Since this method aims for long term profit I'm going with the probability which means that at some point the deviations will start to decrease towards the average.
It's different to play 50 spins which variance could dominate, if the event's horizon would be short I'd have went with the flow instead of the probability.
98% of the world's gamblers will not play 1,000,000 results during their lifetime, except if science finds the way to make us immortals, not like highlander but without death from natural causes.
As unbelievable it might sound it's NOT impossible, actually it has been rumored that in 15 to 20 years from now such practice will be considered formality due to genetic engineering and nanotechnology!
In this case we could continue our sessions into the millions of results and expanding our records into the infinity!
For the rest 2% of the gamblers' population, who by the way could be undercovered vampires, only 10% of them will encounter such session as Nick's.
Guys, we need to work under PRACTICAL terms, in other words what we CAN expect during our gambling lifetime!
That example could be equally possible as a very large comet crushing on earth, astronomical possibility, what's the point?!