Nontransitive game

Imagine you have three different toys – A, B, and C – and you want to find out which one is the best. To help you, let's play a game!

Each toy can either win or lose against another toy, and we'll keep score of how many times each toy wins. We'll start with Toy A playing against Toy B. Toy A beats Toy B and gets one point. Next, Toy B plays against Toy C, and Toy B beats Toy C and gets one point. Now, let's have Toy C play against Toy A. Surprisingly, Toy C beats Toy A and gets one point.

So let's look at the scorecard now:

- Toy A beat Toy B, so Toy A has one point.
- Toy B beat Toy C, so Toy B has one point.
- Toy C beat Toy A, so Toy C has one point.

Now, let's play the game again, but this time we'll start with Toy C versus Toy B. Toy C beats Toy B, and gets one point. Next, Toy B plays against Toy A, and Toy B beats Toy A, getting one point. Finally, Toy A plays against Toy C, but you already know what happens – Toy C beats Toy A again, getting one point.

So let's check the scorecard again:

- Toy A beat Toy B, so Toy A has one point.
- Toy B beat Toy C, so Toy B has one point.
- Toy C beat Toy A twice, so Toy C has two points.

This means that Toy C is the best toy overall, even though Toy A previously won against Toy B, and Toy B won against Toy C. The game is called a nontransitive game, because the relationship between the toys (A beats B, B beats C, and C beats A) isn't transitive like in normal games.

In a nontransitive game, the best choice depends on the situation and the options available. Always keep an open mind and don't assume that just because something won once, it will always win.