If we're ignoring flips to change the average outcome in the end, then of course one can stop flipping when one arrives precisely at 50 heads and 50 tails.

(September 29, 2017 at 1:02 pm)Lutrinae Wrote: But there is still absolutely no way I can grab a coin right now, do precisely one hundred flips, and arrive precisely at 50 heads and 50 tales just from those one hundred flips. That's my point.

No, but you know that the probability tends to 50/50 over time and can be mathematically certain of that, which means you can guarantee that the method results in fair tosses.

A fair coin doesn't mean you get an equal distribution of heads and tails over any specific number of tosses, just that the chances are equal. The method described (flipping twice and disregarding HH and TT) does the same thing.

(September 29, 2017 at 1:06 pm)Lutrinae Wrote: If we're ignoring flips to change the average outcome in the end, then of course one can stop flipping when one arrives precisely at 50 heads and 50 tails.

That's not what we were trying to do though. We wanted to simulate a fair coin toss, one in which you know the probability of a heads was the same as the probability of a tails.

I guess I'll just have to chalk it up to having gone over my head, since I cannot seem to make heads or tails of it.

(September 29, 2017 at 1:10 pm)Lutrinae Wrote: I guess I'll just have to chalk it up to having gone over my head, since I cannot seem to make heads or tails of it.

10 points for the pun.

Steal the coin.

Tibs, you were too eager to tell us the solution!
Never even gave me time to get home and think about it....

But I'm glad to have been on the right track with the multiple tosses.

I think it's somewhat impossible to be fair.

I mean, on paper you'd think a coin flip is fair, ie, 50-50 chance of either getting head or tails.

Whether you get heads or tails after you flip a coin depends on two things:

1) On which side you begin to flip the coin
2) How much force you use to flip it

I mean, I've done it before, it's not perfect but if you get a hang for how much force you're going to use and which side you begin with you can clearly see a pattern as to which side you get after the flip.

Ideally speaking if there was a machine that use this amount of force to flip a coin in this angle, I'm pretty sure enough variables are available to mathematically figure out whether you'll get heads or tails(of course discounting air resistance, winds and such) provided you know which side you begin with before the flip.

To add to that I don't think the angle in which the coin is launched affects the outcome so I guess a certain degree of fairness can be achieved by exerting different amount of force and randomly choosing which side to begin with before coin toss.

In terms of real life I think a degree of fairness can be achieved by asking someone else to flip the coin so there's inherent randomness there in that you don't exactly know which side this this person is going to decide to launch the coin and what amount of force they find comfortable in applying.

(September 29, 2017 at 12:39 pm)SteelCurtain Wrote: Your answer to Poca's question has me piqued.

Thinking like a programmer, if I can toss the com more than once to determine a result, then I can define two tosses as a 'throw' let's say. Now, what say we discount any throw that's HH or TT.

Brain working.... Not sure how this helps yet. Am I on the right track?

But redefining the terms would make it the trick question Tibs said it wasn't

A flip has to mean what it normally means... right Tibs?

Whoops, the only way to solve the problem would be redefining things because it's impossible by definition if we use the normal definitions. Meaning it *is* a trick question

ETA: SCREW YOU NON-TRANSPARENT GIF!