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Fair coins tend to land on the same side they started

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

#161

Post by dfxm12 »

ChocMontePy wrote: post #69
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_...

If anyone wants to test it, someone wrote a short code that simulates doing that 100,000 times: https://www.techiedelight.com/generate-fair-results-biased-c... The coin is biased to come up TAILS 80% of the time, but using Von Neumann's method in the program I got HEADS 50.035%, TAILS 49.965%.

You should change your name to ChocMonteCarloPy :)

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

#164

Post by alkonaut »

fbartos wrote: post #2

About a year ago, we embarked on a quest to answer one of the most intriguing questions: If you flip a fair coin and catch it in hand, what's the probability it lands on the same side it started? Today, we are finally ready to share the results. Thanks to my friends, collaborators, and even strangers from the internet, we collected flippin 350,757 coin flips. We ran several "Coin Tossing Marathons" (e.g., https://you…

> This is more than the casino advantage for 6-deck blackjack against an optimal player (5$)

I have seen that figure (roughly 0.5% edge) but that has to depend on how deep the shoe is dealt? I remember playing only the last hands with dealers playing down to between 1.0 and 0.5 decks left. That meant you could play hands where you knew almost all remaining cards were suited. I guess the average edge assumes constant bet and doesn't include betting strategies based on counting at all? (And those strategies obviously wouldn't work in any real casino because it's "frowned upon").

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

#165

Post by [deleted] »

dataflow wrote: post #99
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_...

I'm confused, how does this help? If coins are biased to land same-side up, then don't I always have an advantage by guessing whatever side is up before the first throw?

[deleted]

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

#166

Post by fbartos »

rax0m wrote: post #95

I watched one of the 12-hour coin tossing marathons. They were sitting with their laptops and pressed a button for every result. I wonder if human error can explain (at least part of) the deviation from 50/50: * locations of the buttons they pressed on the laptops (they only pressed once per toss before enter, meaning the button represented same-side or other-side) * remembering what the coin started out as may be ha…

That's actually not completelly accurate. The study protocol (https://osf.io/hkv8p) describes the procedure in greater detail.

People were pressing one button for heads and another button for heads (which we deemend less error prone and less likely to be subcontiously influenced). The trick was that the next coin flip started the same side-up as the previous landed. Therefore there was no need to record the start (and we randomized the starting position of every 100th flip)

We also did some auditing of the video recordings (trying to decode the outcomes from the videos) and they showed quite consistent degree of bias as the original responses.

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

#167

Post by [deleted] »

cantrevealname wrote: post #128
098799 wrote: post #84

Earlier quoted context omitted.

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…

[deleted]

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

#168

Post by fbartos »

cantrevealname wrote: post #150
fbartos wrote: post #70

Earlier quoted context omitted.

We told people that the coin has to flip at least once (which would bias it for the opposite site). Whenever instructing people, I tried to explaining that the coin flip should look like you were trying to determine an outcome of a bet. You can find the complete experimental protocol here: https://osf.io/hkv8p Also, I wish I had (any) budget to hire proffesional skilled tossers haha.

I assumed that the 1% bias was entirely due to coins that did not undergo any rotation at all. However, reading that you told people that the coin has to flip at least once, I think I assumed wrongly. It sounds like the bias is due to coins that have undergone an integral number of 360-degree rotations (not zero rotations). But what exactly is the physical mechanism causing this bias? It's easy to understand why zero…

It's not about the number of rotations at all. I doubt that you can control it at all even after dozens of hours coin flipping (I did more than 20h and I can't eveb guess how many rotations the coin made) Diaconis, Holmes, and Montgomery (2007) proposed a physical model of coin flipping that introduces the bias as a result of wobblines (i.e., off-axis rotation in the flips).

Diaconis, P., Holmes, S., & Montgomery, R. (2007). Dynamical bias in the coin toss. SIAM Review, 49(2), 211-235. https://doi.org/10.1137/S0036144504446436

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

#169

Post by selimthegrim »

CuriouslyC wrote: post #148
cantrevealname wrote: post #128

Earlier quoted context omitted.

> 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.

This was how I convinced someone (RIP) by really stressing every element in the definition of Bayes’ theorem and probability space.

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

#170

Post by skrebbel »

098799 wrote: post #84
ChocMontePy wrote: post #69

Earlier quoted context omitted.

If anyone wants to test it, someone wrote a short code that simulates doing that 100,000 times: https://www.techiedelight.com/generate-fair-results-biased-c... The coin is biased to come up TAILS 80% of the time, but using Von Neumann's method in the program I got HEADS 50.035%, TAILS 49.965%.

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

> It's not difficult to notice that

Look I found the mathematician

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