Have you ever played Sudoku?
That nine by nine grid that will either leave you feeling like the second coming of Sherlock himself or else the Devil got bored of torturing people with Crosswords and has moved to a more numerical musing. Now there are some interesting little facts you learn while haunting the halls of Hell where Sudoku puzzles are rendered.
For instance, there are around 5.5 billion unique, non-equivalent possible solutions of Sudoku. And that you need at least 17 numbers filled in before you can figure out the remaining 32. How about that? 17. What a strange lower limit. Why? Why is that the minimum? Because that is the lowest mathematically provable number that will leave no doubt. If you are inhumanly smart enough to solve a Sudoku problem with only 17 clues, you can be certain that the ending will be a unique answer that could only result from those numbers in those specific locations. Anything less and you lose your certainty. You lose your unique, non-equivalencies - too many possible answers that will do the trick. How messed up is that? The fewer clues you have, the harder the puzzle is supposed to be... until you sneak below 17. Then your odds mysteriously improve. You get more than one possible answer. But Sudoku is not a game of odds. It is never inductive unless you've done something wrong. It's intended to be deductive at its easiest and threatens to be abductive at its hardest. But we'll get back to that.
Now let's scoot over to Cards. No particular game, just a standard deck of 52 playing cards. More ways for that deck to be ordered than I can muster in words. Suffice it to say 8 *10^67 (8 with 67 "0's" after it). It's a big number. Probability suggests that because of its sheer magnitude, the deck you have nearest to you (if it's well used) is in an order never seen before in human history. Imagine trying to pull off the exact same order with some other deck by shuffles and dumb luck... you get the idea - not happening.
Unlike Sudoku, the randomness of a deck is its charm. It's what allows for so many different games. And for magicians, it allows for so many possibilities to grab randomness by the horns and command it to do our bidding. But in nearly every case I've witnessed over three decades in magic, the routine was always deductive in process or inductive in premise. The magician uses linear pieces of information to come to a conclusion.
For example, say the deck you have is marked, and every card's identity is known to the magician at a glance. The deck may still be random, but it's no longer completely unknown. There are so many tricks, so many routines that are based on what you see in those markings. The card on top, on bottom, or cut to in the middle becomes the anchor, the key card, the clue to color, suit, value or stack. And this means that in most cases, the minimum number of clues required to reach a conclusion in your routine is usually 1—one card. In fact, the more cards you add to your routine with a marked deck, the more cards you must then keep track of as you go. And in a strange dichotomy to Sudoku, your "clues" will keep moving as the deck is shuffled, only making the situation harder.
Now, after all of that build-up, you might ask yourself; "Why would anyone compare Sudoku to Cards?". And here's my answer. An important question we in the magic community are asking is the same one every Sudoku master has asked to get to their elite prowess: What is the least amount of information I need to reach a unique and coherent conclusion? But, what's interesting is the disparate processes followed to reach the answer. We may pride ourselves in the magic world for needing fewer clues to master more variables ("1 Mark vs 52 Cards" as opposed to "17 clues vs 49 squares"). But our pride has blinded us to that mental reasoning that Sudoku masters live by, Abductive Reasoning. It's the type of reasoning that allows you to ask questions like "What isn't overtly expressed but must be true if everything else that is expressed is valid?" Or "What is the only possible answer that satisfies the current set of circumstances".
Inductive reasoning is probabilistic. Deductive reasoning is linear and causal. Abductive reasoning is the only one that is minimalist and destructive in nature, removing anything that cannot be true until the only thing left must be the truth.
The best marked deck workers I have ever met think in this way. They create routines that are based not on what they see, but on what they do not see. They create routines built on the idea that Magic can exists in the necessary if not overt implications of a given situation. They create decks that allow the magician to abduce what is missing by what is present (The card removed from the deck for example). And when they do this, they help us mere mortals to break out of our linear deductive routines and explore what it means to make magic as it happens. Like watching Rain Man do complex math in his head, these paragons make miracles in the moment because they don't fear the logic problems required to make the moment happen.
In fact, they live for the challenge.
For more information on this exquisite style of thinking: See the works of Justin Higham and Joe Barry on Impromptu Card Magic as well as Ondrej Psenicka on marking systems and their many expressions.
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