If we tossed a coin a million times and i had heads and you had tails every time, would we win 500,000 each? I think that some people are luckier than others, some people get lots of good hands somepeople get less, it is ridiculous to think that everyone gets exactly the same number of good and bad hands.
Ok if you tossed a coin 1,000,000 times then would we expect it to land heads up 500,000 times. Yes and no
Yes - because that makes the maths easier to work with probabilities.
No because that would imply some kind of divine intervention.. and thus give the basis for an argument for luck.
Infact you would expect a degree of varience.. but how much?
well using standard deviations, we would expect to be within 1 deviation 68% of the time.
To be within 2 standard deviatins 95% of the time
To be within 3 standard deviations 99.7% of the time.
A standard deviation for a coinflip (2 equaly likely outcomes), is simply the square root of the sample size.
sq. rt of 1,000,000 is 1000.
So 99.7% of the time we will be within 3 standard deviations of the expected result.
so 99.7% of the time we will be within 3000 of 500,000
So if you flip a coin 1,000,000 times you would expect it
heads up between 497,000 and 503,000 times.
what you find is that the bigger the sample the closer it becomes to the expected value
On a sample size of 100, a standard deviation is 10 and so 3 deviations would be 30.
So instead of expecting heads to land 50 times we would expext it to land somewhere between 20 -80 times
So when we talk about probabilities, we talk about the theoretical value. In practice we also need to consider the normal varience which also occures.
The human brain has evolved to quickly reconise patterns.. its a survival thing, we learn by our mistakes and in a hunter gatherer sense we cant afford to make too many.
Thats why expressions like 'once bitten, twice shy' exist.
The trouble with things like poker is that we are too quick to formulate patterns which simply dont exist. We see a guy get a long run of good / bad cards and we formulate a 'pattern' in our minds. This pattern must then be explained and the concept of luck is an easy way of doing that. We have to, in our own minds, explain things because its our nature.. its why we have evolved as a spicies. Its simply how our minds work.
But if you look deeper.. you look for a more 'adult' explaination, a more scientific explaination, we find that luck is not the issue, the real issue is the size of the sample.
100 hands is an evenings live play.. but its too small a sample for the results to not be suceptable to normal varience.
Obviously there is more to poker than starting hands.. the pros seem to make it work.. but honestly.. thats just due to their reading and post flop skills.. and of course a bit of luck!!! LOL