I think the heart of the fallacy is in treating these coin flips as if they're happening in isolation. They're not. You flip 4, then 1st of the second set, it's also 5. And it's 4 for the 2nd flip, overlapping. The truncation is artificial. It is one continuous event, in which all results eventually appear.

You, in fact, have the two arbitrarily excluded, equally probable events in your list of "significant" trends. For example, If #5 occurs, then is immediately followed by #13, the sequence is HHTTTTHH. That sequence includes, in order, #8 HTTT, excluded TTTT because it doesn't fit your theory, and excluded TTTH (ditto).

Each individual occurrence starts its own streak. It is an independent event. And has no relation to or dependence on what happened before. The fact that you can record it means it is in the past, but the next event is in the future. 50/50.

A perfect roulette game is one wherein half the money is bet on Red and half of it is bet on black. The house just uses the loser's money to pay the winner's bets and keeps reaping money because winners are nicked 5.26%.

As far as hurting anyone's head. I suggest that maybe this topic doesn't interest you or others who have said it's idiotic. Anyhow, I think it's been established now that sequences are different than individual outcomes. And a fair bet on any random flip is different than betting on what will happen on a "conditional" flip. The link in the first post explains this better than I ever will. As far as convincing, there is nothing be argued that I know of. Discussion is fun but there seems to be no real disagreement among the posts I've read.

Quote:QFITThe authors are economists, not mathematicians. Economists are famously prone to bad pattern calls.

what you said here is so VERY VERY true. economists love to speculate and intimate that their calls are highly probable when they are not. they use words to make their points, not clear, provable mathematics.

I strongly disagree with your assessment. The article isn’t built on flawed measurement methodology, it exposes an analysis flaw that was overlooked until now. The probable result of a fair coin flip being 50/50 isn’t challenged. In fact, the coin flip example is used because that won’t be challenged.Quote:QFITSorry, but the article is utter nonsense built upon a flawed measurement methodology.

The example illustrates a facet of small sample analysis that appears to have been overlooked: given the occurrence of an event, the probability of a re-occurrence for the next sample is less than the probability of the event occurring in general. This applies to small sample analysis and is in no way useful for predicting when a “hot streak” will start or end.

To summarize what has already been posted in this thread for the coin flip example, 2 of the 16 possible 4-flip sequences yield no result for the given parameters. Of the 14 sequences producing a result, 6 have a 0 probability that a particular head flip will be followed by a head flip, 2 have a 1 probability, 4 have a 1/2 probability, and one has a 2/3 probability. I won’t chew through the math, but the probability that a head flip will be followed by another head flip for a random 4-flip sample is less than 1/2.

The article is about small sample analysis, not prediction. I believe it is only helpful for analyzing event results where the probability for an event can vary and the aim is to uncover that variance. Such as for the sporting events the article cites.

Quote:bazooookaThe only point of this thread was to start a discussion on "hot hand". I don't even play roulette. However I have friends all over the gambling landscape.

As far as hurting anyone's head. I suggest that maybe this topic doesn't interest you or others who have said it's idiotic. Anyhow, I think it's been established now that sequences are different than individual outcomes. And a fair bet on any random flip is different than betting on what will happen on a "conditional" flip. The link in the first post explains this better than I ever will. As far as convincing, there is nothing be argued that I know of. Discussion is fun but there seems to be no real disagreement among the posts I've read.

What???

This topic is idiotic because the content is purely false and your posts are completely ridiculous.

Quote:bazooookaIf we observe a string of 1000 coin flips of a fair coin. And we then pick out any/all sequence of 4 flips that has 1 or more heads in the first 3 spots ex.HHHT or THHT or HHTT or TTHH or HTTH or THHH etc..

Would you bet that the next coin after any observed head, is more or less (or equally) likely to be a head?

In any coin flip string of 1000 flips (or 100 or 10000 or 100000 etc) circle all that have any of the above patterns? What's the odds that the coin "X" after these specific patterns, will be another head.

For example, H H H "X". Do you think X=Heads = 50%? Why or why not?

It was 50% : It is 50% : It will always be 50% right up until the moment it lands and then it will be 0% or 100%

Now stop posting nonsense and links to gibberish. We do understand how someone somewhere has managed to generate ad revenue from one of the sites you've linked to, or maybe has used this sort of publicity to get media to pay for a story. That's the only way that anyone could profit from this complete and utter tosh.

Pack it in please.

I am not one of the "50% religion" crowd. Some people have imbibed too much "i.i.d."Quote:BleedingChipsSlowlyThe example illustrates a facet of small sample analysis that appears to have been overlooked: given the occurrence of an event, the probability of a re-occurrence for the next sample is less than the probability of the event occurring in general. This applies to small sample analysis and is in no way useful for predicting when a “hot streak” will start or end.

In real-life, not some fantasy world, coin-flips are not identical - coins get damaged, they land on their edge, etc...

Basketball players are not machines. If you take a really bad basketball player who freaks out, they can definitely go into a cold streak. For example, I have a hand tremor which gets worse under stress. Question: If you take NBA players in actual games, have they trained themselves enough that their throws can be considered "i.i.d" for practical purposes? Who knows? I'm seen a lot of bad statistics, but haven't looked at the actual analysis in this case. The new software which can track difficulty of throws is an interesting update.

In the gambling world, "hot hand" is possible in non-"i.i.d" conditions; e.g. cards are not perfectly shuffled, cards are collected in a specified order and only shuffled in a limited way, slot machine PRNGs are faulty and produce more/less hot/cold periods than one might expect from an ideal RNG.

I'm going to sound like ZK here, but in real-life some "cheating" exists.

----

The area of “streak detection” is one that would be a lot of fun to teach in an introductory probability class.

Consider coin flips in real-life for a “claimed fair coin”.

(1) If you see about 50/50 heads & tails in the first 100 flips, you might lean towards i.i.d.

(2) If you see 100 heads in the 1st 100 flips, a biased coin might be expected….even if the coin was claimed to be fair.

(3) How many heads in a row do you need to shift your beliefs?

As a Bayesian would say, when & how do your change your "a priori" belief that the "coin is fair"?

------

People’s natural reactions are not “homo mathematicus”. We use reasoning systems biased in certain ways from evolution.

We are animals designed for the real world, where almost all things are not "i.i.d".

We are designed to identify things which are out of the ordinary and will hurt us (e.g. cheating).

So most people have very little natural sense of true “i.i.d.” (e.g. people think a little bit anti-clumped is random). People who learn a little math become "50% religionists" in an attempt to overcompensate for natural reactions.

Finite sequences are more common than infinite sequences for everyday experience. In blackjack or video poker, it takes a huge number of hours to reach N0 or any version of “long-term”. Beginners with a little math knowledge are less familiar with short-term fluctuations (whether dealing with RoR “Risk of Ruin” or Kelly optimal betting).

*** The recent papers are dealing with finite sequence effects. ***

A cool exercise is looking at the expected loss a BJ player with x% edge will see before becoming profitable. Or the flip side, the expected win a regular BJ player will see before heading into long-term loss.

Another cool area is zero-crossings. The behavior of coin flips (or Bernoulli trials) is mostly to stay in long hot streaks and long cold streaks. The expected absolute distance from 50/50 increases over time, although the percentage difference from 0.5 is expected to tend towards zero (one might call this a real-life infinitesimal - the time spent at exactly 0.5 also decreases towards infinity).