4 ms·

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

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.

wesleychen 3y ago
You can solve this easily by always flipping with the same side (doesn’t matter which) facing up for all flips.
- mewpmewp2 3y ago
  Unless they can also introduce bias using strength/technique of the throw.
- havnagiggle 3y ago
  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 3y ago
    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 3y ago
      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.
kqr 3y ago
> 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.
- mewpmewp2 3y ago
  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".
- sebzim4500 3y ago
  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 3y ago
    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 3y ago
      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.
Retric 3y ago
The final calculation is easy 56.25/(56.25 + 6.25) = 90%, unless the persons skills change between rounds or something.
- mewpmewp2 3y ago
  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 3y ago
But wasn't the bias in the paper something like 50.5% vs 49.5%?
- mewpmewp2 3y ago
  Yes, but I used more extreme numbers for ease of calculation and to clearly indicate the direction of a probability.

wesleychen 3y ago

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

mewpmewp2 3y ago
Unless they can also introduce bias using strength/technique of the throw.
havnagiggle 3y ago
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 3y ago
  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 3y ago
    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.

kqr 3y ago

> 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.

mewpmewp2 3y ago
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".
sebzim4500 3y ago
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 3y ago
  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 3y ago
    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.

Retric 3y ago

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

mewpmewp2 3y ago
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 3y ago

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

mewpmewp2 3y ago
Yes, but I used more extreme numbers for ease of calculation and to clearly indicate the direction of a probability.