Three Predictions - Futility Closet

In Season 8, Episode 7 of Penn & Teller’s magic competition show Fool Us, magician Hans Petter Secker appears to predict the outcome of three successive rounds of rock-paper-scissors, though Secker oversees the game remotely from Norway and the players are invited to exchange items before each round. How is this accomplished?

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Reader Tom Ace explains: No matter which object you hold (rock, paper, or scissors), your object beats one of the other two and loses to one of the other two. The performer’s first prediction names one result (Teller beats Penn), but the other two results follow from that prediction: Teller’s object loses to Alyson’s, and Penn’s object beats Alyson’s. In the second round, the performer names two results (Alyson beats Teller and Penn beats Alyson), but this is no more of a feat than naming one result. It’s a cute bit of showmanship that it seems like he’s predicting more with each round. There are six ways to permute three objects. But in terms of who beats who, there are only two possible states: Penn beats Teller; Teller beats Alyson; Alyson beats Penn Teller beats Penn; Alyson beats Teller; Penn beats Alyson A swap — any swap — inverts the state. An even number of swaps preserves the state. The performer controlled the initial state by the order the objects were placed in the box. He asked Penn to grab the object on top (rock), Teller to grab the next one (scissors), Alyson to grab the remaining object (paper). That’s an instance of state 1 as described above. After one swap, we have state 2. It doesn’t matter which pair of people swapped. For the next round, two more swaps maintains state 2. For the final round, three more swaps returns to state 1. Tom writes, “To most observers, the later rounds seem like harder feats of prediction because the number of swaps increases with each round — but it’s all simple.” (Thanks, Tom.)

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Reader Tom Ace explains:

No matter which object you hold (rock, paper, or scissors), your object beats one of the other two and loses to one of the other two.

The performer’s first prediction names one result (Teller beats Penn), but the other two results follow from that prediction: Teller’s object loses to Alyson’s, and Penn’s object beats Alyson’s.

In the second round, the performer names two results (Alyson beats Teller and Penn beats Alyson), but this is no more of a feat than naming one result. It’s a cute bit of showmanship that it seems like he’s predicting more with each round.

There are six ways to permute three objects. But in terms of who beats who, there are only two possible states:

Penn beats Teller; Teller beats Alyson; Alyson beats Penn
Teller beats Penn; Alyson beats Teller; Penn beats Alyson

A swap — any swap — inverts the state. An even number of swaps preserves the state.

The performer controlled the initial state by the order the objects were placed in the box. He asked Penn to grab the object on top (rock), Teller to grab the next one (scissors), Alyson to grab the remaining object (paper). That’s an instance of state 1 as described above.

After one swap, we have state 2. It doesn’t matter which pair of people swapped. For the next round, two more swaps maintains state 2. For the final round, three more swaps returns to state 1.

Tom writes, “To most observers, the later rounds seem like harder feats of prediction because the number of swaps increases with each round — but it’s all simple.”

(Thanks, Tom.)