I found these figures to be surprising, but I assume the math behind them is solid. I am interpreting the figures as saying "luck is xx% and skill is 100-xx% in contributing to your likelihood of experiencing real-life returns consistent with the theoretical return of the game after nn hands" - is that correct? If so, it's fascinating to me that the skill factor doesn't begin to exceed the luck factor until 800,000 hands have been played!
My peak play rate (which I know includes about one error per hour) is about 800 hands per hour, and so that's probably well over my lifetime play range, as I think I only play 4 hours a day, for two-four days a month, and even if it's several times that, it's still many lifetimes.
Even for a pro playing 40 hours a week, 50 weeks a year, and 1,000 hands per hour, which is 2,000,000 hands a year, getting the luck factor under 10% would take a full lifetime of play! Seems a little too tough to me, considering that there are reportedly many successful pro's, and that no one seems to know someone who plays perfectly and yet loses year after year after year, which according to these figures, should be happening to a significant percentage of such players.
As I'm curious what the luck/skill factor is for other games (e.g., blackjack with card-counting producing a 0.5% edge for the player or a 1.0% edge for the player), can you (or anyone) provide a short math tutorial on how to do the calculations that generate such a chart?
THANKS!
--BG
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5b. Re: Bob Dancer's LV Advisor Column - 26 MAR 2013
Edge can be positive or negative, one side or the other has
the edge, for example here's perfect 9/6 Jacks (a negative
edge game):at 1 hand, luck = 99.9%
at 100 hands, luck = 98.9%
at 1,000 hands, luck = 96.5%
at 2,000 hands, luck = 95.2%
at 10,000 hands, luck = 89.8%
at 100,000 hands, luck = 73.6%
at 200,000 hands, luck = 66.4%
at 400,000 hands, luck = 58.3%
at 800,000 hands, luck = 49.7%
at 2,000,000 hands, luck = 38.4%
at 5,000,000 hands, luck = 28.3%
at 10,000,000 hands, luck = 21.8%
at 100,000,000 hands, luck = 8.1%I guess you're postulating a player who plays Jacks so badly
that they have a -3.5% edge? That would look like this
(close to Bob's numbers):at 1 hand, luck = 99.2%
at 100 hands, luck = 92.7%
at 1,000 hands, luck = 80%
at 2,000 hands, luck = 73.8%
at 10,000 hands, luck = 55.8%
at 100,000 hands, luck = 28.5%
at 200,000 hands, luck = 22%
at 400,000 hands, luck = 16.6%
at 800,000 hands, luck = 12.4%
at 2,000,000 hands, luck = 8.2%
at 5,000,000 hands, luck = 5.3%
at 10,000,000 hands, luck = 3.8%
at 100,000,000 hands, luck = 1.2%