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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

#191

Post by c22 »

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…

° Put the coins in a cup

° Shake the cup vigorously and dump coins on the table

° If coins match, go back to step one

° If coins are opposed take the result of the southernmost coin

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

#192

Post by ComputerGuru »

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_...

The same principle is used in embedded systems as the base of a prng when obtaining randomness from a possibly biased or imperfect source of noise (eg adc low bits or uninit memory values).

I find it easier to understand if you say “instead of using the level/value as the source of randomness, use the transition from one level/state to the other as the bit of entropy.” (edge-based instead of level-based) I.E. instead of head is 0 and tails is 1, head to tail is 0 and tails to head is 1, and the other transitions are disregarded.

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

#193

Post by jonahx »

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…

From the Method section:

"In each sequence, people randomly (or according to an algorithm) selected a starting position (heads-up or tails-up) of the first coin flip, flipped the coin, caught it in their hand, recorded the landing position of the coin"

Presumably if you instead allow the coin to land and bounce on a hard surface, the bias would disappear?

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

#194

Post by xp84 »

bee_rider wrote: post #151
havnagiggle wrote: post #46

Earlier quoted context omitted.

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.

Or ask the competitors to flip the coin in a manner they doesn’t allow for skill, like put it in a Yahtzee cup and toss from there.

I was imagining spinning the coin with a flick of the finger. That doesn't seem to be gameable to me, but I supposed you'd need to do a lot of flicks to see if flicking the head side or tails side matters. I'd think there's no way a coin can be more likely to spin an odd or even number of times before falling, but weirder things have happened.

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

#195

Post by cortesoft »

dfxm12 wrote: post #172
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…

The Monty Hall problem is especially unintuitive if you've ever watched Let's Make a Deal, since the problem set up is oh so close to, but not exactly, the set up of the Big Deal in the show. It's too easy to conflate the rules of the show with the math problem, which will lead to confusion. I think seeing the results of a simulation also elucidates the set up of the math problem vs reading a proof.

Yeah, I feel like the Monty Hall confusion goes away if you are explicit about the rules:

"Hall will always open one of the two non-chosen doors and will never reveal the prize"

I think most people who don't understand the problem miss that critical detail.

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

#196

Post by curriculum »

sjducb wrote: post #145

How do I bias a coin flip? Based on the paper it looks like 55% chance that it will land on the same side it started is possible. This was the most extreme subject. The bias is caused by procession so I want my flip to process as much as possible. Maybe I offset my finger as far away from the center of the coin as possible. Also putting as much force into it as possible is probably a good idea. Finally I have to catc…

Give it some spin with your index finger. Imagine putting a coin between your index finger and thumb, heads side up, resting on your middle finger below — not too different than how most people start a coin flip. With your index finger, rotate the coin in its plane, so that it stays “heads up” but the head is rotating. Now try doing this and simultaneously flipping the coin by flicking it with your thumb at a point on the bottom, close to the edge. If you do it right, you’ll impart a spin. If you impart a modest spin, the coin will never actually flip over, but will just wobble, and will therefore land heads up. An observer will likely not know what you did, because it is hard for the eye to tell the difference between a flip and a wobble at high speeds.

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

#197

Post by cortesoft »

noobermin wrote: post #9
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…

>If you bet a dollar on the outcome of a coin toss 1000 times, knowing the starting position of the coin toss would earn you 19$ on average. This is more than the casino advantage for 6-deck blackjack against an optimal player (5$) but less than that for single-zero roulette (27$). This sounds like the plot of a western where a man travels from town to town and gleans a little cash from the local waterhole a little e…

You also have to factor in your time cost. Your hourly rate is going to be really low, better off just getting a job.

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

#198

Post by matsemann »

tacitusarc wrote: post #186
4star3star wrote: post #179

Earlier quoted context omitted.

The way the problem makes sense to me is this. Doors: Goat Goat Car You pick a door. Monty shows you a Goat. You switch or stay. Monty will never show you the Car before offering a switch. He always shows you a Goat. It doesn't matter which Goat he shows you - it's just "not the Car". If your first choice is a Goat, switching will win you the Car. If your first choice is a Car, switching will win you a Goat. You have…

For sufficiently analytical folks that works, but for lay people it tends to still be confusing. The best way I’ve heard it explained to help people get it through intuition is by changing the number of doors and goats. Say there are 100 doors, and they all have goats except one, which has a car. You pick door 1. Monty then proceeds to open doors 2 through 48, skips door 49, and then opens the remaining doors. After…

I've never been happy with that explanation. I don't get why the host would not just open a single door, that's what the host does in the other scenario to me.

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

#199

Post by antisthenes »

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_...

> 2. If you get the same result both times, goto 1

Well, yes. The wiki description basically states that you get to throw away results of coin tosses in some particular cases.

In that sense, it's not really any different from just making up the results of the coin tosses entirely. There's 10000 different ways to make your data garbage.

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

#200

Post by lalaithion »

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_...

Ah, but this assumes a fixed unfairness; with this result, you could pretend to do the von neumann method but change starting sides on each flip, giving a biased result.
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