You might not call it variance kav but others might . Hi Scepticus,
Since we don't know the actual number of spins how can we tell if it was enough to justify a conclusion ? And, how many is sufficient ? I haven't found any mathematician bold enough - or stupid enough - to put his reputation on the line by stating one.
He recorder his returns in 7000+ spins. These spins were played in about 100 casino visits.
Mathematicians have defined how you can spot if the results may be random or not. This is the chi square test . This is the test casinos use to determine if a wheel is "random" or biased and possibly exploitable.
There is also the Van Keelen test for testing the superiority of bet selections on specific wheels.
The "long run" can be practically defined for different bets, meaning that if after XXX amount of spins the results are deviating too much from expectation, something important is happening. For example If you win 3 Standard Deviations above expectation after those spins, this means that you probably have a winning system. If you lose 3 Standard Deviations above expectation after those spins, the game could be rigged. Here are the numbers for the "long run". Note that these tests require to consistently flat bet. When using progressions it is extremely difficult to define "long run". Here are the numbers:
1 single number: 100.000 spins
Split bet: 200.000 spins
3 numbers: 130.000 spins
4 numbers 100.000 spins
6 numbers 60.000 spins
18 numbers 50.000 spins
I have been playing roulette for a long number of years and have yet to see where a mathematician has UNRESERVEDLEY stated his Long Run. The theory of the Long Run says only that the nearer you get TO INFINITY
a roulette player is likely to go burst.Since the human race is unlikely to reach " Infinity " how much less so for an individual ? As Keynes put it many years ago " In the Long Run we are all dead "
Even your posts contains " expectations " and " could " . No "certainty " .
As I have said before we humans are reluctant to think that there is no definitive answer to anything . How many is sufficient ? They don't know so invent the chi-square test. Sure ,it gives an answer . But not without loading the question .What is put into the computer often determines the answer !
I have long suspected the value of strings of numbers, 100,000 - 1 million - who decides ? And what value is a chi-square test of 100,000 when that GREAT number is only ONE of gazillions of 100,000s - a pee in the ocean ?
The chi square test is a guess kav . A "best guess" perhaps but a guess nevertheless.
btw The numbers you gave .Do they represent the chance of it happening ? One number has the same chance as four ? Is that given for one a mistake ?