@Magister:
That means good luck is MORE frequent than bad luck - but the rare bad luck can be much farther from the average than the good cases.
Good post!
You are close to the position of the paper, but I think we have to tighten up the terms.
When you write “good luck is MORE frequent than bad luck”, I’d argue that isn’t true if you take the median outcome as your starting point. By definition, the median is the spot where the luck is neutral - half the outcomes are same/better, half the outcomes are same/worse.
The point is that the magnitude of the good luck is much smaller than the magnitude of the bad luck, so equally “lucky” dice, good or bad, will have a much bigger negative weight. You don’t get more frequent unlucky dice, but the unlucky dice are more harmful than the good lucky dice.
A 90th percentile good outcome could net you +$3 from the median, while a 10th percentile bad outcome could net you -$11 from the median. Those are outcomes of equal luck in terms of frequency, but the magnitude of deviation is quite different.
There is no psychological bias in this negative finding (though the phenomenon you mention is real and significant in its own right, and often overlooked in post-game dissections). The point of the paper is that net bad outcomes are not imaginary; good players actually should get the shaft!
An objective observer will find that standard, perfectly normed dice will result in a significant net loss from the median outcomes over the course of a game (or within 10,000 runs of a battle).
This paper looked at the individual fights. The next paper will measure the magnitude over the course of a game.
Peace