o/t please help settle an argument.

Thing about premium bonds is you can get your full money back, OK no interest paid on them, but you have a chance of winning big money,

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Originally Posted by CAMiller

That's correct but I'd be tempted to call heads as after 19 in a row I'd be questioning the 'bias'.

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That’s applying the statistical averages, this example however isn’t relevant in mathematical probabilities

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Originally Posted by Grist_To_The_Mill

With a perfectly balanced coin and no bias in the flipping process every toss is as near a damn it 50/50. There is a remote chance it could land on its edge, not roll and stay vertical.

Cumulative odds for this process are a myth.

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the first toss is 50/50 the second toss its 51% chance it will be the same

The 50/50 odds don't change with the coins, spreading your number choices on the roulette betting or choosing numbers close together on the wheel make no difference to the odds.

Premium bonds - it doesn't matter. The chronology (or otherwise) has significance and meaning to humans but not a random number generator.

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Originally Posted by gm_gm

That’s applying the statistical averages, this example however isn’t relevant in mathematical probabilities

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Yes, that’s it.

Any measurement has a tolerance that’s dependant on the reproducibility of the technique used to make that measurement. So there is no actual result just a result that’s plus or minus a certain amount. Take for example the length of the NYS pitch quoted as 110 yards, the method used to get that answer is variable so it’s really something more like 110 yards plus or minus a foot ie something between 109 yards 2 feet to 110 yards 1 foot.

So back to our coin if you do the 1 million tosses of the coin the results would be between 499,500 and 500,500 heads or tails, not 500,000 each

There is also the rule of law that says that one in so many the coin will end on its edge!