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Difficulty of plays metric

Posted By: Schigolch
Date: Wednesday, 30 March 2016, at 10:18 p.m.

In Response To: Difficulty of plays metric (Bob Koca)

I'd love to measure the difficulty of a backgammon game! When I tried to identify with a statistical model the factors that have an influence on victory, the difficulty of a game was of course a candidate, after condidering skill and luck. Clearly the difficulty had an influence, albeit less than skill and luck. Having no better indicator, I identified a move to be more difficult when the equity difference between the first 2, 3, 4 possible plays of a roll was bigger then for another roll, and summed those equity differences up to identify a more difficult game. I concluded that: (1) In general, an easy game is when you have a choice among plays that are almost equal in equity. (2) Measured that way, a difficult match would rather end with a defeat, and an easy one rather with a win - all else being equal (3) However, to shed some doubt on the outcome, while the correlation exists, I can't be sure I've measured indeed difficulty. We all know some games appear to be easy because we like the choices and others are not because we don't like the choices we're facing. So I'd like to have an objective measure for "difficulty of game", but know I haven't made more then the first step.

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