16 vs 10 at true count 0 HELP

I have searched for hours and found no definitive answer. Alas, I post here.

I understand the index for 16 v. 10 is 0. Greater than 0 means stand, less than 0 means hit.

However, what about at a true count of exactly 0, when the running count itself is 0.

Illustrious 18 regulates its indices at a count greater than or equal to the index. Therefore, 16 v. 10 at an index of 0 means stand at a true count of 0. However, the Advanced Strategy Lesson 14 on this very website state hit at 0 or lower.
http://bj21.com/gamemaster/GameMasterClassics14.html.

I understand the margin on this decision is incredibly small. However, I feel there should be a definitive answer. I haven't found a simulator where I can run this scenario many times, or else I would just figure it out myself.

Of course, this is when surrender is not available.

"I understand the margin on this decision is incredibly small. However, I feel there should be a definitive answer."

You have your definitive answer*; you just failed to recognize it when you saw it. :-)

Don

*"Illustrious 18 regulates its indices at a count greater than or equal to the index. Therefore, 16 v. 10 at an index of 0 means stand at a true count of 0."

Ha thanks for your quick response and from somebody so prominent in blackjack nonetheless.

Naturally, I would expect your response to be stand, as you developed the Illustrious 18.

Why, then, does the GameMaster blackjack school here say to hit on count 0? Also, what gives with a discrepancy such as Illustrious 18 saying to double 9 v. 7 at 3 but GameMaster saying double 9 v. 7 at 6? I am being nitpicky I know, but I would like to understand everything before I start putting money on the line.

jcbsbrd,

A spreadsheet that I wrote a long time ago shows that for an infinite number of decks at a true count of zero and a bet of $100, you would lose (on average) $57.52 by hitting and you would lose (on average) $57.58 by standing. These numbers include the loss if the dealer has an ace in the hole. Thus, you would save a whopping 6 cents (per $100 bet) by hitting at a true count of zero. Hitting also helps eat cards (which is desirable at neutral and negative counts).

My understanding is that Don�s numbers are based on computer simulations (done by others) which have been rounded to the nearest integer. There is nothing wrong with that. However, Don mistakenly assumes that the numbers are fixed in stone and thus his answer is not quite correct for your question. In other words, the exact index for 16 vs. 10 is some small positive number (e.g. 0.01) which has been rounded to 0. Treating the index as exactly 0 has negligible effect in actual play but it can not be used to answer your question precisely.

Dr 21

When is the last time you played BJ against an infinite number of decks?

Let me know when you write a spreadsheet for 16 v. 10 for a number of decks that we actually use to play blackjack, such as six, with a running count of exactly zero, taking into account every possible holding of 16, and then let me know what you find.

I would welcome such a study. Naturally, when we make plays using indices, we are incorporating an entire bucket of a range over an entire integer, and we are averaging results. It is possible that at the extreme left end of the zero bucket, i.e., at precisely zero, 16 v. 10 would be a hit. But, I don't think so.

Don

"Also, what gives with a discrepancy such as Illustrious 18 saying to double 9 v. 7 at 3 but GameMaster saying double 9 v. 7 at 6?"

An obvious discrepancy such as this (one number double the other) can only be because the first divides by whole decks to ascertain TC while the second divides by half decks. But then, you should see the difference for all such index plays.

The Hi-Lo TC for doubling 9 v. 7, dividing by whole decks, is not +6. So, you'll have to ask GaMaster what their problem is.

Don

In the lesson you reference, they first state:

"The most common decision any player makes at Blackjack is whether to hit or stand, consequently this will be the most common basic strategy variation and you should learn all the important ones. The first is with a hand of 16 against a dealer's up card of 10. You should stand if the count is over 0 and hit if it is 0 or lower. This means that if the running count is 1 or higher, stand. Since the 'decision' number is 0, it's not necessary to calculate the true count -- the running count will do in this situation. Don't get confused here. Almost all basic strategy variations rely on the true count, but for those where the decision number is 0, the running count will suffice."

