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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

#101

Post by raphael_kimmig »

bryanrasmussen wrote: post #82
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_...

ok but if the coin tends to land as starting then 1. starting from heads 2. flip heads 3. flip heads 4. starting from heads 5. flip heads 6. flip tails take 5 = heads? heads should still be more likely to occur than tails under this scenario, although, Zeno-like, with decreasing likelihood approaching zero over time? on edit: of course Von Neumann's process has more restrictions, leading closer to fairness.

If you always start with heads the method works out. The key is that the first and the second toss need to be independent so that HT and TH have the same probability. If you influence the second toss based on the first one it no longer works.

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

#102

Post by fbartos »

nomilk wrote: post #83
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…

It becomes clear why there's a same-side bias when watching the video: https://www.youtube.com/watch?v=3xNg51mv-fk These are fairly gentle coin tosses; barely going a foot into the air! When I think of a coin toss, I think high and spinning fast (like the ones before sports games, where the coin goes into the air and lands on the ground, usually rolls a short way, and is collected on whatever side it landed). I would…

There was indeed a lot of variation in the height of the tosses. I however disagree with the conclussion: two of my friends at the video had the most different height of tosses (one tossed thrice as hight as the other one), yet both of them had exactly the same bias (0.505). The amount of spin is unfortunatelly very misleading from the 30fps videos--the coins often seem like not spinning at all but that's just a result of the poor video quality.

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

#103

Post by [deleted] »

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

[deleted]

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

#104

Post by 1980phipsi »

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_...

You can load a dice, but you can't bias a coin: http://www.stat.columbia.edu/~gelman/research/published/dice...

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

#105

Post by jpeterson »

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?

The probability of [HEADS, TAILS] is always the same as the probability of [TAILS, HEADS], no matter how the coin is weighted.

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

#106

Post by [deleted] »

1980phipsi wrote: post #104
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_...

You can load a dice, but you can't bias a coin: http://www.stat.columbia.edu/~gelman/research/published/dice...

[deleted]

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

#107

Post by kzrdude »

input_sh wrote: post #65
kzrdude wrote: post #3

Earlier quoted context omitted.

Fun that you're showing your own work. Since this is your work, it could have Show HN in the title; I guess.

If there isn't a product one can try, it's not a Show HN material.

I see, it's a bit more narrow than I knew

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

#108

Post by dataflow »

jpeterson wrote: post #105
dataflow wrote: post #99

Earlier quoted context omitted.

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?

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?

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

#109

Post by [deleted] »

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

[deleted]

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

#110

Post by mewpmewp2 »

Retric wrote: post #80
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…

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

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.

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