fizzbuzz is a game I first learnt at primary school, aged about 8. It was introduced as an aid to learning multiplication tables. In essence, it is a simple counting game where specific numbers and the multiples thereof are substituted with the words fizz and buzz. Success is reliant on a knowledge of the multiplication tables of the numbers used.

The Basics

First, decide which numbers (and their multiples) will be substituted with fizz and buzz. For this example I will use three and five respectively, but any others can be used.
Counting from one to ten would run like this:

one, two, fizz, four, buzz, fizz, seven, eight, fizz, buzz.

The game becomes more complicated when the players begin to reach numbers that are divisible by both of the numbers represented by fizz and buzz. When this occurs, the player must say fizzbuzz.

Continuing on from the buzz that represented ten, counting to twenty would run like this:

eleven, fizz, thirteen, fourteen, fizzbuzz, sixteen, seventeen, fizz, nineteen, buzz.

The game continues until one of the players makes a mistake. At that point, the player who made the mistake is 'out', and play continues without them, until there is one player remaining. This player is the winner.

Variations

As well as substituting a number and its multiples for fizz or buzz, the game can also be played applying this rule to numbers that contain the appropriate number without being multiples.

If you apply this rule to the ten numbers from ten to twenty, it would run thus:

eleven, fizz, fizz, fourteen, fizzbuzz, sixteen, seventeen, fizz, nineteen, buzz.

This can frequently lead to heightened confusion, or heightened fun, depending on your viewpoint.

Other Uses

The main reason I have played this game in the several years since learning my multiplication tables has been as a drinking game. The main difference is that when a mistake is made a drink is taken, but the player is not 'out'.