Magic & Math with Cards

Lecture 11 · Performance

Royal Hummer

A royal flush emerges

Video in production

This lecture is still face down. Its script is written; filming and animation are under way.

Meanwhile, play the trick

What you will learn

Perform Royal Hummer and explain how orientation encodes royal-flush membership through even-block turnovers.

The trick in this lecture Royal Hummer Twelve shuffled cards, nine of your leave-or-turn choices, and a royal flush comes out face down. Play the trick

Before this lecture

In this lecture

An outline of the lecture, scene by scene, with the statements that appear on screen. It follows the draft script, so details may change in production.

  1. Establish the packet and code its starting directions

    At the table
    • 12 cards, including a spade royal flush
    • Starting orientation arrangement
    • LEAVE or TURN the whole group

  2. Collect all legal spectator choices in two block passes

    At the table
    • Six choices with pairs
    • Three choices with groups of four
    • Keep each group intact

  3. Perform alternate deal and orientation-normalized reveal

    At the table
    • Turn either whole pile
    • Five hidden cards
    • 10♠ J♠ Q♠ K♠ A♠

  4. Expose all four preparation cases

    • Neither royal: UP, DOWN
    • First only: DOWN, DOWN
    • Second only: UP, UP
    • Both royal: DOWN, UP

  5. Prove preservation under even-block choices

    • p: odd 1, even 0
    • f: up 1, down 0; t: royal 1, filler 0
    • f ⊕ p = t
    • Even-block turnover toggles f AND p

  6. Decode by alternate deal and handle both final choices

    • LEFT receives original odd positions
    • RIGHT receives original even positions
    • Turn RIGHT → royals down
    • Turn LEFT → royals up; turn whole packet once

  7. Separate necessary preparation from flexible performance choices

    • Freedom: every offered block choice
    • Constraint: correct orientation encoding
    • One illegal filler flip → one extra exception

  8. Specify companion with both branches and an error diagnosis

    • Prepare → mix even blocks → alternate deal → decode
    • Exactly five royal cards face down
    • Find the first incorrect membership bit

Companion interactive

Reveal exactly the five spade royal-flush cards face down after all permitted choices.

The trick page is this lecture’s companion: be the spectator, lift the curtain to step through why it works, try the challenge, then learn the handling.

Open Royal Hummer

Sources

How these sources were used
  • Persi Diaconis and Ron Graham, Magical Mathematics: Royal Hummer credited to Steve Freeman. This script uses the book’s four-case pair preparation with an explicit twelve-card packet; the alternative two-hand preparation is not used.