Am I Right or Am I Wrong?
https://www.blackjacktheforum.com/sh...rom-Peek/page3
I made a post in the Software forum (link above) in which I said that I think I have discovered a very serious flaw in the way that many of the greatest authors and experts in the world of Blackjack count cards and use those counts to adjust their strategy and wagers. I must admit the odds that I'm correct about this would appear to be pretty low. After all, who am I to dispute the findings made by all these geniuses who have devoted so much of their lives to the game. People like Thorpe, Braun, Einstein and others?
But please let me tell you. For the longest time now, when I've been playing for money, I get a high True Count (like +6) and bet big expecting to win. But I just lose so often that I have been thinking something must be wrong. So, I wrote my own simulation and in so doing, I discovered a little flaw that turns out to mean I'm losing a lot of money because of a serious flaw in the Counting Systems I've tried. I'm going to show you what I mean. I sure do hope I'm not wrong.
I discovered this supposed "serious flaw" while I was creating my own BJ simulation and this is why I think it's so important for people to either create their own sims or at least to be able to examine the source code used to create the sims they use so they can understand exactly how it works. I pledge that if and when I release my BJ sim, it will absolutely be "open source".
I'd like to explain why I consider this flaw to be so serious. Unfortunately, I'm very worried that I'm the one who has made the "serious flaw" and I will wind up looking foolish.
The flaw concerns Counting Systems. One of the most common system was proposed by Braun and the details can be found in The World's Greatest Blackjack Book on page 207. In his system, the cards count as follows: 2-6 are +1, T-K and A are -1 and 7-9 count are zero. Most every BJ player who counts cards should be familiar with this system.
For the remainder of this post, I will use the following abbreviations: RC (Running Count) TC (True Count)
Most every well known BJ author and expert explains how to use these values to compute the RC as well as the TC. I will assume that everyone here understands how to compute TC.
All the authors explain that when TC (True Count) is a specific value (let's say +6), that means the player should alter their strategy and their wagering in a specific way. My problem is that all these authors have everyone believing that a TC of +6 means the cards will behave in a specific way and they will always behave in the same way just as long as the TC remains +6. I think that is terribly flawed.
A TC of +6 does not always mean the same thing. The shoe can have a TC of +6 but it can be in very different states. The odds that you will be dealt a high card or a low card can be very different even though the TC remains +6. Allow me to demonstrate:
Suppose you are the only player at a two deck table. In the following chart, there are always 52 cards remaining in the shoe. Therefore the TC is computed to be the same as the RC. In the following chart, the RC is always +3 and the TC is always +3 as well. Just look at all the different states that can mean and all the different odds that exist for you to be dealt a high card or low card:
(Thank you ZenMaster_Flash for finding my error here and correcting it so both counts are +3).
In a single deck, there are 3 zero cards in each suit (7-9) and so there are 12 of them in the deck and 24 in the two-deck shoe.
There are 5 high cards in each suit (T-K and A) and so there are 20 in the deck and 40 in the two-deck shoe.
Likewise, there are 20 low cards in the deck (2-6) and 40 in the shoe.
So, when the RC (Running Count) is +3, the shoe can be in any one of the following 11 states:
The following 11 cases are the only cases in which you can have an RC of +3 in a two deck shoe with half the shoe (52 cards) remaining. You can have a RC +3 under any of the 11 following conditions.
But, just remember this. The number of zero cards in the shoe can not exceed 24. Likewise, the number of high cards cannot exceed 40 and the number of low cards cannot exceed 40. OK. Here we go:
Zero High Low RC TC Odds of High Card
1 27 24 +3 +3 27/52 = 0.52
3 26 23 +3 +3 26/52 = 0.50
5 25 22 +3 +3 25/52 = 0.48
7 24 21 +3 +3 24/52 = 0.46
9 23 20 +3 +3 23/52 = 0.44
11 22 19 +3 +3 22/52 = 0.42
13 21 18 +3 +3 21/52 = 0.40
15 20 17 +3 +3 20/52 = 0.38
17 19 16 +3 +3 19/52 = 0.37
19 18 15 +3 +3 18/52 = 0.35
21 17 14 +3 +3 17/52 = 0.33
Remember in a two deck shoe there are a max of 24 zero cards, 40 high cards and 40 low cards. In each of the above cases, there are 52 cards remaining in the shoe and the RC is +3 and the TC is +3.
