Penney's Game

A blue, black and red exhibiti with a round port hole at the top and a red monitor in front.
A blue, black and red exhibiti with a round port hole at the top and a red monitor in front.

In a game of chance, selecting whether to take the first turn, or the second turn can improve the odds of winning.

How it works

Predict via touch screen the order or sequence in which three coloured balls will be sampled from a barrel, then the exhibit's computer will make a sequence prediction and display it on the screen.

Once both sets of predictions are locked in, coloured balls are physically (and randomly) drawn from the barrel and recorded on the screen until the first matching sequence of coloured balls is drawn (and you, or the computer wins).

The calculated odds of you or the computer winning is also calculated and displayed on the screen.

Things to try or ask around the exhibit

Does it matter whether you go first or second when selecting your predicted sequence of coloured balls?

Background

Penney’s Game challenges you to consider whether it’s best to go first or second in a game of chance. Although each of the eight possible sequences of three balls is equally likely, whoever chooses first (Player 1) is more likely to lose.

Player 2 (the computer) knows what Player 1 (you) chose. Player 2 can use that information to increase their chance of winning. For example, Player 1 might choose ‘red, red, red’ (RRR) balls being drawn from the barrel. This sequence will occur with the first three balls one eighth of the time. Player 1 will win and there isn’t anything Player 2 can do about it. However, it only occurs one eighth of the time, which means it doesn’t occur seven eighths of the time. The only way it can not be RRR is if a blue ball gets sampled.