[mewpmewp2]

That's amazing, but I guess it won't help when the person can choose the bias?

Because according to the study the person can choose the bias by choosing which side start up.

So if the person wants tails based on what you've said, they should always

1. Do the first throw starting tails up.

2. If the first one is tails, then they now want to start second one heads up.

3. If the first one is heads, they will want to try and get heads again to dismiss the results. So they will do heads up.

So assuming for example that they have an ability to control bias 75% vs 25%.

Then there would be 75% chance of getting first as tails. After that 75% chance of getting heads.

So they will have 56.25% chance of getting it right the first 2 rounds.

The worst case for them would be if they get heads first (25% chance), and then are unable to get heads again. Which would be another 25% chance so 6.25% odds to lose with the first round.

So 56.25% chance of winning the first round of 2, or 6.25% losing and 37.5% of having to try again.

And I think the odds would converge at somewhere around 90% to 10%. I didn't do full calculations here, but overall it seems this strategy would increase the bias even more.

[kqr]

> That's amazing, but I guess it won't help when the person can choose the bias?

Alice writes on a piece of paper whether to use the result from the first or the second coin, Bob flips the coins however he likes, then once there are two different sides of the coins up, Alice turns over the paper and reveals to Bob which coin contains the result.

Though I guess that unnecessarily complicates the procedure – maybe Alice can just write "heads" or "tails" on a note and then Bob flips without having seen the note. It essentially replaces the second coin with Alice's mind which hopefully doesn't suffer from the same known bias.

[sebzim4500]

If you're going to go that way you can skip the coin flip entirely. Just get both of them to write heads or tails on a note and then compare. This technique is used in some crypto projects, except instead of writing on a note you share cryptographic commitments.

[mewpmewp2]

But they need to remove the possibility of a psychological guessing game. E.g. Bob could've researched before hand that people are 55% likely to pick heads if they can pick by themselves.

[arijun]

That doesn’t remove the possibility of a psychological guessing game, just makes it more convoluted. If Bob knows Alice will pick first, he can still bias the results.

[CuriouslyC]

Inconceivable!

[kibwen]

At this point you can just play odds and evens: one person picks odd, the other picks even, they both hold up either one or two fingers behind their back, reveal them at the same time, then sum the result. This prevents the randomness from being in any one actor's control. If you're worried that your brain's RNG can be gamed, then put an odd-denominated coin in one hand and an even-denominated coin in another, and mix them up so that even you don't know which hand has which.

[InitialLastName]

I can feel the difference between denominations of my local coins no problem. What you need are a pair of coins with an odd year imprint and an even year imprint.

[mewpmewp2]

We still need a study then to confirm that when people try to mix the coins in their hands like that, it would be random enough. And that would take another year...

[mewpmewp2]

Suppose Alice needs to take the coin first to herself, to use the aforementioned strategy without intentionally introducing bias, and then using result of that, which would determine whether the first or the second result from Bob would be used. Because otherwise Bob may be able to make psychological "guesses".

[amluto]

There are nice protocols like this that don’t require anyone to visibly flip a coin. See, for example:

https://en.m.wikipedia.org/wiki/Commitment_scheme

[c22]

° Put the coins in a cup

° Shake the cup vigorously and dump coins on the table

° If coins match, go back to step one

° If coins are opposed take the result of the southernmost coin

[wesleychen]

You can solve this easily by always flipping with the same side (doesn’t matter which) facing up for all flips.

[havnagiggle]

There is skill to coin flipping. You'd need to blind the flipper, either physically blindfold or make it so they don't know which result is the positive outcome ahead of time.

[bee_rider]

Or ask the competitors to flip the coin in a manner they doesn’t allow for skill, like put it in a Yahtzee cup and toss from there.

[xp84]

I was imagining spinning the coin with a flick of the finger. That doesn't seem to be gameable to me, but I supposed you'd need to do a lot of flicks to see if flicking the head side or tails side matters. I'd think there's no way a coin can be more likely to spin an odd or even number of times before falling, but weirder things have happened.

[mewpmewp2]

Unless they can also introduce bias using strength/technique of the throw.

[Retric]

The final calculation is easy 56.25/(56.25 + 6.25) = 90%, unless the persons skills change between rounds or something.

[mewpmewp2]

Yeah, thought so as well, interesting how easily those numbers worked out, but then again it's because 75/25=3 and 3x3 = 9 so the final difference must be 9x between the probabilities or 100 / (9 + 1).

I was still lucky with the numbers as for example with 80% vs 20% it would've been 4x4=16 and so 1 to 16 comes to 100 / 17.

[asimpletune]

But wasn't the bias in the paper something like 50.5% vs 49.5%?

[mewpmewp2]

Yes, but I used more extreme numbers for ease of calculation and to clearly indicate the direction of a probability.