After the trick he explained how he had done it. It was very clever and revolved around the test subjects instinct to try and take the least obvious option, and the first person was coerced by beckoning with one hand to subconsciously make them choose the other. I think the next 5 people choosing an order exactly the same as your one, LRRLRL. He also uses this method to play rock paper scissors, winning time after time. He is very much a master of the bluff, double bluff, triple bluff, etc!

]]>Here’s how you can win: start reciting 0,0,0,… until eventually the guy guesses “non-random” (he must eventually since, if you kept this up forever, that would clearly not be a random sequence, and the guy is perfectly rational). Now you have a finite string of 0’s which makes him guess “non-random”. To that, start appending numbers randomly and reciting them, until eventually your opponent guesses “random”. He must eventually, because if the process continued forever, the sequence really would be random. So now you have a sequence of finitely many zeros followed by some random numbers, which forces the enemy to eventually guess non-random then later switch to guessing random. Now to this sequence start appending and announcing zero’s. Eventually he must switch his guess to “non-random”… and so on forever. In this way you force him to change his mind infinitely often.

(What if you’re not allowed to make your sequence up as you go, but must fix it in advance? Then you no longer have a winning strategy, but neither does your opponent. Because if your opponent had a winning strategy, you could incorporate that strategy into the sequence you initially choose, and replicate the above situation.)

For more on this kind of thing, see: https://www.xamuel.com/guessability/

]]>You are absolutely right. I am even planning to discuss that in my next piece on the subject. Having said that, I find it very useful and educational to throw students off from time to time.

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