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This article covers blackjack ace sequencing and shuffle tracking false key card probability errors in David McDowell's Blackjack Ace Prediction.
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(From Blackjack Forum XXIV #2, Spring 2005)
© 2005 Blackjack Forum

One of the biggest errors David McDowell makes in the severely flawed Blackjack Ace Prediction is his elimination of far too many "false keys." A false key is a card of the same suit and rank as an actual key card, but one that is not in fact the card being tracked. False keys must be addressed because they trigger bad bets, that is, big bets placed at a disadvantage. False keys are important in blackjack ace location strategies because they reduce, or even eliminate, the player’s edge from the strategy.

Radar O’Reilly has already pointed out, correctly, that McDowell’s false key rate must be quadrupled due to errors in the book’s shuffle tracking assumptions. To keep that article at a manageable length, O’Reilly deliberately limited this criticism to the errors in McDowell’s tracking assumptions. However, O’Reilly’s corrections do not completely address the errors in McDowell’s false key rates, which will be even higher in practice than shown by O’Reilly.

This article will show why the false key rate for McDowell’s methods will be even higher than the .40 false key rate shown by O’Reilly (or the .10 false key rate incorrectly shown by McDowell).

On page 100, McDowell begins his discussion of false keys with an incorrect definition of false keys. He says: "A false key card is one of identical suit and value to a genuine key card, but with no Ace following."

This is incorrect because, in fact, a false key card is one of identical suit and value to a genuine key card which may, or may not, have a random Ace following. This is an important distinction for any player who actually puts his money on the line, as you will see.

McDowell then states, again on page 100, "since any false key card will not fool us occurring after a real key/target card sequence, we need only concern ourselves with one or more false key cards that appear in isolation and before the genuine key card."

As a result of this assumption, plus McDowell’s assumption that the player has tracked his key card and ace to a 26-card segment, he concludes that he only has to calculate the probability of a false key in a 12-card segment.

Specifically, he says, "Since half the time, on average, the false key card will occur after the genuine sequence, the size of the sample n is assumed to be 12 cards (26 cards minus the genuine two-card sequence, divided by two)."

The only way this assumption could be correct, however, would be if two other criteria are met. These criteria are:

  1. Every real key is followed by an Ace, and
  2. Every false key is NOT followed by an Ace.

Unfortunately, in actual casino play, these criteria are simply not realities. Let me give you some examples.

Let’s say you are standing behind a full 7-spot blackjack table where back-betting is allowed. It is a two-riffle shuffle, so as per McDowell you will be betting on the 4th spot after your key card comes out.

Your key card comes out as the last card of a round, so you place a bet on spot number 4 for the following round.

Unfortunately, you do not get a first-card Ace on this round. But the third-base player (spot #7) does get an Ace. Here is the question you must answer: Is that Ace that you missed by three cards your Ace, the one predicted by your key card, or is that a random Ace?

This is not an easy question to answer. The "real" Ace will actually land on the spot you bet (#4) only a small percentage of the time, according to McDowell, even when you are betting based on a real key card, due to very slight discrepancies from two perfect riffles. For example, if on the first riffle, two cards happened to drop between your key and its Ace, then the second riffle was perfect, your Ace would now follow the key card on spot #6. On the other hand, if your Ace and key stick together on the first pass, with no cards riffled between them, but the second riffle is perfect, then your Ace will follow the key on spot #2.

In fact, very slight discrepancies in the shuffle can easily deliver your Ace to any betting spot from #1 to #8 (the dealer’s hand). There will be a greater likelihood of the ace following the key on spots #2 to #6, but if an Ace lands on spot #7 when you’re betting on spot #4, this does not mean that you can assume with any confidence that the Ace that hit spot #7 is a random Ace, and that if you see another key, that will be the "real" key.

And there is still another serious problem. If the key you saw prior to betting on spot #4 was a false key, there is close to a 50% chance that a random Ace will follow it within 7 cards, in which case you would be wrong to assume that this was your "real" sequence, and wrong not to bet on the real key card when it appears later.

Likewise, you must consider the probability that a real key card will appear, but that no Ace will follow within 7 cards because the predicted Ace was either broken away from the key by a cutting action, or was separated from the key by more than 7 cards due to a clumpy riffle. In this case, you will be likely to assume that your real key was a false key, and proceed to bet on an actual false key if it shows up after the real one.

So, assuming that the probability of one or more false keys appearing in a 26-card segment can be automatically reduced to the probability of these false keys appearing in a 12-card segment is a gross, and potentially costly, oversimplification (one of many in Blackjack Ace Prediction).

In fact, in a 2-pass shuffle with 26-card grabs, a good tracker may be able to track an Ace to a 52-card segment, not a 26-card segment. And the false key rate should be calculated based on the probability of a card of similar suit and rank to the real key appearing at random within a 50-card segment, not 12 cards, at least the vast majority of the time. ♠

Spring 2005 Blackjack Forum

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  Understanding the Math Behind Advanced Blackjack Plays like Shuffle Tracking and Ace Location
Read this article to understand more about the mathematics behind blackjack shuffle tracking and ace location, and to understand the many errors in David McDowell's Blackjack Ace Prediction.