A coin and a roulette ball have no memory so future results cannot be predicted . . .
True but roulette is not played solely with a little white ball and a roulette wheel, it is played with people and those people do have memory and hopes and dreams so asking the players to consider the little white ball rather than their own hopes and dreams is not likely to gain you any friends.
Note: I sure do like that "Casino Enemy No. 1" tag line.
I've fallen for such false reasoning and when you add in a festive atmosphere, low cut evening gowns, perfume, alcohol, music, the sounds of chips and coins, etc. do you really think those who are not already enemies of the casino will think clearly. Those annunciator boards showing recent results bring in alot of money. Half the players are followers of the board, half are contrarians, but few ignore it as being utterly unrelated to the next spin.
I had a physics teacher in high school that used a bit of trickery like this to explain that lights do not emit light and that in fact they are "dark suckers" similar to a black hole. The closer you get the more dark they suck in and the further away the less powerful they are, etc, etc. At the end of the day all of us idiotic high schoolers were like "omg mathematically he's right" then he promptly made fun of us for accepting a couple of his base lines where he did some trickery like this that were essentially false claims.
He also had another experiment, which I think even today is still cute, but it involves similar trickery. Basically, you can "mathematically prove" a 50/50 is ONLY a 50/50 if you believe it is. What it boils down to is sampling size. Say craps pass/don't pass was a perfect 50/50. If someone only played craps 10 times in their life for 1 throw only... Then their results will be PURE variance. It will NOT be 50/50 it will literally just come down to luck. It's the same idea with a coin toss or any 50/50 (or even other odds)... The idea is if the person doesn't get enough trials in their lifetime, then from the perspective of their lifetime the event is NOT a 50/50 (or whatever the true odds are). One could use math to show that over multiple lifetimes it does come out to the true odds, sure... BUT do I personally care about multiple lifetimes? If from the time I'm alive to the time I die the odds aren't 50/50 for me, then it's not a 50/50, regardless of what you say mathematically. This is a fun one to ponder over different scenarios and really makes you think about real life perspective when relating to mathematics... something mathematicians don't often do =).
Also, I don't really hate casinos and the reason is I remember the old illegal gambling dens that use to exist around town. They were organised mainly along ethnic lines and the police were always raiding them and shutting them down. Today, it is much better as the games are properly supervised in a safe environment. Sure, the odds are with the house in the vast majority of cases and that is the price of entertainment. My local store makes good profits, pays heaps of tax and employs literally thousands of people.
Anyhow, here is the academic paper linked below showing that heads following heads (which is now a restricted sequence) is indeed closer to 40%.
""The researchers began their paper with a basic example to illustrate their findings: an experiment in which a person throws a coin in the air four times. "We noted the results of each throw, and calculated the percentage of heads tossed immediately after another head for all possible throw sequences. The results were unexpected: the proportion is not 50%, as we intuitively believe, but actually around 40%," Sanjurjo tells us, adding that "these results suggest the existence of a bias."""
What this paper takes 32 pages to say is that if you use an incorrect method of recording results, you will come to an incorrect conclusion. Measured correctly, the answer is 50% on average.
Yes. Is it me, or was that source paper pretty badly written? Almost like it was written to deliberately bamboozle? It sure got some coverage, which is probably getting monetized somehow.
The guys that wrote the paper surely aren't idiots (nor are the people who I've know to make money at roulette). How they do it is in dispute though? To me this topic is interesting. I suspect the same for many who read this site.
Good find at the link you posted that shows the counter argument: https://sinews.siam.org/Details-Page/hot-hands-streaks-and-coin-flips-how-the-new-york-times-got-it-wrong
Not many here would be daft enough to waste there time reading flawed proofs of the gambler's fallacy.
I took a quick look and as soon as I saw that someone was taking the unweighted average of a set of ratios, I concluded I was reading the work of idiots and saved myself any more wasted time.
Well, just a tiny bit.
.405 is the answer to a maths question: It is not the probability of any fair coin toss.
JUST IMAGINE THE GIGANTIC EDGE THAT YOU WILL HAVE IF YOU BET BLACK AFTER 10 REDS IN A ROW HAVE COME
MY GOD YOUR EDGE MUST BE AROUND 90% WHEN THAT HAPPENS
i can't talk anymore, i've got to go. i'm taking out a 2nd mortgage and then i'm headed out to track red and black on roulette wheels. i won't be back for a few months.