This is an illusory challenge.There is no single hand in the casino analogy, millions of hands are dealt, and yet we'd still be suspicious of 3 royal flushes in a row, not because it's less probable, but because the pay-off provides a motive, a better explanation
For an observer who happens to be present for an unlikely event, it would seem impossibly lucky.
But consider the lottery.
The odds that any one person will win the $100 million jackpot are vanishingly small.
Yet there is a 100% probability that someone will win.
And that someone will wonder what he did to inspire the gods to grant him the impossible, ie, it cannot be mere chance.
Evolution does have very large populations which reproduce over lengthy periods of time.Evolution does need to deal a very lucky single winning hand for every significant design improvement, millions of them, to produce one single sentient being- the only means we know of by which the universe can contemplate itself.
I don't see it as lucky.Even most evolutionist acknowledge an extraordinary degree of 'lucky coincidences' for humanity to appear. Staggeringly improbable I think would be a better description
The millions of other species alone tell us that this is not the sort of thing evolution tends to spontaneously achieve.
It's just what happened.
Any number of other scenarios could've happened, & they'd all be equally "lucky".
This is wrong because you addressed only the special case of it occurring in 10 trials.chance is not impossible, I just think there are less improbable explanations
ten heads in a row.. gets into semantics here
each time as in individually is 50/50
each as in every time in sequence
2^10 or 1024 to 1
You didn't ask me how many trials there were.
The general case is for n trials.
The probability of it increases, approaching 1 for large values of n.
This little example illustrates how probability is usually more complex than most people think.
They typically look at a narrow straw man of a problem, & fail to see the larger picture.