Hello again Origami, hope you're doing well.

I have a way to write a program to test the coin flip hypothesis, but you may not agree with it on philosophical grounds.

The idea is to use a bunch of seeded coins. I don't know if you're familiar with what that means, so I'll just explain briefly. A seeded random number generator is a random number generator that is deterministic with respect to its seed. So if you seed it with the letter a, it will produce a sequence of random numbers one after the other - let's say we generate 10 numbers - and if you start again and seed it again with the letter a, the same 10 numbers will come out. But if you seed it with b, a completely different sequence of 10 numbers will come out. And, much like in chaos theory, there's no way to predict the output other than just generating the output. So knowing what the seed "aaa" produces doesn't give you any information about what "aaaa" produces. It's chaotic. It's effectively random, while being deterministic in another sense.

And that's the philosophical problem. Effective randomness. You might reject the experiment on the grounds that effective randomness isn't the same as true randomness - I think it's a sort of interesting question.

For example, say we want to make a bet on a coin flip, so we get a fair coin and I bet on tails and you bet on heads, and the result comes and one of us wins and one of us loses. And then, I present to you a slightly different bet. I bring up a bag full of coins and I say to you, every coin in this bag is perfectly rigged. Each coin will either come up heads 100% of the time, or tails 100% of the time, but the bag is 50/50 split between coins loaded with heads and coins loaded with tails. If we get a third party to come in, select a coin at random, and then we make our bets and she flips it, the question is, do you consider this a fair bet?

Because the result is determined after she selects the coin, before we make our bet. But, neither one of us knows what it was determined to be, so from our perspective, it's still effectively random.

If you agree with effective randomness, and you agree that that bet on loaded coins is still fair, then we have a potential avenue to test our claims, by using seeded random number generators, which are effectively coins pre-loaded with their flips.

What do you think?