But then, later, below, they say:

"12 vs. 4 Stand at 0 or higher (Yes, if the running count is at all minus, you hit 12 against a 4. It drives the other players at the table crazy!!!)"

Now, you may think that they actually are trying to make a fine distinction between the two plays -- and that is your right -- but I'm not so sure. I think they are just being inconsistent in their interpretation of what to do at exactly zero, but I may be wrong.

Bottom line: I think it's ridiculously close at exactly zero, with no practical importance whatsoever, but I understand the interest in knowing the theoretically "correct" answer.

Don

Never thought of that. Should have.

Thanks.

Don

Don wrote:

It is possible that at the extreme left end of the zero bucket, i.e., at precisely zero, 16 v. 10 would be a hit. But, I don't think so.

It is interesting that your post was titled �Not true� but your response stated that it is possible that at precisely zero, 16 v. 10 would be a hit.

If a player should hit his 16 against a dealer 10 at a true count of zero with an infinite number of decks, then he should definitely hit with 8 or fewer decks! If he hits his 16, he is obviously hoping to receive a 5 or less. If he gets a 6 or higher, he will lose regardless of the effect that his hitting has caused on the dealer�s hand. If he gets a 5 or less, not only has he improved his hand, but he has increased the likelihood of the dealer busting (due to the removal of a small card). This increase in the likelihood of the dealer busting due to the removal of a single small card would not show up in the �infinite deck� game. Thus, he would save even more than 6 cents (per $100 bet) by hitting with a finite number of decks.

In conclusion: If a player should hit his 16 against a dealer 10 with an infinite number of decks, then he should definitely hit with 8 or fewer decks!

Dr 21

I guess I don't really understand the concept of "risk-averse".

At certain counts, shouldn't there be a most statistically favorable play just as basic strategy is the most statistically favorable play given the knowledge of only the hand dealt and the dealer's upcard. I don't understand how doubling 9 v. 7 at 3 could be to "risky" as with 4 and 5 but at 6 it is "risk-averse."

I feel like either it is favorable to double 9 v. 7 at 3 or not. There isn't a "risk-averse" basic strategy and a "risky" basic strategy after all.

I appreciate the advice.

Would it be wise then to hit at exact index numbers when the count is unfavorable (say, less than 1) in order to eat cards?

For example, one source of Illustrious 18 (http://jay.purplewire.com/blackjack/ill18.html) says hit at less than or equal to 0 for 12 v. 4. Another source (http://wizardofodds.com/blackjack/count/highlow1.html) implies stand at greater than or equal to 0 for 12 v. 4. So, at exactly 0, one says hit, the other stand. But, since the count is at 0, should we hit to eat up cards to hopefully raise the count? Or have you done a spreadsheet for this and found it favorable one way or the other?

I think I'm being too meticulous but it does drive me a bit crazy when two source of the same figure (Illustrious 18) differ in its subtleties.

Also, is there some program that I can run "infinite" trials on to figure this out myself?

jcbsbrd,

What you should get from Don's and my posts is we are talking pennies on the $100 for very close plays. You do not win money in this game by knowing every index and hand dependent index. In fact, a counter can win with basic strategy only. (I personally would recommend that you at least use Don's I18 except for splitting tens.)

The way to win money is to bet high when the count is in your favor and bet as small as possible (or not at all) when the house has the edge. That's the easy part. The hard part is getting away with it. Of course, you cannot over bet your bankroll and expect to survive. I would recommend Don's book to help you to learn the meaning of risk averse and appropriate bet spreads based on the count (and your bankroll).

When the house has the edge, you will generally have a very small bet (e.g. $10) and the cost of an incorrect hit or stand for close plays will generally be less than a couple pennies. Certainly in single and double deck, seeing an extra card is worth several pennies and I agree that hitting (even when mathematically incorrect) is worth it.

Dr 21

Risk-averse indices seek to sacrifice a small amount of EV to decrease variance.

