ACAAN

Craig Petty’s Atomic Deck released recently and there’s lots of hype and complaints. The product is an ACAAN effect. A big negative that people identified with the release is that it requires a phone. The flagship routine requires the spectator to go to a specific website to enter their choice of card and number. The website will then spit out a “percentage” which the magician needs complete the effect.

If you’re willing to require a phone, there’s a much easier way to achieve an ACAAN. Instead of having the website be some strange page that gives statistics about the likelihood of card-number combos, just have it be a random generator site. You can use the excuse that human’s are bad at generating true randomness. The spectator will be invited to go to the site and press a button that randomly chooses a card. The spectator is free to press this button as much as they like. Then once satisfied, the spectator presses a different button to generate a number. The spectator can even generate multiple numbers. The secret of course being that the numbers will exactly match the index in one of the stacks you’ve prepared.

The ACAAN effect has a \(\frac{1}{52}\) chance of happening by coincidence. Some magicians try to hype up the effect by emphasizing the fact that there are \(52\) possible cards and \(52\) possible positions and imply the probability is \(\frac{1}{52} \cdot \frac{1}{52} = \frac{1}{2704}\) but this isn’t correct.

To see why, let’s start by considering randomly chosen card \(C\) and randomly chosen position \(i\). Assuming a full, standard deck and valid card and index choices, the chance of card \(C\) being somewhere in the deck is exactly \(1\). The card must be at one of the 52 locations. That is