6 ms·

The ‘Hot Hand’ Debate Gets Flipped on Its Head

18 points by ssivark 11y ago

ssivark 11y ago
The actual paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2627354 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2627354
- clarkevans 11y ago
  This seems similar to the Monty Hall problem, which is also quite unintuitive. Perhaps what makes it work is that the person doing the predicting sees the sequence as a whole, and hence, future events are dependent upon historical ones -- and are no longer purely random. Consider this question, "You're somewhere in the middle of a 4 coin toss, and the last toss came up heads, what's the probability of the next one coming up heads?" I think the paper is saying it's a 40% chance -- you know you're in an finite series, and, you have partial information about that series.
  - DennisP 11y ago
    That's what I counted, and got a 50% chance.
    - deleted 11y ago
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IkmoIkmo 11y ago
Is this a joke or am I the only one who thinks this is a ridiculous article?
darkxanthos 11y ago
I think that this is flawed in the sense that most people (including the article's author) might misinterpret it. The paper assumes that we know when a streak ends. So given that we have had a streak of tails and that it's broken what's the probability of heads? That will be biased toward heads. I've only skimmed the paper, but maybe they ultimately mean this is the source of the incorrect bias in the layman's intuition?
Beltiras 11y ago
Very naive Monte Carlo: https://gist.github.com/arnists/228c4e77b1e2aa6d33f1 https://gist.github.com/arnists/228c4e77b1e2aa6d33f1 Consistently comes back around p. 50 runs have a span of .25%. Haven't read the paper yet, but if the PRNG isn't broken, I'd say it invalidates the naive presentation at the start of the article. EDIT: I think I understand the fallacy the authors present. This holds true for short runs. E(H|H) will be lower in short runs but asymptotically approaches p when number of trials rise.
- gtr 11y ago
  I enumerated the sequences that the article mentioned, and counted how often a tail filled a head, and vice versa, and got 12 instances where a head follows a head, and 10 where a tail followed a head. So there is a difference for just counting up all the possible 4 flip sequences where at least one of the first three is a head. However, doing a randomised test where I generated a random 4 length sequence, rejecting it if none of the first three was a head, then doing the same test showed no real difference. Code here https://github.com/gregryork/Flips/tree/master/src/flips https://github.com/gregryork/Flips/tree/master/src/flips
  - Beltiras 11y ago
    Take a look at the updated gist. There's an asymptote for P(H|H) when trials grow approaching p. EDIT: Graph is empirical H|H against run length (output of the last function in a linear graph)
    - gtr 11y ago
      I'm not really sure what I am looking at there. Is the X axis the number of trials run, or the length of the run?
- DennisP 11y ago
  What do you mean by short runs? If you mean just the total sample of 4, probability H|H is .5.
deleted 11y ago
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DennisP 11y ago
Here's the paper's first paragraph, matching what the article said: "Jack takes a coin from his pocket and decides that he will flip it 4 times in a row, writing down the outcome of each flip on a scrap of paper. After he is done flipping, he will look at the flips that immediately followed an outcome of heads, and compute the relative frequency of heads on those flips. Because the coin is fair, Jack of course expects this empirical probability of heads to be equal to the true probability of flipping a heads: 0.5. Shockingly, Jack is wrong." But actually Jack is right. Here are all the possibilities. A "streak" means a head was followed by a head, and a "break" means it was followed by a tail. Streaks Breaks TTHT 0 1 TTHH 1 0 THTT 0 1 THTH 0 1 THHT 1 1 THHH 2 0 HTTT 0 1 HTTH 0 1 HTHT 0 2 HTHH 1 1 HHTT 1 1 HHTH 1 1 HHHT 2 1 HHHH 3 0 total 12 12 The paper's argument later is more complex than the first paragraph implies, putting the sequences in groups with fixed numbers of heads. I don't see the point of that but it doesn't seem to help. They get into some math, but just counting the cases doesn't seem to support their argument at all. If anyone can explain their argument in a simple way, I'm interested. If they're really confident in this, they should go to Vegas, find a high-rolling gambler, and start betting on coin flips. After each heads, offer 55/45 odds that the next coin flip will be heads. I'm sure it won't be hard to find takers.
- Beltiras 11y ago
  See my MC in a post below. I think I understand what they are on about. It's biased against repeating in short runs.
- deleted 11y ago
  [deleted]

