151–160 of 277 posts
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You can solve this easily by always flipping with the same side (doesn’t matter which) facing up for all flips.
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.
I always tell people that result of coin flip is highly start state dependent. Imagine a sequence of H(ead), T(ail), H, T, H, T, ... if the sequence starts with H first, in no way can the number of T exceed that of H, but the number of H might be 1 greater that that of T. I never tested my self, but I hypothesize that the propability will be more skewed if the number of revolutions is less, i.e. having a shorter Head…
If the coin is resting on your hand waiting to be flipped, it is currently mid-way through being on side up. This is because the switch between being e.g. heads up to tails up is done when the coin is vertical. If it isn't a clear explanation, try imagining catching the coin and "flattening" it at different angles, while 50% of angles will match either side, at the moment the coin is flipped, it is already half-way through the angles representing the current side.
This means that the correct sequence you describe it not THTHTH but rather THHTTHHTTHH. Taken at even intervals, both sides will appear the same number of times. Taken at odd intervals, at half of the intervals there are more Ts and the other half have more Hs.
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Why would you test it? Probability of two heads: p*p Probability of two tails: (1-p)*(1-p) Probability of head followed by tails: p*(1-p) Probability of tails followed by heads: (1-p)*p It's not difficult to notice that if you remove the first two, the last two form a 50/50 distribution
Why would you not - analytical solutions are the rare occurrences might as well approach everything with simulation...
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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.
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.
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> Why would you test it? I recall conversations on Usenet decades ago about the Monty Hall problem[1] in which people gave elementary proofs that probabilities don't change by opening a door. Even from mathematicians and statisticians. People were very insistent that the analytical solution was simple and obvious and that switching doors didn't change anything. The only thing that changed some people's minds was a pr…
You can demonstrate the Monty Hall problem solution analytically with Bayesian statistics using prior probabilities, no need to go all the way to Monte Carlo methods.
Von Neumann described a very elegant way to get fair results from a biased coin. 1. Flip the coin twice 2. If you get the same result both times, goto 1 3. Now that you have different results for your pair of flips, use the first element of the pair of flips as your result. https://en.wikipedia.org/wiki/Fair_coin#Fair_results_from_a_...
With all due respect to Von Neumann, intuitively I would change it to use the information in the two coins: one for (X, Y) and another for (Y, X). Not the first.
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The probability of [HEADS, TAILS] is always the same as the probability of [TAILS, HEADS], no matter how the coin is weighted.
I get that but I don't see how it answers my question?
1. keep flipping until you get HT (and so you choose 'heads') 2. keep flipping until you get TH (and so you choose 'tails')
Since HT and TH are equally likely, results 1 and 2 are equally likely, i.e. there's a 50% chance of choosing heads, 50% change of choosing tails.
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Why would you test it? Probability of two heads: p*p Probability of two tails: (1-p)*(1-p) Probability of head followed by tails: p*(1-p) Probability of tails followed by heads: (1-p)*p It's not difficult to notice that if you remove the first two, the last two form a 50/50 distribution
> Why would you test it? I recall conversations on Usenet decades ago about the Monty Hall problem[1] in which people gave elementary proofs that probabilities don't change by opening a door. Even from mathematicians and statisticians. People were very insistent that the analytical solution was simple and obvious and that switching doors didn't change anything. The only thing that changed some people's minds was a pr…
Von Neumann described a very elegant way to get fair results from a biased coin. 1. Flip the coin twice 2. If you get the same result both times, goto 1 3. Now that you have different results for your pair of flips, use the first element of the pair of flips as your result. https://en.wikipedia.org/wiki/Fair_coin#Fair_results_from_a_...
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…
50 authors in a paper about flipping coins?