Backgammon is a game of luck and skill. To a casual observer, it may appear to be all luck. As one gains more skill and familiarity with the game, the depth of skill required to play well becomes increasingly clear. The luck is still there, though, much to our joy and frustration.
Sometimes one wants to strip away the luck. Is move A better than move B? Is player X stronger than player Y? A proper respect for the luck in the game is needed. Below, we will consider a method for cancelling most of the luck in backgammon, and will apply it to analyze a game between the computer programs Jellyfish and Snowie, both set on levels much stronger than I am.
I call the following equation the fundamental equation of games of luck and skill:
Final - Initial = Net Luck + Net Skill
Final refers to the final score. This might be +1 or -4 for a money game, or 100% mwc (match winning chances) or 0% mwc for a match. Initial refers to the starting equity or mwc of the situation considered. Net Luck, as outlined in "A Measure of Luck," has average value 0 on each roll. It also has average value 0 in each game or match. Net Skill is the difference in the total magnitude of the errors of the players when compared with technically perfect play.
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