so good.
"For example, if you have a 14 vs. a 10 in single deck (if my memory serves me correctly) you should hit unless your 14 is composed of 2 sevens. In other words, the fact that there are only 2 sevens left in the deck change whether or not you should hit. You know this and I know this."
Yup.
"However, my reasoning as stated in my previous post is:
'With an infinite deck, the removal of a finite number of cards is negligible and thus basic strategy becomes the same as the correct strategy at a count of zero.'"
You said more! You added: "Which for 16 vs. 10 is zero." What does that mean, with respect to infinite deck? ALL true counts are zero, always! If you want us to reference what "correct strategy for 16 vs. 10 at a count of zero" means, it would have to be for some game other than infinite deck. Otherwise, the comment makes little sense.
So, as soon as we reference that index, it has a meaning: STAND if the TC is greater than or equal to zero. I'm criticizing you for introducing this superfluous idea into the infinite-deck discussion.
"Both your numbers and mine show that you lose less money by hitting, so why wouldn�t you hit?"
You would hit. But, you wouldn't invoke a true count of zero as your reason for doing so.
"If you still think I�m wrong, please explain the fallacy in the quoted statement above."
See my explanation, above. And, don't put words in MY mouth. My statement isn't a fallacy.
"Don�t put words in my mouth such as 'Your premise is that the concept of correct basic strategy is based on a true count of zero.' Thanks."
OK, I understand that you understand that. But, you're still missing a point by invoking an extraneous index of zero, which doesn't belong in the discussion. Discussing indices, with respect to infinite-deck makes no sense.
Don
Don,
For convenience, I have copied and pasted the 3 posts in question:
************BS question
Posted By: Blackjack Rookie
Date: 7 Jun 10, 7:59 am
Hi,
What is the correct play (stand or hit) for 16 versus 10?
Here are the details:
- infinite deck;
- 16 consists of 3 or more cards, or is a split hand;
- resplits are not allowed.
Blackjack Rookie
***********Hit
Posted By: Dr 21
Date: 8 Jun 10, 9:51 am
In Response To: BS question (Blackjack Rookie)
Blackjack Rookie,
With an infinite deck, the removal a finite number of cards is negligible and thus basic strategy becomes the same as the correct strategy at a count of zero; which for 16 vs. 10 is to hit.
Dr 21
***********Ahem!
Posted By: Don Schlesinger
Date: 8 Jun 10, 4:02 pm
In Response To: Hit (Dr 21)
"and thus basic strategy becomes the same as the correct strategy at a count of zero; which for 16 vs. 10 is to hit."
You might want to check that. The Hi-Lo index for 16 v. 10 is zero. The interpretation of that is: STAND if the true count is greater than OR EQUAL TO zero.
So, your reasoning isn't very helpful here.
Don
**************************************************
I think we are getting somewhere, but you keep confusing the issue by trying to change what I have said. Let�s go back to my original post and your original response. You will see that I did not bring up the �Hi-Lo index for 16 v. 10 is zero� - you did. BS players don�t count and thus Hi-Lo in not relevant here. My stated conclusion was �which for 16 vs. 10 is to hit.� I now believe that we both agree on my conclusion. I did not say �Which for 16 vs. 10 is zero.� (What does that mean?)
Your first post states �So, your reasoning isn't very helpful here.�
My reasoning was: �With an infinite deck, the removal a finite number of cards is negligible and thus basic strategy becomes the same as the correct strategy at a count of zero.� I still like my reasoning regardless of your semantics arguments. Now, I do agree that my philosophy professor would have preferred an argument where I did not skip so many steps. He would have preferred an argument like this:
1. In a fair game of blackjack, regardless of the number of decks, the true count starts at zero.
2. It takes a finite number of cards to deal a hand.
3. With an infinite deck, the removal of a finite number of cards results in a negligible change in the true count.
4. After dealing a hand, the true count will remain at zero.
5. No matter how many finite number of hands are dealt, the true count will remain at zero for the infinite deck.
6. Basic strategy �is determined by which action the player can take which will maximize the player's return based only upon the knowledge gained from the player's hand and the dealer's upcard.� (BJ21 Glossary)
7. A player�s return will be maximized if he always chooses the play which will give him the highest EV.
8. As the count is always zero for the infinite deck, the correct basic strategy play is the same as the play which will result in the highest EV for a true count of zero.