In the 1st case. There is one zero card, 27 high cards and 24 low cards. The total is 52 cards. There are three more high cards than low cards which means the RC is +3.
In the 2nd case. There are 3 zero cards, 26 high cards and 23 low cards. The total is 52 cards. There are three more high cards than low cards which means the RC is +3.
In the 11th case. There are 21 zero cards, 17 high cards and 14 low cards. The total is 52 cards. There are three more high cards than low cards which means the RC is +3.
In all these cases since there are 52 cards remaining out of the original 104, that means the TC is the same as the RC.
But, now look at the odds you will be dealt a high card:
In the 1st case, there are 27 high cards out of a total of 52 total cards. That means the odds are 27/52 or 52% your next card will be a high card.
In the 2nd case, there are 26 high cards out of a total of 52 total cards. That means the odds are 26/52 or 50% your next card will be a high card.
In the 11th case, there are 17 high cards out of a total of 52 total cards. That means the odds are 17/52 or 33% your next card will be a high card.
Do you see the flaw? Even though the TC remains at +3 for all 11 cases, the odds of being dealt a high card vary from 33% to 52%. 33 is only 60% as much as 52. So that is a very large difference.
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Would you like to see how this applies to a single deck game? The following chart pertains to a single-deck game in which exactly one half the deck has been dealt and 26 cards remain.
In the following 6 cases the RC is always +3 and the TC is always +6.
Zero High Low RC TC Odds of High Card
1 14 11 +3 +6 14/26 = 0.54
3 13 10 +3 +6 13/26 = 0.50
5 12 9 +3 +6 12/26 = 0.46
7 11 8 +3 +6 11/26 = 0.42
9 10 7 +3 +6 10/26 = 0.38
11 9 6 +3 +6 9/26 = 0.35
Remember in a single deck game, there are a max of 12 zero cards, 20 high cards and 20 low cards. In each of the above cases, there are 26 cards remaining and the RC is +3 and the TC is +6.
In the 1st case. There is one zero card, 14 high cards and 11 low cards. The total is 26 cards. There are three more high cards than low cards which means the RC is +3.
In the 2nd case. There are 3 zero cards, 13 high cards and 10 low cards. The total is 26 cards. There are three more high cards than low cards which means the RC is +3.
In the 11th case. There are 11 zero cards, 9 high cards and 6 low cards. The total is 26 cards. There are three more high cards than low cards which means the RC is +3.
In all these cases since there are 26 cards remaining out of the original 52, that means the TC is computes as double the RC.
But, now look at the odds you will be dealt a high card:
In the 1st case, there are 14 high cards out of a total of 26 total cards. That means the odds are 14/26 or 54% your next card will be a high card.
In the 2nd case, there are 13 high cards out of a total of 26 total cards. That means the odds are 13/26 or 50% your next card will be a high card.
In the 11th case, there are 9 high cards out of a total of 26 total cards. That means the odds are 9/26 or 35% your next card will be a high card.
Do you see the flaw? Even though the TC remains at +6 for all 6 cases, the odds of being dealt a high card vary from 35% to 54%. 35 is only 64% as much as 54. So that is a very large difference.
I have put a lot of work into this post. I sure do hope that I won't come away looking like a fool.
P.S. I think I should explain one of the reasons why I consider this to be such a serious flaw is because if the odds can vary so wildly that your next card dealt will be a high card or a low card, then it would be highly suspect that you should alter the Basic Strategy based on the TC. Most authors have a table that shows when the TC exceeds a certain value, you should Stand instead of Hit or vice versa. Also they show you should change the way you Double or Spllit based on the TC. My point is that since the odds swing so greatly that you will be dealt a high card or low card, it's really not very wise to base these kinds of decisions strictly on the TC. After all, if you hit instead of stand, I think you expect not to be dealt a high card since you will be more likely to bust. I think before changing the decision as to what Action to do (whether you Stand, Hit, Double or Split), you really need to know what the odds are that you will be dealt a high card or low card and as I have shown in the above charts that is MOST DEFINITELY NOT THE SAME AS THE TRUE COUNT! The high swings in the odds of being dealt a high card next make the TC a bad way to make those decisions.
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