Check the glossary in the Blackjack Basics section of this page. There is a lot of good information available here, even on the free site.

"Risk-averse indices seek to sacrifice a small amount of EV to decrease variance."

The point, however, is that we actually win MORE using r-a indices. How is this possible? Because, if we bet optimally, our bet size is a function of bankroll times edge divided by risk. So, by lowering the risk even more than we lower the e.v., we increase the optimal bet size and, eventually, the SCORE, or hourly win rate.

So, if we are able to bet optimally, we don't win less when we use r-a indices; we win more.

Finally, as you can see from the study on this topic in BJA3, the whole concept doesn't amount to a hill of beans! ;-)

Don

First, let me say your spreadsheet is apparantly quite accurate. Griffin lists 0.06 (in percent) for the infinite deck EV delta on hard 16 v T (pg. 231 ToB), so that matches your 6 cents on a $100 bet exactly.

But I can't agree with: "If a player should hit his 16 against a dealer 10 at a true count of zero with an infinite number of decks, then he should definitely hit with 8 or fewer decks! If he hits his 16, he is obviously hoping to receive a 5 or less. If he gets a 6 or higher, he will lose regardless of the effect that his hitting has caused on the dealer�s hand."

The problem with this logic is that the strategy EoRs for 6 and higher are all over the map!

From Don's BJA3 pg. 515 ...
EoR 16 v T (6): +1.6446
EoR 16 v T (7): -0.7109
EoR 16 v T (8): -0.0567
EoR 16 v T (9): +0.5524
EoR 16 v T (T): +1.1151

It seems the fact a 7 might show up as dealer's hole card is more important than its role as a hit card.

There's a fairly simple procedure for calculating an index based purely on the EoRs. It's described here:
http://www.blackjackforumonline.com/content/AlgebraicIndices.htm

I carried out the procedure for 16 v T, based on removal of the T upcard, for 1, 2, 6 and 8 decks. They came out as follows...
1 deck index: -0.1238
2 deck index: -0.02502
6 deck index: +0.04428
8 deck index: +0.0532

These follow the interpolation by 1/decks fairly well. So apparantly, the index changes in sign somewhere between 2 and 6 decks.

I also did the 1 deck calculation with the player's first two cards removed along with the T up. That makes quite a difference for one deck...
1 deck index for T,6 v T: +3.72646
1 deck index for 9,7 v T: -0.20216

The gamemaster does say to hit h16 v T for 6 decks at TC=0, and I think he's correct about that, especially since hitting is a little more risk averse than standing (i.e. better chance for a push). Then in his single deck matrix (lesson 19) he has an index of 0 for 9,7 v T (and says to stand right at 0) and an index of +4 for T,6 v T. Right again! The man is psychic.

ETF

ET Fan,

If I am reading your post correctly, you are confusing basic strategy with the correct strategy for a true count of zero. In the original post, jcbsbrd asked about the correct strategy for 16 v 10 for a true count of zero. For a finite number of cards at a TC = 0, it is assumed that you have already included your two (or more) cards and the dealers up card in the count and thus the EOR of the dealer�s ten and the exact cards that you are holding to make your 16 do not affect the correct strategy for a true count of zero. If the question was about basic strategy, then the cards in your hand and the dealer�s up card should be considered in the analysis.

Dr 21

"True Count = 0 is not the same as Basic Strategy"

I just reread my post and I can't fathom how you got the impression I didn't know that.

"For a finite number of cards at a TC = 0, it is assumed that you have already included your two (or more) cards and the dealers up card in the count and thus the EOR of the dealer�s ten and the exact cards that you are holding to make your 16 do not affect the correct strategy for a true count of zero."

The cards were, in fact, removed, therefore the effects of removal have an effect. Those particular cards are no longer available for player or dealer hitting, or for the dealer's hole card. The count is just a general indicator. It doesn't have that level of specificity. I'm sure you can see that.

ETF