@playerafar, If only I could go on vacation every time someone brought up my dice metaphor…
Obviously no one thinks that if you throw a die 12 million times it will fall exactly 2M times on each #. In fact, the probability of that is close to zero, as was already calculated here.
What I was trying to illustrate with the dice metaphor is that even though each roll is random, the spread does not go crazy, and the more rolls you run, the tighter the spread gets.
The real question that bothered me at the time is whether every game of chess is determined before it even starts? Is the future already fixed? Does true randomness actually exist? One thing is for sure: my question still stands, and the best philosophers are still debating it, with no clear conclusion in sight.
any other clarification, or is all clear now?
Actually - the more rolls you run - the more variations you can have.
Which isn't getting 'tighter'.
But the bell curve may be taking better shape with more rolls - and more representative of the general tendencies.
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Regarding 'true randomness' - philosophy overlaps with science and math.
And starting with Heisenberg and Schrodinger - it was proven that the universe intrinsically contains randomness. My way of wording it there.
Its very important in quantum mechanics (apparently) and has various implications.
But what about generating truly random numbers - mathematically?
Turns out that there's still that connection to physics there too.
Via quantum computers and Qbits.
One could argue that math plays 'second fiddle' to physical reality. Could be called 'physics'.
Consider Cantor proving you can have one infinity greater than another.
But those are mathematical infinities - not physical infinities.
Many people don't like physical infinity.
But inward infinity (the continuum of such) seems popular. Why?
Easier to get one's 'mind around it'. Pun not intended but its there.
Point: true randomness apparently comes from physics as opposed to math.
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Regarding the idea of a game of chess - its result - being decided in advance ... I would tend to reject that myself.
Fatalism versus determinism versus 'pre-determined' versus 'purely random'
Those are all positions that people might take - each with some but limited validity.


ok then