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Thread: David Spence: Blackjack Ace Prediction

  1. #1
    David Spence
    Guest

    David Spence: Blackjack Ace Prediction

    [Sorry for the duplicate post. I originally posted this in Don's Domain, but, after receiving no response, thought it might benefit from the wider audience here].

    As often happens when one reads a book on a subject about which he knows little, I think I've found a mistake in McDowell's Blackjack Ace Prediction. Also, as is often the case, I'm probably the one who is mistaken. So, if nothing else, I'm looking for clarification regarding one of McDowell's claims.

    McDowell states "if a small group of cards is known to contain an ace, simply knowing its suit increases the probability of one or more additional random aces in the group." The effect is not subtle, resulting in over a twofold increase in the probability of at least one additional random ace in a group of four cards.

    I'm aware of the effect of conditional probabilities. That is, I understand that an answer of "yes" to, "Is there an ace of clubs in these four cards?" results in a greater number of expected aces than an answer of "yes" to, "Is there any ace in these four cards?" (Lest there's any confusion, these example questions are not meant to parallel precisely the situation in BJAP. They're just meant to illustrate a principle).

    However, in the case described by McDowell, the only difference is that the player remembers which ace is expected. It's the same ace, and the same group of four cards, whether the ace's suit is remembered or not. In other words, one would not expect the group of four cards to change spontaneously if the player suddenly forgets or remembers the suit of the predicted ace.

    Further, the remembered ace is not being used as a key card for subsequent aces. Thus, knowing the suit of the expected ace does not result in a decreased false key percentage for subsequent aces; additional aces are random and unkeyed.

    Any clarification on this matter would be greatly appreciated.

    David Spence

  2. #2
    kc
    Guest

    kc: Re: Blackjack Ace Prediction

    > [Sorry for the duplicate post. I originally posted
    > this in Don's Domain, but, after receiving no
    > response, thought it might benefit from the wider
    > audience here].

    > As often happens when one reads a book on a subject
    > about which he knows little, I think I've found a
    > mistake in McDowell's Blackjack Ace Prediction. Also,
    > as is often the case, I'm probably the one who is
    > mistaken. So, if nothing else, I'm looking for
    > clarification regarding one of McDowell's claims.

    > McDowell states "if a small group of cards is
    > known to contain an ace, simply knowing its suit
    > increases the probability of one or more additional
    > random aces in the group." The effect is not
    > subtle, resulting in over a twofold increase in the
    > probability of at least one additional random ace in a
    > group of four cards.

    > I'm aware of the effect of conditional probabilities.
    > That is, I understand that an answer of
    > "yes" to, "Is there an ace of clubs in
    > these four cards?" results in a greater number of
    > expected aces than an answer of "yes" to,
    > "Is there any ace in these four cards?"
    > (Lest there's any confusion, these example questions
    > are not meant to parallel precisely the situation in
    > BJAP. They're just meant to illustrate a principle).

    > However, in the case described by McDowell, the only
    > difference is that the player remembers which ace is
    > expected. It's the same ace, and the same group of
    > four cards, whether the ace's suit is remembered or
    > not. In other words, one would not expect the group of
    > four cards to change spontaneously if the player
    > suddenly forgets or remembers the suit of the
    > predicted ace.

    > Further, the remembered ace is not being used as a key
    > card for subsequent aces. Thus, knowing the suit of
    > the expected ace does not result in a decreased false
    > key percentage for subsequent aces; additional aces
    > are random and unkeyed.

    > Any clarification on this matter would be greatly
    > appreciated.

    > David Spence

    I agree with you. In blackjack only the rank of the card matters unless you are considering bonus payoffs for suited hands, which is not the case here.

    As an aside, consider the number of ways a single deck can be shuffled, 1) considering each suit of each rank individually and 2) considering all ranks equal, regardless of suit.

    Case 1: Permutations = 52! = 80658175170943878571660636856403766975289505440883 277824000000000000

    Case 2: Combinations = 52! / 16! / (4!)9 = 1459243014608741105832394919396033250000000

    I can't see how knowing the suit of the ace changes the probabilities.

    kc

  3. #3
    Magician
    Guest

    Magician: Re: Blackjack Ace Prediction

    > I agree with you. In blackjack only the rank of the
    > card matters unless you are considering bonus payoffs
    > for suited hands, which is not the case here.

    True enough for payoff probabilities but when your trying to determine the probability that the next card is an ace via sequencing, the suits are very important and tens, jacks, queens and kings are all different.

