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Fair coins tend to land on the same side they started

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31–40 of 277 posts

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

#31
Interestint, my intuition was inverse to the result: landing on the opposite side takes an odd number of flips and on the same side it would be an even number of flips.

Since for every number of flips either the number of odds is the same as the number of evens, or higher by 1, the chances of getting an odd number of flips is higher. There seems to be more at work here, and only testing validates a model!

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

#32

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 absolutely love that even with a corrupted system you can use properties of the system to ensure just outcomes.

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

#33

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_...

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…

You can solve this easily by always flipping with the same side (doesn’t matter which) facing up for all flips.

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

#34

Based my back-testing of stock market, I found a similar conclusion: if a stock rise yesterday, then today the probability of raise > the probability of fall. P(raise) is about 50.1%, P(fall) is about 49.9%. Vice versa. Having this theory means you can't rely on a single bet, you have to bets many many times to make profit from stock market. Even though I knew that, I am still working as a developer, I wish one day I…

Alert: It's not going to be as simple as this to make money even with large numbers. So don't fret about not having the money and missing some golden opportunity.

There are enough actors out there trying to develop complex algorithms to find an edge, and so there wouldn't be any simple edges like this left anywhere as they would be arbitraged away.

If there is a simple pattern, it is noticed and traded until the pattern disappears.

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

#35

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_...

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 Alice can just write "heads" or "tails" on a note and then Bob flips without having seen the note. It essentially replaces the second coin with Alice's mind which hopefully doesn't suffer from the same known bias.

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

#36

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…

You can solve this easily by always flipping with the same side (doesn’t matter which) facing up for all flips.

Unless they can also introduce bias using strength/technique of the throw.

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

#37
post #10
post #6

Earlier quoted context omitted.

This was my intuition in childhood. If you choose tails to be yours and start with tails then catch it, it is most likely to be tails. I came up with this observation myself. Weird.

Yeah, I think you were just lucky that your superstition happened to be true. Trying not to be disrespectful but I don't believe you intuited a 50.8 % bias. So nothing weird going on at all.

I know it's not on par with any real stats, but still... I just had this strong conviction that worked this way. The really interesting stuff is why it is so. I would think along lines of brain timing tossing and catching, eye-brain-timing rather than gravity and coin itself. Added: Yeah, now I remember actually manipulating timing of catch to achieve this.

> Trying not to be disrespectful

No worries, it is just me using high context communication style, where I assume that you know that I know this and I just share what was my experience in childhood (it was not like a single thought).

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

#39

Based my back-testing of stock market, I found a similar conclusion: if a stock rise yesterday, then today the probability of raise > the probability of fall. P(raise) is about 50.1%, P(fall) is about 49.9%. Vice versa. Having this theory means you can't rely on a single bet, you have to bets many many times to make profit from stock market. Even though I knew that, I am still working as a developer, I wish one day I…

Alert: It's not going to be as simple as this to make money even with large numbers. So don't fret about not having the money and missing some golden opportunity. There are enough actors out there trying to develop complex algorithms to find an edge, and so there wouldn't be any simple edges like this left anywhere as they would be arbitraged away. If there is a simple pattern, it is noticed and traded until the patt…

Has hmate9 pointed out, a simple pattern like the one described can persist indefinitely – but the risk of exploiting it is priced in already.
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