The Department of Computing Science and Maths at the University of Stirling
Rock, Paper Scissors Game

Rock

Paper

Scissors

Scores
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### Can a Computer Learn Game Strategy as it Plays?

The game of Rock, Paper, Scissors is very simple. Each player picks one of the three objects (usually by making the appropriate hand shape on a count of three!) and these rules are applied to see who has won that round:
• Paper wraps (beats) Rock
• Scissors cut (beat) Paper
• Rock blunts (beats) Scissors
The challenge of the game is to guess what your opponent will choose and pick the appropriate object to beat them.

People find it quite hard to pick a sequence of perfectly random choices, so any pattern that a player develops could be learned by the opponent and used to win the game. That is what happens in this example. As you play, the computer learns the pattern of objects that you are most likely to pick.

How Does it Work?
The computer keeps track of the conditional probabilities of you picking each of the three objects given the object you picked last. The computer always picks the object that beats the one that it thinks you are most likely to choose. Although it knows what you have actually picked (you press one of the buttons to make your choice), it is honest and doesn't cheat!

You can observe the computer learning by picking a strategy and sticking to it for a while. Here are a few things to try:

1. Pick Rock, then Paper, then Scissors, then Rock again and keep that pattern up. See how quickly the computer learns to beat you every time?
2. Having done that a few times, change strategy and pick Paper 5 times in a row. See how the computer spots your change of strategy and alters its play?
3. Pick any strategy of your own and see if the computer can spot the pattern.
4. See if you can be perfectly random in your choices and beat the computer.
There is a worksheet on this subject covering machine learning with probabilities to download here.