# Comparing Games of Skill and Chance - Backgammon Blog

## Comparing Games of Skill and Chance

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Have you ever wondered about the delicate balance between skill and luck in various games? How do different games measure up against each other when it comes to the interplay of skill and chance? Let's dive into these intriguing questions in a more approachable manner.

### Question 1: The Skill-Luck Conundrum in Backgammon

The first question that often comes up is this: What's the ratio of skill to luck in the game of backgammon? However, this question is not as straightforward as it seems. Backgammon is a fascinating blend of both elements, and untangling them is like trying to separate the ingredients of a perfectly mixed smoothie.

Imagine trying to assign specific percentages, say 80% luck and 20% skill, to backgammon. But what do these percentages truly represent? If someone else claims it's 90% luck and 10% skill, could we ever devise an experiment to definitively prove one view over the other? It's quite the puzzler.

While a clear-cut ratio of luck and skill remains elusive in backgammon, there's another way we can explore its dynamics in comparison to other games. Let's proceed to explore this fascinating avenue.

### Question 2: Comparing Backgammon Across the Spectrum

Now, let's delve into our second question: How does backgammon fare when matched against other games in terms of skill and luck balance?

To tackle this question, we'll borrow a method from the world of chess, a game that's been analyzed and played for centuries. Chess aficionados owe thanks to Arpad Elo, a brilliant mind from Wisconsin, for crafting a rating system that ranges from approximately 2800 (masterful) down to nearly zero (novice). In this system, a 200-point gap between players implies a 75% chance of the higher-rated player prevailing.

Here's an Interesting Experiment:

1. Choose the world's top player, let's call them "Player 1". (For chess, it's the likes of Magnus Carlsen.)
2. Identify a player, "Player 2", who is beaten by Player 1 approximately 75% of the time.
3. The difference in skill between Player 1 and Player 2 represents one "skill differential."
4. Find another player, "Player 3", who is beaten by Player 2 about 75% of the time. This yields another skill differential.
5. Continue this pattern until you reach a total beginner.
6. Count the skill differentials – this yields the game's complexity number.

For chess, this complexity number hovers around 14. In essence, it quantifies the game's difficulty – how many steps you need to ascend to move from novice to grandmaster.

### Applying the Concept to Various Games

This approach isn't exclusive to chess; it can be applied to any game. Picture a contest spanning around four to five hours, akin to a typical chess match. For backgammon, a 25-point match fits the bill – similar in duration to a chess game. By examining backgammon rating systems and extrapolating for beginners, we deduce a complexity number of roughly 8 for backgammon.

When considering other games, we must envision a contest of similar duration. In poker, it might be a head-to-head match. For Scrabble, a best-of-five series could work. Here's an estimated ranking of popular games based on their complexity numbers (remember, these are rough estimates based on available information):

• Go: 40
• Chess: 14
• Scrabble: 10
• Backgammon: 8
• No-limit hold'em poker: 8
• Checkers: 8

While games like Gin Rummy and Othello certainly have their merits, I don't have precise complexity numbers for them. Also, as wonderful as bridge is, it doesn't fit the criteria of a two-player game for this comparison.

### Deciphering the Puzzle of Skill and Chance

In essence, this approach cuts through the haze of uncertainty regarding luck, skill, and the diverse spectrum of games. Games purely reliant on luck, such as roulette, naturally score a zero on this complexity scale. For other games, it's not merely a dichotomy of luck versus skill; it's the intricate interplay of skill, chance, and overall complexity that defines each game.

Even in the case of profoundly intricate games like chess and go, there lies a threshold to human comprehension. The complexity number provides a tangible measurement of the journey required to master a game, unveiling the captivating layers that lie beneath the surface of every gaming experience.

So, as you embark on your next gaming adventure – whether it's pondering a chess move or strategizing in backgammon – remember that it's not merely a question of luck or skill. Instead, it's the harmonious fusion of these elements that crafts an engaging, thought-provoking, and captivating experience.