# Combinatorial Games

Combinatorial Games are a group of games that don’t involve any elements of chance such as dice or cards. They are based purely on the skill of the player. As such they are really good for analysing best moves and games that have been played for mathematical thinking.

In Nim, you can analyse the patterns of numbers. It’s the numbers that you will use to decide what to do each move and so you’ll need to be able to notice something about them in order to play well.

In yucky choccy, the patterns that can help you win are to do with shape and the number of rows and columns. You can experiment with smaller bars to investigate the best shapes to help you win.

One of the key things to notice about combinatorial games is that each move creates a new game and may change the advantages that the players have. This is especially the case in hackenbush where games can be given values based on the advantage that one player has. These values can even be analysed algebraically and take on fractional values!

It is even possible to combine different games and add and subtract games to work out who has a competitive advantage.

Some related topics:

• Counting and Arithmetic
• Edges and Vertices
• Grids (Rows and Columns)
• Combinations
• Algebra

To try this activity: