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If you've taken a basic probability class, then you probably know the solution to this issue of obtaining a fair toss with a biased coin. Flip the coin twice. I
by shaddi 17y ago
If you've taken a basic probability class, then you probably know the solution to this issue of obtaining a fair toss with a biased coin. Flip the coin twice. If both are heads, or both are tails, discard the pair of tosses and try again. If the first flip is a heads and the second is a tails, then count the pair as a "heads". If the first is a tails and the second is heads, count the pair as "tails". Even with a bias, the probability of getting a heads-tail pair equals the probability of getting a tails-heads pair.
Here's a blog post that explains this in more detail: http://www.billthelizard.com/2009/09/getting-fair-toss-from-biased-coin.html http://www.billthelizard.com/2009/09/getting-fair-toss-from-...
You can be sure all future coin tosses I do will use this technique!
- markerdmann 17y agoAccording to the article, you could still bias the toss. For example, let's say you're trying to get heads, which in your system is "first heads, then tails". You would hold the coin heads up on the first toss, and tails up on the second toss.
- shaddi 17y agoThen perhaps there will soon be a market for automated coin-flipping machines that impart a consistent, if unknown, bias into every flip!
- Agent101 17y agoJust go quantum and measure single difracted photons.
- whatusername 17y agoI wonder if you've seen this: The automatic dice-roller http://gamesbyemail.com/News/DiceOMatic http://gamesbyemail.com/News/DiceOMatic It can generate 1.5 million dice rolls per day.
- vinutheraj 17y agoWell, you can prevent that by stipulating that the orientation should be same on both flips.
- shaddih 17y agoThe issue is that if probability will still vary between flips, if the adversary is good enough. Say heads is up both times. Flip one could be done so that p(heads) = .6, but flip two could be done so that p(heads) = .4. It's up to the person who flips.
- ars 17y agoIt's not a biased coin. It's a biased flip. Your solution does not help with that.
- sorbus 17y agoThen simply have the same side facing up each time; in that case, there would be no difference between a coin which is biased and a flip which is biased - the bias remains in the same direction, and thus the method works.
- shaddih 17y ago(I noprocrast'd myself out, but I couldn't stop thinking about this.) It's still an issue, GP is very right. The problem is that you can get any desired outcome with some probability p: it's effectively a coin that changes bias depending on the flipper's preference. I'm trying to think of a solution that resolves this... thoughts encouraged. :)
- Retric 17y agoHave the other party call it in the air.
- bh3 17y agoThen the other dude lowers his hand 1 inch. And yeah, same type of thing I was going for, preferably in that case it should land on a table unaffected by either party. Preferably the guy calling it shouldn't see the trajectory, he might be an alien who could calculate it. lol. Generally though you want both parties to be ignorant towards what is happening in my opinion.
- bh3 17y agoOnly thing that comes to mind is to add some sort of blind element. For example having two people, one flips two coins but both remain ignorant of the actual outcome and assume that they have opposing interests (and so would not be likely to try to help the other in any way). Depending on the outcome of the preliminary flip, the one of the second person is either kept the same or inversed. Again still not perfect but removes some level of manipulation. Which is sort of interesting because you'd have to wonder should the preliminary tosser try to make the probability as even or skewed as possible. If he is likely to skew it it becomes a whole new scenario.
- seanos 17y agoOr toss the coin twice, the first toss to decide which side starts face up for the second toss and the second toss to determine the result. If the bias is 60% in favour of the side intitially facing up on a single toss, then it will have been reduced to 52% for the side facing up on the first of the two tosses with this method. Not perfect but only two tosses are ever needed.
- fgimenez 17y agoFor the record, that technique was developed by Jon von Neumann. It's called a randomness extractor. Obligatory wikipedia link: http://en.wikipedia.org/wiki/Randomness_extractor#Von_Neumann_extractor http://en.wikipedia.org/wiki/Randomness_extractor#Von_Neuman...