9. Thus, basic strategy becomes the same as the correct strategy at a count of zero for an infinite deck.
10. For a count of zero, the EV for hitting with a player's 16 vs. a dealer 10 is greater than the EV for standing.
11. With a player 16 vs. a dealer 10, the BS player playing an infinite deck game should hit.
Frankly, I prefer �With an infinite deck, the removal a finite number of cards is negligible and thus basic strategy becomes the same as the correct strategy at a count of zero; which for 16 vs. 10 is to hit.�
Without misquoting me, please let me know exactly why you wrote �your reasoning isn't very helpful here.� By the way, the reason your index argument does not work is because of rounding. The true index for 16 vs. 10 is slightly greater than zero. No one wants to memorize indices like 0.05 for 16 vs. 10. (Also please note that -0.5398 > -0.5404.)
Dr 21
I am beginning to understand why war is such a popular human enterprise.
I will be happy to let you have the last word. I have explained myself to the best of my ability; there's little more that I can add.
You continue to write things like:
"As the count is always zero for the infinite deck, the correct basic strategy play is the same as the play which will result in the highest EV for a true count of zero."
Why would you bother with the notion of a true count -- at zero or any other value? What possible role does it play in an infinite-deck discussion? By definition of "infinite deck," referring to the true count is totally unnecessary, confusing at best and utterly useless, at worst. Basic strategy is basic strategy, and, whether for one deck, six decks, or infinite decks, has NOTHING to do with the notion of a true count of zero. Why introduce a red herring? It's illogical.
"Thus, basic strategy becomes the same as the correct strategy at a count of zero for an infinite deck."
The statement isn't incorrect, but, for the last time, I call into question the need to have ever made it in the first place. I could say, "In infinite deck, the correct play for 16 v. 10 is to hit, and Albany is the capital of New York," but the last part of the sentence isn't terribly useful or informative for my BJ play, is it?
Feel free to have the last word. I won't respond.
Don
Don,
This discussion has gotten very �wordy� especially with my adding the step by step solution that my philosophy professor would have liked. Let me remind you of the original statement that you questioned:
�With an infinite deck, the removal a finite number of cards is negligible and thus basic strategy becomes the same as the correct strategy at a count of zero; which for 16 vs. 10 is to hit.�
In your last post you wrote: �Why would you bother with the notion of a true count -- at zero or any other value? What possible role does it play in an infinite-deck discussion?�
That question is easy for me to answer (and hopefully easy for you to understand).
1. I know that at a true count of zero, the correct strategy is to hit.
2. I know that the true count is always zero for a fair, infinite deck game.
Putting these 2 facts together allowed me to easily answer the question at hand: �What is the correct play (stand or hit) for 16 versus 10?� Obviously you and I think differently. Why is this so hard for you to grasp? Feel free to respond, I am not the type that needs the last word.
Dr 21
"I know that at a true count of zero, the correct strategy is to hit."
You state this as some kind of universal truth, applicable, in advance, to all numbers of decks. Clearly, that isn't true. So, you must be stating it only for infinite deck, otherwise the statement is patently false.
So, yet again, since it's only for infinite deck, there is zero need to state it at all. There is only one correct BS play for every hand in infinite deck, and I don't need to refer to a count of zero to know what it is. In fact, I don't need to refer to any true count whatsoever.
So, of two things, one is forcibly true, and you may take your pick: You are making believe that there is a general cause-and-effect relationship between your statements 1 and 2, which is false, OR your statement number one is completely irrelevant and unnecessary in order to conclude statement number two. Take your pick.
Don
I certainly don't think, and don't mean to imply, that I am the final arbiter of all things blackjack, especially given my almost nonexistent posting history, but this bickering is getting on my nerves :-)
Anyway, here's a random nobody's take on the argument:
Dr 21 states
1. I know that at a true count of zero, the correct strategy is to hit.
2. I know that the true count is always zero for a fair, infinite deck game.
Statement 1 is true in this case (this case being 16v10 for an infinite deck). Statement 2 is also true. Don seems to agree with the truth of these statements, but it's the logical connection between them, and hence the validity of the argument, that he questions.
Assuming a true count of 0 and applying it to an index chart for, say, 6 decks, to determine basic strategy for an infinite deck could possibly give a wrong answer for some decision, but it's an excellent approximation. In fact, I would hazard a guess that it's correct in every single case, using unrounded indices, as Dr 21 stipulates. I realize that correlation, even 310 instances of it, does not imply causation, but it's a stronger argument than many we use to derive blackjack or other gaming strategies. So the random nobody's decision: Dr 21 is correct.
