[pdurrant]

Here's a Simple Probability Puzzle, taken from http://toshuo.com/2007/a-simple-probability-puzzle/

You are monitoring an automatic coin flipping machine. It flips a coins every second, and you can see whether the coin lands show Heads (H) or Tails (T). You will be looking for non-overlapping sequences of three results. For instance, if you were looking for HTH, the sequence THTHTHHHTHTT would have only two HTH sequences in it (bold) THTHTHHHTHTT.

Your first task is to keep watch until 10 sequences of THT have appeared. After you've seen the 10th THT sequence, you note the total number of coin tosses you've observed while monitoring for THT

Once you've spotted 10 sequences of THT, you start monitoring again with the next coin toss after the last T of your tenth THT sequence. This time you're looking for sequences of THH. Again, after you've seen the 10th THH sequence, you note the total number of coin tosses you've observed while monitoring for THH.

The coin tossing machine is fair (H 50%, T 50%) and random. You are vigilant, and do not make any mistakes in your monitoring of the coin tosses.

On average, will the number of coin tosses you observe while monitoring for THT be greater, the same or less than the number of coins tosses you observe while monitoring for THH?

Please vote!

You may also give an argument for your vote in comment, in

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