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Learn A Derren Trick:
Heads Or Tails
It seems impossible to predict whether a coin will come up heads or tails in a fair game of coin flipping. But in 1969 mathematician Walter Penney devised a seemingly impossible coin tossing bet in which the odds were skewed in your favour.
It works like this. You ask someone to give you a sequence of three heads (H) or tails (T). For instance they might choose HHH or TTT. More likely it will be a combination of heads and tails as in HHT. You also choose a sequence of heads and tails. For example, THH.
The bet is that your sequence will show up first if a coin is tossed over and over again, the upper side being noted each time.
It seems a fair bet. In a fair game it is impossible to predict which side of a coin will land uppermost. This might lead you to believe that one sequence is as good as another. But this isn’t true. The reality is that your chosen sequence is more likely to show up earlier than your opponent’s sequence. That’s because you use a secret formula to decide which sequence you will bet on.
Mathematicians call this a non-transitive game. In effect it means that no matter which sequence your opponent picks you can always pick a better one. It is like the game of rock, scissors, paper. If you knew what your opponent chose, you could always beat them.
There is an easy to remember formula for deciding which sequence you choose.
You ask the other person to make their choice first. This isn’t courtesy, it’s vital. From what he says, you work out what you’ll say. You do this by taking the middle one of his three, reversing it and putting it at the start. So if he says HHH, you say THH, and ignore the last one.
If the opponent chooses TTT, you choose HTT. If the opponent chooses HTT, you choose HHT. If they choose HTH, you choose HHH.
There are only eight possible sequences, so if you can’t be bothered to work them out, write them down on a hidden cue card. On average your sequence will win two thirds of the time. Those are great odds if you play this game several times.
