Heck, I'm not even a math guy but I can (and you should) see why when there is H,H,H,X - X is not a 50/50 proposition for H or T when we limit our pick sequences with a "condition" to "how often a head follows a head" "after any of the preceding 3 tosses that at least 1 head" in its discrete 4 toss sequence.
***Read Bleeding's post on page 4 or the original article until that makes sense to you.
I must say that "knowing people who've done quite well" at roulette is amazing; I'm very impressed. But I do wonder just how one might have determined that these other people have done so well. And given what a small world that'd be, whether it might include anyone we've come to know here.Would any of them happen to have previously done well at divining the patterns of the machines on the casino gaming floors, before taking up roulette?
The article isnít built on flawed measurement methodology.....
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 wonít 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.
I'm not exactly sure what the point of departure is but I see a lot of talk about flipping coins. As I've been saying for 20 years now, assuming a fair coin, the probability of every flip is 50/50 and it doesn't matter what the pattern of heads and tails was preceding it. This also goes for dice, roulette, keno, and all games of independent trails.
As it relates to sports, that is getting more subjective. I tend to think that streaks and momentum are overrated by squares handicapping sports. For example, if I heard a tout saying that the Patriots have a lot of momentum because they have beaten the spread the last several games, I would be inclined to bet whatever the other team was in the next game, if forced, because I know a lot of squares will put too much stock in the momentum theory, creating value the opposite way.
It really bothers me when announcers say things like "Adam Vinatieri has missed his last three field goal attempts from the 50-yard-line." Who cares about sample size of 3? I'd rather hear his percentage the last three seasons or so.
I think most of us here are talking past each other. I still contend that there are event sequences where heads will be less than 50%.
Since there are "16" 4 flip sequence and only "14" has at least 1 head in the first 3 spots thus 2 sequences will be excluded. Of the 14 left, 6 have a zero probability that a head will be followed by a head and the others have different degrees of probability that "head will follow a head".
It all adds up to around 40% as shown in charts linked below. Flip sequences have different odds than individual flip outcomes.
Agreed there is no gambling edge to be found here..
Point is that sports (and I look at sports only through the lens of sports betting) doesnít relate well to gambling games where the instruments (e.g. cards, wheels) donít have emotions; and an accomplished AP isnít supposed to have emotions.
But in all "16" 4 flip sequence only "14" has at least 1 head in the first 3 spots thus 2 sequences will be excluded.
Nope. The study is fatally flawed as it uses a technique of recording that is silly.
I'm a sports bettor too and I'll stick to that. I'm not sure how people (and I know some) make serious money at roulette.
That being said I do believe in "hot hand" for basketball. And this study linked in the original \post does have implications for online betting that does allow one to bet on whether a player will make/miss his next shot.
Nevertheless, the approx. 60% occurrence of tails following heads under "restricted scenarios" and sampling as shown in links a few posts above, do seem sound. If not; what do those graphs show?
If not; what do those graphs show?
"There are three kinds of lies: lies, damned lies, and statistics." --Benjamin Disraeli
One must be extremely careful when presenting stats as misapplication of statistical theory can result in absurdity.