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## 'Ante Up' printed from http://nrich.maths.org/

A computer is programmed to produce a long string of Hs and Ts
which are printed out onto a piece of ticker tape which has been
divided into square boxes.

Each time a button is pressed the tape advances by one 'unit' and
the bottom box cut off, so there are always three boxes visible in
a line. The number of units of paper remaining inside the machine
is indicated in the circle.

Alan Turing, the great code breaker, and I are each given
a slip which we each mark with Hs and Ts. Whoever sees their
sequence emerge first from the machine wins. I choose HTT and
Turing chooses HHT as shown in the diagram.

If the machine configuration is as shown in the diagram at the
moment, who is more likely to win: Turing or me?

Suppose we were going to play again and Turing chooses the sequence
THT. Being a bit of a spy, I find this information out before I
choose my sequence. Before we play we are going to reload the
machine so that it contains 6 units of paper. Can I choose a
sequence which is more likely to win than Turing's?

Difficult Extension: After
playing with these choices many times, Turing is fed up with losing
and wants to choose TTH. He also wants to load the machine with
infinitely many units of paper. Can I choose a sequence which
is more likely to beat Turing's new choice?
You can experiment with our Turing Machine interactivity if you
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