Gamblers Fallacy

[gingle]

In the gamblers fallacy it is said that an event with given probability can occur or fail to occur an infinite number of times......


Lets consider an event with probability of success p and probab of failure q = 1-p.

As far as I know, the probability of n consecutive succeses or failures is expressed as p^n or q^n.

Even from highschool i know that the limit of q^n when n tends to infinity is 0 if -1<q<1. That would mean that the probability of an infinite success or failure is 0. Conversely, it is certain that this will not occur.


Are my thoughts correct?

Regards
gingle.

[Ion Saliu]

Are my thoughts correct?

Gitser:

No. Your thoughts ain’t correct. After a large number of trials (something like 50 times the number that represents p in 1/p), the real-life results get very close to what mathematics calculates.

The gambler’s fallacy is mostly advocated by those who have a vested interest: CASINOS. That might even infer “legitimacy” of cheating! You only hear that the gambler is fated to lose … to lose forever, that is!

In truth, you play roulette, flat-betting: You are fated to lose at a rate of around 5.26% of the time. If they say you are going to lose infinity of times — the reverse is also TRUE. But can you expect to WIN infinity of times? NOT! But you won’t hear those advocates claiming the reversed gambler’s fallacy: Win forever, gambler!

This gambler’s fallacy thing is the weapon they fire at me more intensely lately. They ain’t got anything else but that pathetic slogan. They aim at my Fundamental Formula of Gambling (FFG). It is not only probability, p. There are also two more fundamental elements: The number of trials, N, and the degree of certainty, DC.

You can expect, knowingly, to lose 4-5 times in a row in some 100 trials (roulette spins, blackjack hands, etc.). Equivalently, you can expect to register streaks of 4-5 consecutive wins. That’s what makes the casinos mouth-foam in desperate anger. I did experience that in 2003, in Atlantic City. The surprise to me was the screamer. She was a simple roulette dealer, who did not benefit directly from a gambler’s loss! Actually, she would have benefited only from a friendly reaction to me: I would have tipped her! In that case, I didn’t give her a dime! But I tipped generously the waitress! BRRRRRRRRAHAHAHAHA!!!!!!!

It’s all mathematical, axiomaticule! Nothing escapes mathematics, from the tiniest atoms in your blood to the most gigantic galaxies. That’s the reason why I loudly say: “God fears mathematics, while Einstein hates gambling.”

Best of luck! (You might as well get those 5 consecutive wins at any time — just be prepared to bet bigger!)

Ion Parpaluck Saliu

[gingle]

Best of luck! (You might as well get those 5 consecutive wins at any time — just be prepared to bet bigger!)

Ion Parpaluck Saliu

well Ion, here I think its somehow tricky. Personally i see no way how I can consistently estimate the exact moments or even a finite interval favorable for a bet increase, unless we are dealing with limit cases.(or better said those limit cases exist)

Please apologize, only now i have noticed that this cathegory is not for topics related to mathematics, gambling etc.

Multa bafta!

gingle

[Ion Saliu]

Please apologize…

Gitser:

No problem, axiomaticule! The debates are good if conducted bona fide. And debate means like in Romanian (from the Latin language): battle (a competitive act).

Personally i see no way how I can consistently estimate the exact moments or even a finite interval favorable for a bet increase…

The real fallacy here is your belief (and those vested advocates of gambler’s fallacy): absolute certainty. There ain’t no absolute certainty in the Universe. But things follow the rules of randomness. There are skips and streaks. Don’t you tell me that you had an infinite number of losses in a row; or that you’ve never won more than once… In that case, you are just a casino MOLE!!!

If an honest individual, just write down everything at the roulette table, or the blackjack table. You gonna see very clearly the streaks (WWW or LLL)… Furthermore, you gonna see that the streaks follow mathematical formulas. The longer the streak, the rarer it occurs. The gambler fallacists (sounds like fascists, yeah!) would always tell you that the longest possible losing streak has the same chance as a single losing streak! Now, that ends any bona fide debate, because the Earth is not flat.

Ion Saliu

[gingle]

Itser:

i do not play roulette (dont know why...), but i've made an interresting experiment at the 6/49 lottery:

For the last 1000 drawings i made a report on the skip values of the pairs in a drawing. The cases where at least one pair had a skip value >= 375 were of interrest to me. After a hit of such case, i counted then the skips until the next hit.

In total there were 121 strategy skip values. A consecutive hit (the case when 2 times in a row at least one pairing of the drawing had a skip value of >=375) I counted 1 and not 0.

Of the 121 strategy hits skips, 25 of them had a value of 2. Dividing 25 by 121 gave me about 20%......


Next I ran streaks.exe with settings probability .2, streak length 1 and number of trials 121. Next, probability .2, streak length 2 and trials 121.

Una peste alta, the values obtained from streaks.exe coincided exactly with the reality (at least in these 121 cases). Single length streak according to streak should be 15 and streak of 2, 3 times. I checked the file and there were exactly these values.

The reason why the count of 25 doesnt fit is, because there were not only 2 in a row but also 3. Single length streaks were exactly 15.

Now, there are about 5-7-8 pairs left after 375 drawings, I could skip to play the first 2 times after a win (win is considered if there are no more then 2 draws between cases when a pair had a skip>=375). However, I'm not so sure that if i wait 2 single W in order to play after for a double WW, I will not miss some cases.....


I wish you Merry Christmas and a Happy New and full with accomplishments year of 2011 !

gingle

[Ion Saliu]

I wrote the last word on gambler’s fallacy and the reversed gambler’s fallacy. Wikipedia has already pirated the new concept reversed gambler’s fallacy. But they did the same thing after I wrote the last word on the Reversed Birthday Paradox. The software I wrote, which is still unique, has a function named … well … Reversed Birthday Paradox!

Gambler's Fallacy, Reversed Gamblers Fallacy, Probability, Streaks

Birthday Paradox: Formula, Probability, Duplication, Coincidences, DNA, SSN

Ion Saliu