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Response to Zenfighter's analysis

 Posted by Arnold Snyder on 9 February 2005, at 4:01 p.m., in response to Good post on, posted by Michael Dalton on 5 February 2005, at 8:16 p.m.



A few points regarding “Zenfighter’s” analysis:


1) Zenfighter says:


> Rules: 6dks, das, spl3, nrsa BSE = - 0.41%


I do not see in McDowell’s book where he defines this rule set and house edge. The only house edge McDowell defines is -.005 (p. 114), without specifying any set of rules. So, I used his number as the base house edge, -0.50%.

2) Zenfighter says:

> Total cost for the 87% of the failures = - 4.067175 = - 4.07%


> Here, is where McDowell’s targeted equation 7-3 seems to have underestimated the real cost of the failures (while betting on predictive aces only). By assuming a simplified mathematical formulae, obviously what you get is an inflated EV = 3.85%, which is not the case, as you can see from the above table. (Even if the dealer doesn’t get any of the key(s) predicted aces)


I agree with this 100%. In fact, that was the major point I was making in my criticism, which Dalton and others refuse to acknowledge as correct. My number disagrees with Zenfighter’s number only because I am assuming the house had a 0.5% edge (as per McDowell’s number), and he is assuming that the house has a 0.41% advantage (and I do not know why he is making an assumption different from the number McDowell provides).


This error that I pointed out, and that Zenfighter agrees with, in fact, is precisely why McDowell’s system is not a valid money-making system. It is so weak that it can be used only to reduce the house edge, not beat the house. Who wants a system that doesn’t win?


I will note here that Zenfighter is using the number of Ace hits for the player (13%) that McDowell says in his Errata sheet should instead be only 10%. Why is Zenfighter ignoring the Errata sheet, which produces much worse results for players?

3) Zenfighter says:

> Total improvement over random distribution = 1.248 – 0.41 = 0.838%


> Thus the final EV = 1.283 – 0.838 = 0.445


This is the exact number I came up with for the player’s edge when betting on an Ace in my initial analysis when I used McDowell’s 13% estimate, splitting extra Aces between the player and dealer (from his book, not the Errata sheet). So, I have no big argument with Zenfighter on this except that Zenfighter should have acknowledged my work, which predated his.


Zenfighter then advises players using this technique: “...don’t quit your daily job anyway.”


But, again, since Dalton has made such a big issue of the fact that I used the numbers from the book, and not the Errata sheet, why didn’t Zenfighter use the numbers from the Errata sheet? If Zenfighter would insert those “corrected” numbers that McDowell provided for the Errata, he will find, exactly as I did, that the player has NO advantage when betting on an Ace.


Furthermore, even if McDowell’s Errata is incorrect, and as per the book he can get a 0.45% advantage when betting on an Ace (instead of the 4.2% McDowell provided in his book), why does Zenfighter ignore the most important point that I made, that the Ace predictor only has this advantage when betting on the Ace? He still must play against the normal house edge (be it 0.50% as per McDowell, or 0.41% as per Zenfighter) on all of the hands where he is not betting on an Ace. That 0.45% advantage would apply only when an Ace is predicted. That’s like playing in a game as a card counter where the biggest advantage you ever saw with the Hi-Lo count was less than a true count per deck of +2, and this edge only occurred on about 10% of the hands played. No counter would play in such a miserable game because it would take a spread of 1-to-10 just to break even.


Finally, Zenfighter makes a HUGE mistake of his own. He says:


> Obviously the player’s final expectation as a function of 1,2,3,4,5,6 or 7 players is:


> EV = Sum Ei {for i = 1 to 7}/7


> This is a figure between 1 and 2 percent. An elementary mathematical interpolation between both extremes should convince even an obtuse disbeliever.


He is somehow under the impression that having more players at the table will increase the Ace predictor’s win rate because this will decrease the dealer’s chance of getting the Ace. This assumption is true but it does not increase the player’s win expectation at all.


As an extreme example, let’s say the player is at a full seven-spot table, back-counting so that he need place no waiting bets. On average a seven spot table will use 22 cards per round. In order to be able to bet on the Ace for the next round, the key card must come out as one of the last three cards of the round. If it comes out as any one of the other 19 cards (on average) dealt in that round, either the Ace will already have fallen onto the table, with the predictor getting no chance to bet on it, or the Key card will have proven to be either a false Key or part of a broken sequence. But the fact is, with a full table, only 3/22 (or 13.6%) of the Key cards will be usable. So, instead of having a 1.28% advantage on 4 bets per shoe, the predictor at a full table will be able to bet with a 1.28% advantage on one Ace every other shoe.


Zenfighter has no more practical experience with ace prediction than McDowell.


I have no intention of ever writing a book on this subject, and I have never had any serious intention of writing a book on this subject. However, I can tell players that McDowell wrote a book of theory without having tested his theories in live casino play, and that there are far more problems with this book than the mistakes he has made, both in the book and the Errata sheet, in calculating a win rate. His tracking methodology is even more flawed than the math on his estimation of advantage.


The fact is: you cannot make money tracking Aces using McDowell’s methods or assumptions. It’s a book of theory, not fact, and has no practical system for beating the casinos.


My argument is that this book should not be promoted as a book with a winning method for players. It’s not. And Zenfighter’s analysis agrees with me on that point. It would agree with me even more if he would apply analysis to the numbers provided in the Errata sheet.


Assuming you want to put out an accurate method (since I never will do this) let me give you some pointers.


1) You get rid of false keys by using multiple key cards. McDowell’s single-key method is betting suicide. Also, his false key rate using a single key should be about 4 times the rate he claims. See Radar O’Reilly’s article about this at my Web site (, as well as S. Yama's letter and Steve Forte’s comments that McDowell’s use of a technique from his book to eliminate false keys made no sense to him.


2) You must play at tables where there are no other players. You must take over the table, control the number of spots bet, and use multiple hands to steer the Aces as necessary. You NEVER want the Ace to go to the dealer if you can help it.


3) You must attempt to key 8 to 12 Aces per shoe if you intend to bet on 3 or 4 of them. In a six-deck shoe with 75% penetration, you will see on average, 18 Aces per shoe. You probably cannot key all of them, but you should try to get most of them.


4) None of this is easy. Players who do this successfully devise immensely complex memory systems, and work for months practicing.


5) Before the next book, someone should go into a real casino and do it. There are a hundred fine points that have to be worked out regarding specific dealers, types of shuffles, etc.


6) When you bet on an Ace, you want to hit the Ace at a minimum on one-third to one-half of your bets. Not 13% or 10%. McDowell’s weak methods won’t work. You will lose your shirt if you attempt to use them.


7) Finally, I’m going to ask Michael Dalton to stop promoting this book as the “secrets of the pros.” There are more secrets of the pros in the six points above this one than in all of McDowell’s book. You know, Michael, that numerous endorsers of this book have retracted their endorsements on my Web site. And you know that you have been personally contacted by other endorsers who have instructed you to have their names and endorsements taken off your Web site as well as future issues of the McDowell book. So, why don’t you stop the phony hype, and apologize to your customers. I know you published the book in good faith, thinking it contained a winning system. And I know McDowell wrote the book in good faith, thinking he had figured out the math when he was miles away.


But read Zenfighter’s analysis. He comes to the same basic conclusion I came to, and addresses the same error. (Zenfighter’s error on the increase in value with multiple players is not McDowell’s error.) McDowell’s book, as is, has no value except for players who want to read about some of the non-random shuffle studies. There is no system that works in that book.




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