Re: Experiment to show doubling cube magnifies luck.

[Timothy Y. Chow]

MK wrote:
Before running my experiments, I asked readers whether a weak player 
would do better against a strong player, in long enough cubeless or 
cubeful sessions. They all predicted that he would do better cubeless, 
(based on the "intuitive" fallacy that cube promotes skill), but the 
results were to the contrary.

These experiments are interesting, and I'm sure they violate some people's 
intuitions. Not too long ago, two of my colleagues were discussing more or 
less this same topic. One of them thought that their chances against a 
stronger player would be reduced if the cube were in play. The other was 
less sure, pointing out that the cube increases variance, and higher 
variance (as a general principle) often favors the weaker player.

The slogan "cube magnifies luck" is catchy but can cause confusion because 
there are many different ways to interpret it. MK gives one 
interpretation:

Set one player to, let's say, one ply and the other to three ply. Let 
them play, let's say, 10,000 cubeless money/point games and write down 
the ratio of points won by each side.

The ratio of points is one measure, but another measure is the difference 
in points. For example, you can imagine two players of unequal skill 
playing money-game backgammon for five hours. We expect the stronger 
player to come out ahead, but there are different cube-releated questions 
one can ask; e.g.,

1. Will the stronger player expect to earn more money during the five-hour 
session if the cube is in play, or if there is no cube?

2. Will the weaker player's probability of coming out ahead increase or 
decrease if the cube is in play?

If someone is asked whether the weaker player would "do better" with the 
cube, they might have something like Question 1 in mind, but Question 1 is 
very different from Quesiton 2, and Question 2 might be closer to the 
question of whether the "cube magnifies luck."

In short, it has always been obvious that the cube magnifies *variance*, 
but whether this means that the "cube magnifies luck" or whether the 
"weaker player does better" depends on exactly what question is being 
asked.

Tim