Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Fair coins tend to land on the side they started (2023)

researchgate.net

Post reply on HN
Print view View original

61–70 of 193 posts

Re: Fair coins tend to land on the side they started (2023)

#61

Post by two_handfuls »

outsidein wrote: post #39
two_handfuls wrote: post #23

Earlier quoted context omitted.

That only works for a fixed bias, it's gameable if the person tossing the coin controls the bias.

That is outside the preconditions of the paper: „if the person tossing the coin controls the bias“

Let me explain.

You said:

> Flip it twice. Once to determine which side is up at second throw. Reverse to counter bias at start of second throw. Then flip again for final result.

Suppose I'm throwing the coin using your technique and I want to favor heads.

I hold tails up for the first throw, making tails more likely.

Then as per your rule, I put heads up for the second throw. Now, heads is more likely.

Choose the opposite starting face to make tails more likely. So, your technique does no prevent the coin tosser from being able to favor their desired outcome.

Re: Fair coins tend to land on the side they started (2023)

#62

Post by brewdad »

grraaaaahhh wrote: post #7
swayvil wrote: post #4

This is clearly the law of conservation of reality at work. Likewise, when you hear a word for the first time suddenly you hear it five times in a row. Or if you see somebody once you suddenly start running into them all over the place. It's because it's cheaper to repeat past realities than to create new ones.

Or how when you look for something it always ends up in the last place you look, if it weren't there would have been some number of places you looked that were completely unnecessary.

Personally, I like to keep looking for the thing long after I've found it simply to prove the adage wrong. My keys weren't in the last place I looked because I checked three more places after I had them in my hand.

Re: Fair coins tend to land on the side they started (2023)

#63

Post by morning-coffee »

bgroat wrote: post #27

This has been commonly known by magicians for decades. I doubt that any single magician had conducted 350k flips, but I know I personally did ~2,500 to test the effect when I was a kid. And I'm sure if you got 30 magicians together to pool data we'd have a meta-analysis of about this size but with experiments a century ago

Well, I suppose if you need fodder to fill your CV, this is one way to do it.

Re: Fair coins tend to land on the side they started (2023)

#66

Post by FartyMcFarter »

steeeeeve wrote: post #65

I learned a trick with flipping coins from a barber at my grandpas shop when I was probably 6 or 7. Since then I've always been able to flip a coin and determine what the outcome is. It's really just being consistent with the flip and the catch.

If this is done with a quick toss and the coin is flipping rapidly in the air, that's pretty impressive.

Re: Fair coins tend to land on the side they started (2023)

#68

Post by CoastalCoder »

morning-coffee wrote: post #63
bgroat wrote: post #27

This has been commonly known by magicians for decades. I doubt that any single magician had conducted 350k flips, but I know I personally did ~2,500 to test the effect when I was a kid. And I'm sure if you got 30 magicians together to pool data we'd have a meta-analysis of about this size but with experiments a century ago

Well, I suppose if you need fodder to fill your CV, this is one way to do it.

Especially on LinkedIn!

A single person would write 17000 posts about their "amazing journey" coin flip outcomes, and another 17001 "humbled by success" coin flip outcomes

Re: Fair coins tend to land on the side they started (2023)

#69

Post by zahlman »

japoco wrote: post #25
onion2k wrote: post #22

Earlier quoted context omitted.

That's the opposite of what the paper says. If the coin was biased you'd expect it to land on heads more often regardless of what side it starts on. The coins land on the side they start on more often.

No, first of all due to imperfections in the manufacture of real coins, there are actually no fair coins. Also the bias in the probability affects the first throw as well as all the rest. If your dataset is composed of first throws/rest of the throws, you’re going to see they are correlated.

You're missing the point.

A coin that is biased towards heads is one that would more often land on heads regardless of how you hold it when you start the flip.

The study finding is that every coin is more likely to land on heads if you start it with heads facing up, and will also be more likely to land on tails, if you start it that way instead. This bias, while small, is greater than the typical observed bias due to imperfections in manufacturing.

It's not about the "first throw" vs the "rest of the throws". It's about how you hold the coin when you go to flip it. That's what they mean by "started".

Re: Fair coins tend to land on the side they started (2023)

#70

Post by vikingerik »

ComplexSystems wrote: post #3

I am curious how this changes if we condition on it flipping in the air at least once. Can we think of this result as a mixture distribution of a fair 50/50 chance of it flips at least once, and a delta function that is 100% at the side it started on, if not flipped at all?

Seems likely it would change. Here's another way to think about it:

0 rotations is more likely than 1 rotation, since there is a wider range of rotation speeds that lead to exactly 0 rotations than to exactly 1. Similarly, 2 flips is more likely than 3, 4 is more than 5, and so on. So you're always biased towards an even number of flips and the starting side.

Take out the 0 case by your conditional, and you're left with 1 > 2, 3 > 4, 5 > 6, and so on, now biased towards an odd number and the non-starting side.

Post reply on HN