By that metric, it's impossible to say that anything has ever happened.

I would stake my life and the future of our civilization on the judgement that a coin flipped heads 1,000 times is not a fair coin (or the flipper is not an honest one). It's not random happenstance if that occurs.

Yes, you can calculate the odds of it happening by chance, and arrive at an answer that's not exactly 0. But you can do that for anything else you'd call "definitive". Which means we've created a requirement for that term that's impossible to fulfill.

For example, the poker player in this article. What if we found text messages on his phone that said. "OK, going to the casino for another round of poker cheating!" Would that be definitive? There is a minuscule chance that someone at Verizon conspired to plant those text messages in their records, and use a 0-day exploit to make them appear on the phone. I'd wager the odds of that frame up are much better than flipping heads on a fair coin 1,000 times in a row.

They could find electronics embedded in his hat (with radio and bone-conducting speaker). But there's a small chance that the Under Armor factory mistakenly sent him that hat instead of the normal one he ordered. (The cheater hat being intended for a blackjack player in Missouri instead!)

When we're talking about a small number (0.000...) with a googol^3 zeros after the decimal point, we're talking about 0 itself. At least when trying to determine if evidence is "definitive" or not.

> hey could find electronics embedded in his hat (with radio and bone-conducting speaker). But there's a small chance that the Under Armor factory mistakenly sent him that hat instead of the normal one he ordered. (The cheater hat being intended for a blackjack player in Missouri instead!)

See here is the problem I see with that. The hat alone with the speaker in it would be only one part of the process. How does the hat read the cards? Personally I would say the hat would be just the speaker which is tied back to something that is the actual "tap". So the hat alone but be an indicator but still not proof imo.

See if Postle had some sense (And this is presuming he did infact cheat) they should of got fitted for a pair of Widex smart hearing aids (Or something similar, sure they are costly, but think of it as an investment against your future winnings). Those things allow you to use them as headphones as well as use them as hearing aids and who is going to question the hard of hearing person if they had been wearing them from day dot (Or allowed some time to, say months of turning up wearing them, not cheating before enabling the "god mode" app on the phone)

But at this point the electronics in the hat is just a theory, none have been found as of yet.

Having electronics in a hat that wasn't supposed to have them in stands out like a swore thumb and would be grounds to investigate further, ban them from taking part until that investigation has taken place (Or just outright ban them from taking part ever again), heck even call in law enforcement. I'm not sure of the law's in the state this game is being played as I didn't check where this game is being played but you can be questioned and detained in a Las Vegas casino by the casino's security. But your not going to be labelled a cheater to the world at those early stages as I can see that leading to a defamation case.

Back to the coin flip, Sure check the coin after the flips, if you were running a contest to flip 1000x times hand them the coin they need to use to flip. Heck investigate the person after the event. But just the act of it being done imo is not enough evidence to say it can't be done fairly.

EDIT: Btw I'm not saying that if someone comes up to you in the street and says "Hey I can flip 1000x heads in a row" you don't presume that they don't have a trick up their sleeve. But if you ran a contest for someone to do it then you take the act of someone completing the challenge as proof they cheated in order to do so.

I'm not saying its easy, I'm not saying its likely, I'm not saying I would even see it done in my life time if I got the whole worlds population doing nothing but flipping coins for the rest of my years. I'm just saying the act of doing so isn't imo definitive proof they cheated in order to do so.

> But if you ran a contest for someone to do it then you take the act of someone completing the challenge as proof they cheated in order to do so.

That's exactly what I would do. If I provided the coin, and someone flipped 1,000 heads in a row, then they either figured out how to control the outcome of those coin flips, or they swapped coins. There's no chance they accidentally flipped 1000 heads in a row.

1/(10^100)^3 is === 0 for everything we make judgements on in life. If every single atom in the universe (about 10^100) were to do these flips for 15 billion years (about 10^19 seconds), we would not expect to see 1,000 heads in a row, never mind your lifetime. That's how vanishingly small the odds are!

You are far, far more likely to win a lottery jackpot (about 1 in 10^9) every single time you play the game, for the rest of your life, than you would be to flip 1,000 heads in a row. But if there was such a person, we'd know for certain they were rigging the game, right?

Any other explanation is going to be overwhelmingly likely against those odds.

You're falling victim to the base rate fallacy here, sure the evidence isn't definitive but it is alarmingly close. The probability that his win rate is in fact ~1000bb/100 is effectively zero whereas even if there were only a single cheater on earth the base rate for that would be on the order of one in single digit billions.

Then what is definitive evidence for you? For the many criminal cases, fingerprints, DNA, and eyewitness testimony are all considered to be strong enough evidence for conviction. And all are less mathematically solid than the odds of this guy’s poker success.

> I'm saying it is possible that 1000 coin flips could come up heads in a row and doing so isn't proof of cheating. Unlikely, but possible.

FWIW, I think the '1000 coin flips' thing was an exaggerated analogy used to illustrate the point; I doubt the evidence here is anywhere near that strong, even if it is extremely strong.

But the problem that people are trying to point out is that you seem to be asking for a literally impossible standard of proof (think about it: for any evidence you could possibly gather, there's a non-zero chance that it has all been fabricated, or you're consistently misreading the data, or your memory is playing tricks, or...).

If your point is not that 'proof requires literal 100% certainty', what is it? It seems that you might be bothered by the idea of convicting someone based on certain types of evidence? (Maybe you're intuiting that when someone claims statistical evidence at the '1000 coin flips' level, the actual chance of a false positive is much higher than the claimed amount, because of the possibility of human error or mendacity?)

The problem is that you are conflating things.

The only explanation for observing 1000 coin flips coming up as heads is that something other than random chance made that happen.

Simply observing a series of events does not immediately explain the source and reason those events occurred.

Naturally, there could be several explanations - the overwhelmingly most likely is that he was cheating.

> The only explanation for observing 1000 coin flips coming up as heads is that something other than random chance made that happen.

> Naturally, there could be several explanations - the overwhelmingly most likely is that he was cheating.

But you can't have it both ways, You can't say their could be several explanations and something other than random chance made that happen for the same thing.

I'm not trying to say its likely. Just thats its possible and because its possible that can not be the sole basis to prove guilt. You say "overwhelmingly most likely" and yes I agree its very unlikey but its still possible and because it is possible we shouldn't use that as the sole basis to prove guilt.

Use it as a pointer to start digging into them sure. find other things to build your case. But don't use that sole thing as the basis of guilt.

All I've been saying all this time is that its possible. And because it is possible that I personally won't "throw someone under the bus" because its improbable and not impossible.

You're still ignoring the point everyone is trying to make: whatever set of evidence you have, however strongly it points to someone's guilt, there are always possible alternative explanations. 100% certainty is a requirement that will never, ever be met.