Probabilistic games

6.4 Penney’s game

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Transcript: Penney's game

Individual activity: Try it

As you saw in the video, the game we want you to try is Penney’s game, named after Walter Penney, who discovered it in 1969.

Grab a friend and a coin and have a go. If either one is not easily to hand try this applet.

To recap, two players choose a set of three-coin tosses, for example HHH, or THH, etc.

Once each player has chosen their set of three, a coin is continuously tossed until the coin tosses produce one of the sequences in consecutive throws. For clarity let us consider an new example:

Player 1 chooses HHH.

Player 2 chooses THH.

  • The coin is flipped and we get H.
  • It is flipped again and we get a T so we have HT.
  • We keep flipping and we will end up with some sequence like: HTTTTHTHH

In this case player 2 wins, as the first sequence to be thrown consecutively was THH.

Pause and reflect

Once you have finished playing, in your blog or elsewhere, jot down a few comments to each of these questions:

  1. Is the winner of this game completely random?
  2. If not is there a definite strategy to always win?
  3. Is there a strategy to be more likely to win?
  4. Does it matter if you go first or second?
  5. Are some sets of three more likely to come up than others?