# Backgammon

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How much of backgammon is luck and how much is skill? If I said it was 60 per cent skill and 40 per cent luck, what would I mean? If you said it was half skill, half luck, how could we prove who was right? The answer is we couldn't. Let's look at the problem from a different perspective and compare the skill and chance factors involced in different games.

Chess has a formal rating system ranging from around 2800 for the world champion to zero for a beginner. The scale is designed so that a 200-point difference between two players means that the higher-rated would expect to score 70-75 per cent against thelower-rated over a series of games. Now consider this experiment: (i) Take the best player in the world. Call him Player 1.

(ii) Find someone - Player 2 - against whom Player 1 makes a score of 70-75 percent.

(iii) Call the difference between Players 1 and 2 one skill differential.

(iv) Continue the process with Players 3, 4, 5, 6 ... each losing 70-75 per cent of the time against his predecessor.

(v) Continue until the chain has reached a total beginner.

(vi) Count the number of skill differentials separating top to bottom. This is the complexity number of the game.

We can apply this process to any game, after some thought as to what consitutes a meaningful contest. In chess it may be a single tournament game, in Scrabble a best-of-five series and in backgammon a 25-point match.

The table below is a rough chart of how various games rank on the complexity scale: Complexity Numbers Go 40

Chess 14

Scrabble 10

Poker 10

Backgammon 8

Draughts 8

Blackjack 2

Craps 0.001

Lotteries 0.0000001

Roulette 0

It resolves at one stroke all the muddled thinking about luck, skill, games of skill and games of chance. Any game demanding no skill falls automatically to zero. For all other games, the relevant issue is the interplay of skill, chance and complexity.

I am indebted to Bill Robertie, twice world backgammon champion, for the research for this article. I do not have a figure for bridge - perhaps a reader may care to submit an opinion.

This is the first of an occasional series on backgammon by Chris Bray which will be appearing on this page at approximately monthly intervals.