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?"
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.