A (nearly) analogous argument might be the following:
Every time Don Schlesinger makes a mistake (e.g. initially saying that basic strategy for 16v10 with an infinite deck is to stand [see his "Ahem!" post]), he becomes stubbornly entrenched in an inane argument to distract from his original transgression.
Therefore, Don's mistake causes his stubbornness.
Though admittedly an inductive argument, it's more than good enough for government...I mean blackjack...work.
"Every time Don Schlesinger makes a mistake (e.g. initially saying that basic strategy for 16v10 with an infinite deck is to stand [see his "Ahem!" post]),"
I said no such thing. I actually provided the correct expectations for the hit/stand plays in my very next post. Don't put words in my mouth, especially when you didn't understand the original post.
What that post said was that the way players USE index numbers is to interpret the index such that, AT THE INDEX OR HIGHER, we stand. So, if you wanted to state some kind of "universal truth" that "the index for standing on 16 v. 10 is zero," and you further wanted to say that all indices are, by definition, zero, for infinite deck, and that, therefore, we always play basic strategy, invoking any reference to an index of zero is both counterproductive and confusing.
There's an outside chance that I knew that the correct play for 16 v. 10 in infinite deck is to hit before you were born, so don't go spouting nonsense. Rather, reread what I wrote.
Don
I don't doubt that you knew the correct play for 16v10 for an infinite deck.
What you did do was erroneously say that the method of assuming a TC of 0, then using an index chart to determine basic strategy for an infinite deck, gives the incorrect decision of stand for 16v10, thus proving Dr 21's approach invalid (or even unsound, since you may have been questioning his premises too at this point). However, the precise index for this play is slightly above 0, so the method gives the correct decision of hit.
One of my favorite quotes of Samuel Johnson is: "Sir, I've furnished you a reason; I'm not obliged to furnish an understanding." And yet, I've tried mightily (and, clearly, failed) to make you, Dr 21, and others understand why the REASONING behind his methodology and conclusion is faulty. That it might work MOST of the time is neither relevant nor impressive. If it fails a single time, then the reasoning is faulty. Below, I will furnish such a counterexample.
"What you did do was erroneously say that the method of assuming a TC of 0, then using an index chart to determine basic strategy for an infinite deck, gives the incorrect decision of stand for 16v10, thus proving Dr 21's approach invalid (or even unsound, since you may have been questioning his premises too at this point)."
What I said was that a) if you use an index of zero for the 16 v. 10 play, and you state that, for infinite deck, all indices are zero, then you could be led to the WRONG conclusion, since indices are used to STAND if we are exactly at the index in question; but b) more importantly, such REASONING, in any event, even with an alleged (somewhat meaningless) "precise" index, isn't always correct. Again, see below.
"However, the precise index for this play is slightly above 0,"
And that "precise index" would be for how many decks, exactly? An infinite number? No, I guess not. That wouldn't make any sense, now, would it?
So, now, consider the following: The "precise" index for doubling A,4 v. 4 is negative, and by a non-trivial amount. So, since the TC of infinite deck is always zero, and zero is above this negative number, by your reasoning and Dr 21's, we are led to double, right?
Only problem is, it's the WRONG play! For infinite deck, we HIT A,4 v. 4; we don't double. In fact, Peter Griffin is kind enough to inform us that the crossover point is at the 27-deck level.
REREAD my original post. All I ever claimed was not that the PLAY (hit) was wrong, but that the REASONING that led to the conclusion of hitting was wrong. That it (the reasoning) works (by accident?) in this particular case is irrelevant: in mathematics, you don't have a rule (reasoning) if it doesn't work ALL the time.
I stand by every word I've written.
Don
Exactly what about
"Assuming a true count of 0 and applying it to an index chart for, say, 6 decks, to determine basic strategy for an infinite deck could possibly give a wrong answer for some decision, but it's an excellent approximation. In fact, I would hazard a guess that it's correct in every single case, using unrounded indices, as Dr 21 stipulates. I realize that correlation, even 310 instances of it, does not imply causation, but it's a stronger argument than many we use to derive blackjack or other gaming strategies."
would suggest that I don't understand that Dr 21's method is an inductive APPROXIMATION, rather than a deductive RULE?
I even granted that it could possibly be wrong for some case. The guess that I hazarded turned out to BE a hazard, since there is at least one case where the approximate method doesn't work (maybe A2v5 is another). But, again, this was a KNOWN weakness, which I explicitly acknowledged. To imply that Dr 21's method only gets the right answer "by accident" is ludicrous. It's not simply a stroke of amazing fortune that Dr 21's method gives the right answer almost every time, including the question of the original poster, and that the one or two cases where it fails are marginal.