    However, I can't help with the original poster's question.

  4. #4
    Gabriel
    Guest

    Gabriel: Re: Blackjack Ace Prediction

    Maybe the answer is (if I understand you correctly), as simple as comparing these two situations:

    A - You think that an ace is coming due to some sort of ace tracking technique, usually you are 1 out of 5 to guess that in your own trials. Youa re 20%

    B - You have been tracking the A of clubs and think it is to come. Now you are 20% PLUS the probability of one of the 3 aces coming.

    I don't have the text here, so only you know if that is what the author was trying to explain based on the context.

    > [Sorry for the duplicate post. I originally posted
    > this in Don's Domain, but, after receiving no
    > response, thought it might benefit from the wider
    > audience here].

    > As often happens when one reads a book on a subject
    > about which he knows little, I think I've found a
    > mistake in McDowell's Blackjack Ace Prediction. Also,
    > as is often the case, I'm probably the one who is
    > mistaken. So, if nothing else, I'm looking for
    > clarification regarding one of McDowell's claims.

    > McDowell states "if a small group of cards is
    > known to contain an ace, simply knowing its suit
    > increases the probability of one or more additional
    > random aces in the group." The effect is not
    > subtle, resulting in over a twofold increase in the
    > probability of at least one additional random ace in a
    > group of four cards.

    > I'm aware of the effect of conditional probabilities.
    > That is, I understand that an answer of
    > "yes" to, "Is there an ace of clubs in
    > these four cards?" results in a greater number of
    > expected aces than an answer of "yes" to,
    > "Is there any ace in these four cards?"
    > (Lest there's any confusion, these example questions
    > are not meant to parallel precisely the situation in
    > BJAP. They're just meant to illustrate a principle).

    > However, in the case described by McDowell, the only
    > difference is that the player remembers which ace is
    > expected. It's the same ace, and the same group of
    > four cards, whether the ace's suit is remembered or
    > not. In other words, one would not expect the group of
    > four cards to change spontaneously if the player
    > suddenly forgets or remembers the suit of the
    > predicted ace.

    > Further, the remembered ace is not being used as a key
    > card for subsequent aces. Thus, knowing the suit of
    > the expected ace does not result in a decreased false
    > key percentage for subsequent aces; additional aces
    > are random and unkeyed.

    > Any clarification on this matter would be greatly
    > appreciated.

    > David Spence

  5. #5
    kc
    Guest

    kc: Re: Blackjack Ace Prediction

    > True enough for payoff probabilities but when your
    > trying to determine the probability that the next card
    > is an ace via sequencing, the suits are very important
    > and tens, jacks, queens and kings are all different.

    Also, multiple decks would complicate things since there would be many cards of the same suit/rank.

    > However, I can't help with the original poster's
    > question.

    I guess a sequencer needs to know both the suit/rank of each of a small group of cards. I think probability-wise the fact that one of the cards is a specific suit/rank makes no difference just as it makes no difference in a larger group of cards.

    kc

  6. #6
    David Spence
    Guest

    David Spence: Re: Blackjack Ace Prediction

    To clarify, here's a restatement of the problem:

    A player notices a particular ace (say, the ace of clubs), and uses key cards to track this ace. In the next shoe, the player sees the key cards for this ace, and knows that this ace will appear in the next four cards.

    The Question:
    What is the probability that there will be one or more additional aces in this group of four cards?

    McDowell claims that there are two distinct situations:
    Situation 1: The player remembers the suit of the tracked ace.
    Situation 2: The player does not remember the suit of the tracked ace.

    McDowell claims that the two situations yield different answers to the question, though I think the answers will be the same.

    I should point out that I just received some valuable answers to this question on bj21.com. I appreciate the responses I've gotten here as well, but I think the matter has pretty much been wrapped up. In any event, thanks again for the thoughtful, well-reasoned answers you've already provided.

    David Spence

    > Maybe the answer is (if I understand you correctly),
    > as simple as comparing these two situations:

    > A - You think that an ace is coming due to some sort
    > of ace tracking technique, usually you are 1 out of 5
    > to guess that in your own trials. Youa re 20%

    > B - You have been tracking the A of clubs and think it
    > is to come. Now you are 20% PLUS the probability of
    > one of the 3 aces coming.

    > I don't have the text here, so only you know if that
    > is what the author was trying to explain based on the
    > context.

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