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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

#211

Post by rootusrootus »

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…

> procession [...] process

Nitpick: Precession. This is one case where a minor mispelling really does throw off the meaning of the sentence. At least to me.

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

#212

Post by lukasb »

4star3star wrote: post #179
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 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…

Even simpler - you pick, knowing nothing, so there's a 2/3 chance you're wrong.

If you're wrong, Monty points to toward the right door.

So you should switch.

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

#213

Post by esafak »

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_...

Basically rejection sampling, which is about obtaining variates from one distribution using variates from another. We have samples from p-coins (where p is the probability of flipping heads) and we wish to generate samples from 0.5-coins.

https://www.newton.ac.uk/files/seminar/20100623134014301-152...

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

#214

Post by rootusrootus »

quietbritishjim wrote: post #162
havnagiggle wrote: post #40

I've always caught the coin and flipped it onto the back of my hand to display the result. So I guess I have an opposite-side bias.

That's the usual way of doing it.

Huh. I thought everyone did it my way. Flip it onto the floor, hunt it down, and see which side came up.

I'm mostly serious. I know that's not ideal. But I've never been able to master the art of flipping a coin onto the back of my hand, and even catching it mid-air is hit-or-miss for me. The vast majority of time I or anyone I'm with has flipped a coin it's ended up on the floor.

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

#215

Post by InitialLastName »

kibwen wrote: post #78
kqr wrote: post #35

Earlier quoted context omitted.

> 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 mi…

I can feel the difference between denominations of my local coins no problem. What you need are a pair of coins with an odd year imprint and an even year imprint.

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

#216

Post by evouga »

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…

The situation is now counterintuitive in the other direction: if Monty Hall had opened those 48 doors at random and they just happened to not contain the car, then there is no advantage to switching, though many people would insist otherwise.

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

#217

Post by s1artibartfast »

naniwaduni wrote: post #171
I_Am_Nous wrote: post #142

Earlier quoted context omitted.

The Monty Hall Problem is a fun one because you can try to approach it from a purely analytical perspective and get one answer, while incorporating the whole situation (especially the fact that the final probability is not natural as they force the final decision into far fewer doors than originally present) and testing you can find a different answer entirely. I suppose this is an interesting corollary with discover…

Fundamentally, the trouble with the Monty Hall problem isn't that analysis comes to the wrong answer, it's that people often come to the wrong model when reasoning about it informally. It's not any harder to do the "correct" analysis than to write up a simulation. It's mostly just easier to convince yourself that the simulation matches the problem description when it reaches the unintuitive result.

Fundamentally, I think the real trouble with the Monty Hall problem is that the assumptions of the game are not clearly stated. Because of this, people come up with different models.

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

#218

Post by oakwhiz »

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_...

Pocket change is Manchester encoded by default.

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

#219

Post by matsemann »

cstrahan wrote: post #201
matsemann wrote: post #198

Earlier quoted context omitted.

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.

> that's what the host does in the other scenario to me. Is it, though? It seems apparent that, after the first guess, the host opens all but the last two doors, which just so happens to be 1 door. To check the math: Start with the $NUM_DOORS open doors. Now open all but the last two. So that’s $NUM_DOORS-2, which is 3-2, which equals 1 open door.

My interpretation of the host opening a single door and asking if you want to switch is equally valid when you expand it to 100 doors.

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

#220

Post by tomrod »

thaumasiotes wrote: post #188
tacitusarc wrote: post #186

Earlier quoted context omitted.

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…

There's a better way to think about it. 1. You pick a door. 2. You get the offer "Do you want to keep that door, or choose both [all] of the other doors? In either case, you'll keep anything that isn't a goat." 3. Nobody opens any doors. Should you keep your one door, or switch to the two doors?

This is the right way to think about it. Very clear and concise, thank you.
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