For some uncontrollable reason I feel I must add to this.
-The most unlikely event in any random situation will be the statistically perfect event.
-At any 9 handed poker table, over time, you will get dealt the best hand 1/9th of the time (11.111111111111111~%). It is too easy to think that you will get cards once every 9 hands. Statistically statistics can't really even take effect until the sample numbers are much larger than 9 hands, or 90, or really even 900 samples. Though at 900 some trends can begin to appear.
-Against one opponent poker hand odds will stand up over time.
-Everyone tends to ignores or forgets the 'schooling' effect. If against a single opponent you are favored, or against any of many opponents you are favored, if you put all of those opponents together against you, you fall below a 50% expectancy. Think total outs against you.
This being said, OP's original thought about a consistent 51-49 'luck factor' edge are actually within statistical norms until you get close to an infinite number of comparisons.
I am reminded about a California
man who has won the California lottery twice.
I have to consider that the OP has a correct thought. I also have to believe that all samples before now have been me being on the underside of the 51-49 split, and that any day now, statistics and nature will force me to the other side!