However, I do think that belief in the hot hand, in the continued absence of conclusive statistical evidence in support of it, is irrational–and I say that as someone who thinks that there probably is such a thing as a hot hand.

I think that if you contend that paper “disproved the hot hand” by “rejecting the null hypothesis of streakiness,” you’ve probably misinterpreted the paper (or else misstated your understanding of it).

So my guess is that if you aren’t losing money playing blackjack, you’re probably keeping track, consciously or subconsciously, of whether the deck is high or low. That may provide enough bias to prevent you from losing in the long run. You may feel it’s the Martingale, but it isn’t.

Your second point is probably an understatement. Assuming that the last four digits are uniformly distributed, you only need to have about 118 listings on a page to get a 50-50 chance of a duplicate. Google birthday paradox.

One thing that happens a lot is result merchanting. You of course intend to put the ball in the hole, so when it does get in the hole, it obviously did what you wanted. And when that happens several times in a row, the obvious explanation is that you’re zoned in, that your body is executing what you want it to do better than usual. In a certain sense, it clearly is, but the question (as always) is whether it’s doing that for some basal physiological reason, or whether it’s just random variation. The infuriating thing is that you aren’t a reliable judge of which it is, because your brain insists on using results as a diagnostic test.

My intuition says that the “hot hand” exists, but is more of a lukewarm hand, or perhaps more the lack of a “cold hand.” (The idea in the latter case being that you have an optimal “true” shooting accuracy, and as long as nothing is hampering that, like an injury or an illness–a cold hand, essentially–you shoot with that true shooting accuracy, and everything else is random variation.) The hot hand, assuming it exists, is probably pretty weak and easily swamped by other factors (such as an uptick in the shooter’s confidence leading to poorer shot selection); otherwise, it would be easy to discern.

I also think it’s important to remember the true value of the paper–not its conclusions, because anyone can draw mistaken conclusions–but the actual experiments and measurements. Don’t throw the baby out with the bathwater.

@Pyramid: The terms are ill-defined in large part because the phenomenon hasn’t been clearly identified in the data yet. Once you identify the phenomenon (again, assuming it exists), then you can better define it. But at this point it’s still in the “black cat in a dark room” stage.

If you define them specifically enough, you will have a fewer disagreements, because really most of the arguments are about what the words actually mean and imply.

I think 1/100 is the right odds, unless you are in a US state without sales tax in which case I’d expect to see a bias towards .99, .98, .97… I wonder what the average number of items purchased is?

Hah! You claim to understand probability and randomness and then you post this? Physician, heal thyself!

Is it “shocking” to have repeat winners? No. Would it be “shocking” if we did not have repeat winners? Decidedly NOT.

BC

I’m here to tell y’all, there is such a thing as a “hot streak” in sports. You must know that. I’m no athlete, by any means. In the little bit of sports I have played, golf, intramural basketball, whatever, occasionally I’ve gotten “hot”. Suddenly, for a time, I can’t miss a putt under ten feet. It’s not a statistical accident either. I can SEE the line in a way I’m normally unable to. The least athletic amongst those posting here have also played sports about like I have, I imagine. You know that on occasion your probability for success changes for a time, either for the better or for the worse. It’s a feedback loop thingy, I imagine.

If studies don’t show that, perhaps the fault lies with the methodology… or the interpretation. I imagine with studies and statistics the devil is in the interpretation a lot.

Only when one looks at very long periods of time can broad mathematical theories be inferred, particularly statistical theories. This is certainly the case with regard to basketball and also with regard to the stock market.