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Fair coins tend to land on the same side they started

arxiv.org

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Re: Fair coins tend to land on the same side they started

#71

Post by aspenmayer »

Philip-J-Fry wrote: post #22
fouronnes3 wrote: post #4

Earlier quoted context omitted.

What is the physical explanation for this bias?

After reading this the first thought I had was how do you stop people flipping the same way? Like, give me a baton and I could throw it at varying heights and control which side I caught it on. In theory the same applies to coin flipping. You can get quite consistent with your positioning and power. You could probably control for it by making people alternate which side was face up before the flip. That's my intuitio…

Your comment reminded me of two-up.

> Two-up is a traditional Australian gambling game, involving a designated "spinner" throwing two coins, usually Australian pennies, into the air. Players bet on whether the coins will both fall with heads (obverse) up, both with tails (reverse) up, or with a head and one a tail (known as "Ewan"). The game is traditionally played in pubs and clubs throughout Australia on Anzac Day, in part to mark a shared experience with diggers (soldiers).

https://en.wikipedia.org/wiki/Two-up

Re: Fair coins tend to land on the same side they started

#72

Post by drexlspivey »

brettwall wrote: post #23

Based my back-testing of stock market, I found a similar conclusion: if a stock rise yesterday, then today the probability of raise > the probability of fall. P(raise) is about 50.1%, P(fall) is about 49.9%. Vice versa. Having this theory means you can't rely on a single bet, you have to bets many many times to make profit from stock market. Even though I knew that, I am still working as a developer, I wish one day I…

Surely the armies of quants would have found this most trivial edge and exploited it if that was the case?

Re: Fair coins tend to land on the same side they started

#73

Post by sebzim4500 »

kqr wrote: post #35
mewpmewp2 wrote: post #30

Earlier quoted context omitted.

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…

> 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 Alic…

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.

Re: Fair coins tend to land on the same side they started

#77

Post by tiagod »

shapefrog wrote: post #25

Can someone who has access to a precision robot and controlled environment please check; if one applies the same force on the coin in flipping, with it landing on a (soft) surface at the same height it - will it land the same side every time.

Your comment sniped me into thinking of some over-engineered systems to measure this with the human factor included. Some sort of RFID coin balanced on all axis with an IMU chip that measures the force applied to the force (through acceleration) and the mode and number of rotations of the coin. Maybe a computer vision solution would also work

Re: Fair coins tend to land on the same side they started

#78

Post by kibwen »

kqr wrote: post #35
mewpmewp2 wrote: post #30

Earlier quoted context omitted.

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…

> 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 Alic…

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.

Re: Fair coins tend to land on the same side they started

#79

Post by roflmaostc »

a_c wrote: post #56

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…

Of course that is true, if you wait not significantly long enough.

Imagine the situation that you flip the coin (starting at H) and you grab it in air immediately. Of course, you will get H as result.

But let's say, the time to stop the coin can be a relatively long time T. Then, I think the probability is some kind of sum. Let's choose \Delta T= 10ms as time discretization:

P(H) = 1 / T * (10ms-0ms) + (30ms-20ms) + (50ms-40ms) + ... = 1/T \sum_{i=0}{floor(T / (2 * \Delta T))} \Delta T

P(T) = 1 / T ((20ms-10ms) + (40ms-30ms) + (60ms-50ms) + ... = 1/T \sum_{i=0}{floor(T / (2 * \Delta T)) - 1} \Delta T

For T -> \infty P(H) and P(T) getting more similar.

But, in practice you wouldn't wait equally distributed in time but more like a Gaussian distributed time period. Hence, each term of the sum would get weighted differently. And the variance and the offset of the Gaussian distribution can shift the probability in favor of H or T. It's really dependent of the concrete parameters. If you grab always after 35ms, then you'll always get T for example.

Re: Fair coins tend to land on the same side they started

#80

Post by Retric »

mewpmewp2 wrote: post #30
jbandela1 wrote: post #16

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…

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