Is gambling more Luck then Skill in the longterm?

[Sandra Bullett]

Speaking as an arm-chair statistician, "long-term" means, <u>by definition</u>, a large enough sample that luck has been ELIMINATED (or, more practically, reduced in effect below the level of precision you want to work at).

Therefore, by definition, long-term poker has 0% (or insignificant) luck.

Simple examples, let's say a game had a +$10/hour EV, with $100/hour standard deviation (these are vaguely accurate values for a poker game, but you can get your own values from Poker Tracker).

Your earning rate after 1 hour is dominated by luck. Expected earnings +$10, but 2/3rds the time will be up to /- $100, ie. 2/3rds the time you can get a result up to 10x away from your expectation. More importantly, std dev is +/- $100 PER HOUR (and hugely obscures what your real earning rate is)

Play for 100 hours and you expect to win $1,000, but 2/3rds the time will be +/- $1,000 (std dev [=luck] is now only 1x your EV). The effect of Std Dev on your earning rate is now 2/3rds likely to be only +/- $10/hour.

Play for 10,000 hours and EV= +$100,000 and Std Dev = $10,000. The effect of Std Dev on your earning rate is now 2/3rds likely to be only +/- ONE DOLLAR/hour.

If you are only interested in knowing your earning rate to within, roughly, $1/hour, then the definition of "long-term" for your needs is 10,000 hours. After this period of time you have eliminated luck's effect on your EV estimation. Your calculated EV is (to within $1) entirely due to skill.

If you're really anal, and want less than $1 error in your EV, increase the long-term sample size until the desired accuracy is achieved. (It takes 1,000,000 hours to get down to Std Dev having a +/- $0.10 effect on your hourly EV. I hope you're not that anal, as playing 40 hours per week for 50 weeks per year, 1,000,000 hours takes 500 years).