Tim wrote: > MK wrote:
> ..... The other was less sure, pointing out that the cube > increases variance, and higher variance (as a general > principle) often favors the weaker player. Since "skill" can't favor the weaker player, it can only be "luck" that can favor him, which is the product of what you call "variance". > The slogan "cube magnifies luck" is catchy but can > cause confusion because there are many different > ways to interpret it. I agree that it's difficult to find the right words for it. What I mean is that the "luck to skill ratio" in cubeful games is higher (for both players). > The ratio of points is one measure, but another measure > is the difference in points. I guess you are getting at comparing players in terms of "ppg" which doesn't work in comparing performances in cubeful vs cubeless games. > 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? Obviously more in cubeful games because the "average points per game" (in the true meaning of the words) is higher in cubeful games. This is irrelevant to the subject of whether the cube "promotes luck" (a better alternative to "magnifies luck"?) and thus "favors the weaker player". > 2. Will the weaker player's probability of coming out > ahead increase or decrease if the cube is in play? Yes, just replace "probability" with "ratio" of points won and we may be talking about the same thing, which is to compare one ratio with another ratio. The reason for this is that a player's performance (doing better) is based on his luck to skill ratio in the equation "skill + luck = 1". Let's say that our above two players' ratios are: Stronger Player-A = .75 skill + .25 luck = 1 Weaker Player-B = .25 skill + .75 luck = 1 If after playing 100 cubeless games, the combined total points won by both players is 200, we would expect that Player-A will have won 150 and Player-B 50 points (if we assume that luck will have evened out by that time). Using this as a base-line for our comparison, after playing 100 cubeful games, if the combined total points won by both players is 400, we would expect that: 1- Both players will win the same ratio of points (i.e. 300 and 100 respectively) if the cube does neither promote luck nor skill. 2- Player-A will win more than 300 if cube promotes skill. 3- Player-B will win more than 100 if cube promotes luck. We can say this because skill of the players won't vary (not decisively anyway) after hundreds or even thousands of games but their luck will vary between cubeful and cubeless games. Let's say that cube "injects" 20% luck into the game (equally both players). Their above ratios will become: Stronger Player-A = .75 skill + .25 + .05 luck = 1.05 Weaker Player-B = .25 skill + .75 + .25 luck = 1.15 As you had stated yourself many times, it's the weaker player who needs more luck to do better against the stronger player. Most of the additional luck that the stronger player receives will go to waste, so to speak, while the weaker player will benefit more from added luck and win more (do better) against stronger player. Thus, if we calculate the ratios backwards after the 100 cubeful games (assuming that luck has evened out between the players by then) and see that Player-B won more than .25, we can conclude that cube magnifies luck. And based on the difference between the ratios, we can further calculate by what percentage the cube magnifies luck, which will surely be much less than in my above exaggerated example but will still be clearly observable. I will welcome any arguments and/or empirical test results to the contrary. MK PS: I tried to use various different words as possibly better alternatives to "magnify" (which I still prefer) hoping that they may help Tim and other understand my arguments better.