18 points by ssivark 11y ago

The actual paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2627354 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2627354

clarkevans 11y ago
This seems similar to the Monty Hall problem, which is also quite unintuitive. Perhaps what makes it work is that the person doing the predicting sees the sequence as a whole, and hence, future events are dependent upon historical ones -- and are no longer purely random. Consider this question, "You're somewhere in the middle of a 4 coin toss, and the last toss came up heads, what's the probability of the next one coming up heads?" I think the paper is saying it's a 40% chance -- you know you're in an finite series, and, you have partial information about that series.
- DennisP 11y ago
  That's what I counted, and got a 50% chance.
  - deleted 11y ago
    [deleted]
  - deleted 11y ago
    [deleted]

IkmoIkmo 11y ago

Is this a joke or am I the only one who thinks this is a ridiculous article?

darkxanthos 11y ago

I think that this is flawed in the sense that most people (including the article's author) might misinterpret it. The paper assumes that we know when a streak ends. So given that we have had a streak of tails and that it's broken what's the probability of heads? That will be biased toward heads. I've only skimmed the paper, but maybe they ultimately mean this is the source of the incorrect bias in the layman's intuition?

Beltiras 11y ago

Very naive Monte Carlo: https://gist.github.com/arnists/228c4e77b1e2aa6d33f1 https://gist.github.com/arnists/228c4e77b1e2aa6d33f1 Consistently comes back around p. 50 runs have a span of .25%. Haven't read the paper yet, but if the PRNG isn't broken, I'd say it invalidates the naive presentation at the start of the article. EDIT: I think I understand the fallacy the authors present. This holds true for short runs. E(H|H) will be lower in short runs but asymptotically approaches p when number of trials rise.

gtr 11y ago
I enumerated the sequences that the article mentioned, and counted how often a tail filled a head, and vice versa, and got 12 instances where a head follows a head, and 10 where a tail followed a head. So there is a difference for just counting up all the possible 4 flip sequences where at least one of the first three is a head. However, doing a randomised test where I generated a random 4 length sequence, rejecting it if none of the first three was a head, then doing the same test showed no real difference. Code here https://github.com/gregryork/Flips/tree/master/src/flips https://github.com/gregryork/Flips/tree/master/src/flips
- Beltiras 11y ago
  Take a look at the updated gist. There's an asymptote for P(H|H) when trials grow approaching p. EDIT: Graph is empirical H|H against run length (output of the last function in a linear graph)
  - gtr 11y ago
    I'm not really sure what I am looking at there. Is the X axis the number of trials run, or the length of the run?
DennisP 11y ago
What do you mean by short runs? If you mean just the total sample of 4, probability H|H is .5.

deleted 11y ago

[deleted]

DennisP 11y ago

Here's the paper's first paragraph, matching what the article said: "Jack takes a coin from his pocket and decides that he will flip it 4 times in a row, writing down the outcome of each flip on a scrap of paper. After he is done flipping, he will look at the flips that immediately followed an outcome of heads, and compute the relative frequency of heads on those flips. Because the coin is fair, Jack of course expects this empirical probability of heads to be equal to the true probability of flipping a heads: 0.5. Shockingly, Jack is wrong." But actually Jack is right. Here are all the possibilities. A "streak" means a head was followed by a head, and a "break" means it was followed by a tail. Streaks Breaks TTHT 0 1 TTHH 1 0 THTT 0 1 THTH 0 1 THHT 1 1 THHH 2 0 HTTT 0 1 HTTH 0 1 HTHT 0 2 HTHH 1 1 HHTT 1 1 HHTH 1 1 HHHT 2 1 HHHH 3 0 total 12 12 The paper's argument later is more complex than the first paragraph implies, putting the sequences in groups with fixed numbers of heads. I don't see the point of that but it doesn't seem to help. They get into some math, but just counting the cases doesn't seem to support their argument at all. If anyone can explain their argument in a simple way, I'm interested. If they're really confident in this, they should go to Vegas, find a high-rolling gambler, and start betting on coin flips. After each heads, offer 55/45 odds that the next coin flip will be heads. I'm sure it won't be hard to find takers.

Beltiras 11y ago
See my MC in a post below. I think I understand what they are on about. It's biased against repeating in short runs.
deleted 11y ago
[deleted]