Hypergammon Fun
Tom Keith, 2018

The game of hypergammon is a simplified version of backgammon. It uses all the same rules as backgammon, and the same board. The only difference is that hypergammon starts with just 3 checkers per side instead of 15.

The games are shorter, but hypergammon is still a fascinating game. One important difference between hypergammon and backgammon is that hypergammon has been solved. Computers can play perfect hypergammon. That means we can answer many questions about hypergammon that we can’t answer about backgammon.

This is a series of 12 articles originally posted on the BGOnline Forums that explore the strange properties hypergammon.

1. Hypergammon
• Backgammon Funfair
• Hypergammon
• Returning to the Start

2. Counting Positions
• Returning to the Start
• Number of Different Hypergammon Positions
• “Legal” versus “Reachable”
• How Many Legal Positions Are Reachable?

3. a. Counting Positions Mathematically
• Factorials
• Combinations
• Arrangements
• Bearoff Positions
• Arranging Three Black Checkers
• Counting Hypergammon Positions

4. Unreachable Positions
• Unreachable Positions in Backgammon
• Unreachable Positions in Hypergammon
• How Many Positions are Reachable?
• A Hard-to-Reach Position
• Postscript

5. Hard-To-Reach Positions
• Perfect Backgammon
• Creating a Hypergammon Bot
• Dealing with Cycles
• Some Questions

6. Luck and Skill
• Largest Joker
• Largest Anti-Joker
• Biggest Checker Play Error
• Gammon Rate

7. Opening Equities
• Gammon Rate
• Almost Gin

8. Biggest Turnaround
• Wastage
• High Wastage
• Low Wastage
• Wastage in Hypergammon

9. Wastage
• Wastage with One Checker
• Wastage with Two Checkers
• Wastage with Three Checkers
• What Is Contact?

10. Contact
• Overlapping Contact
• No Possible Contact
• No Practical Contact
• No Significant Contact
• Block-Only Contact
• Which Positions Have Contact?
• Measuring Contact

11. Contact Wastage
• Bearoff Wastage
• Contact Wastage
• Block Wastage
• Hit Wastage
• Defining Best Play
• Computing Wastage
• Wastage in Hypergammon

12. Measuring Contact
• Improving Backgammon Bots
• Wastage
• Holding Game Example
• Blitz Example
• Measuring Contact
• Another Way to Measure Contact
• Most Contact
• Least Contact
• How Long Does It Last?

13. Length of a Game
• Shortest Possible Game
• Longest Possible Game
• Average Length Game
• Median Length Game
• Most Common Length Game
• The Five M’s

 Next Hyper Fun 01