GAMBLERS FALLACY PARADOX
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Quote: CasinoCrasherLet's say 3 7's are rolled in a row consecutively (no rolls in between 7's). Gamblers Falacy would tell you that 7 is just as likely to occur on the next roll as any other roll because the dice have no memory and there are still 6/36 ways to get a 7 on the next roll as any roll.
No, math and logic would tell you that. The Gambler's Fallacy would cause one to incorrectly believe that a seven is less likely the next throw, because anything other than a seven is overdue.
Some A-hole had to say it. I volunteer to be that A-hole.
Quote: CasinoCrasherI have a question about "Gamblers Falacy". The Falacy says in one way or another that just because an event has occurred it isn't less likely to occur in the future. The particular scenario I have in mind is with craps. Let's say 3 7's are rolled in a row consecutively (no rolls in between 7's). Gamblers Falacy would tell you that 7 is just as likely to occur on the next roll as any other roll because the dice have no memory and there are still 6/36 ways to get a 7 on the next roll as any roll. However, if 7 were still just as likely to occur, wouldn't you see 3 or 4 7's in a row just as frequently as you saw 1 or 2?
No, because the odds of rolling just a seven is 1/6 while rolling two in a row is 1/36, and three in a row is 1/216 (Romes, L2math). That's not taking into account the 5/6 odds on the next roll to not be a 7, though.
Obviously if you've already rolled three 7's, it's going to be more likely you see four 7's right now than normal......because you've already got the first three out of the way.
I guess I have to be the one to say itQuote: CasinoCrasherwouldn't you see 3 or 4 7's in a row just as frequently as you saw 1 or 2?
You may be right because there is a report that once you see a couple of Yo's in a row, you often see 18 in a row!
Quote: CasinoCrasherLet's say 3 7's are rolled in a row consecutively. Gamblers Falacy would tell you that 7 is just as likely to occur on the next roll as any other roll because the dice have no memory. However, if 7 were still just as likely to occur, wouldn't you see 3 or 4 7's in a row just as frequently as you saw 1 or 2?
"see" is operative word
The event takes place or does not take place according to the same six faces, two dice math that always applies, but you take note of the event only if that next event is the one you have extreme interest in.
There are more advanced factors in the "real world".Quote: FleaStiff"see" is operative word
The event takes place or does not take place according to the same six faces, two dice math that always applies, but you take note of the event only if that next event is the one you have extreme interest in.
Gambler's Fallacy does not address the likelihood of a biased game (or cheat...).
For example, in Vegas I might assume P=99.99% of legal dice.
In a street game, I might not make that assumption.
If I saw 100 Yo's in a row (not in a computer simulation, but in reality), I would assume the dice are illegal or the shooter's technique is non-standard.
For 10 Yo's in a row, I might still feel like the dice are legal in Vegas, but that's a huge maybe.
For 3 Yo's in a row, I would stick with "Gambler's Fallacy" and assume that the odds of a 4th Yo are the same.
Exactly where I might make the shift... I would use Bayesian analysis, estimate a prior probability, calculate likelihood of a biased game, estimate the degree of bias, and use that to create an estimate for the next Yo. (Now which "estimator" I might use, is a more difficult question in probability & statistics theory. Should it be an MLE - "Maximum Likelihood Estimator", or what properties should the "estimator" have; e.g. do you use "mean, median, mode, some non-linear estimator, a Monte Carlo estimator, etc...)
You could use Gambler's Fallacy as the main focus of an introduction class to many topics in probability & statistics theory.
What my younger dumber brother (name this movie quote) was trying to say is... if you've already rolled three 7's in a row. The odds of the fourth 7 are now 1/6, instead of 1/1296 which is the odds of rolling four 7's in a row, since you have already rolled three 7's.Quote: RS...Obviously if you've already rolled three 7's, it's going to be more likely you see four 7's right now than normal......because you've already got the first three out of the way.
RS shops at MathRUs for his answers.
Quote: WizardNo, math and logic would tell you that. The Gambler's Fallacy would cause one to incorrectly believe that a seven is less likely the next throw, because anything other than a seven is overdue.
I agree, thanks for correcting me, I stated that incorrectly.
Quote: RomesWhat my younger dumber brother (name this movie quote) was trying to say is... if you've already rolled three 7's in a row. The odds of the fourth 7 are now 1/6, instead of 1/1296 which is the odds of rolling four 7's in a row, since you have already rolled three 7's.
RS shops at MathRUs for his answers.
Thanks for the clarification, I'm drawing a blank on the movie quote though.. "Dumb and Dumber" maybe?
Quote: RomesWhat my younger dumber brother (name this movie quote) was trying to say is... if you've already rolled three 7's in a row. The odds of the fourth 7 are now 1/6, instead of 1/1296 which is the odds of rolling four 7's in a row, since you have already rolled three 7's.
RS shops at MathRUs for his answers.
I don't shop at MathRUs for answers. If I'm not mistaken, it's the other way around Mr. "The EV of this game is $55,000 a minute!" 😹😹😹
Circus Circus craps table EONS ago. Table positioned near the hallway leading to their buffet. Crew calling out "sevens shooter here, sevens shooter here" after the dice came to me and I rolled three sevens in quick succession. Guy walks up and puts a C-note on the Don't and calls out "Money Plays". (they used to let you do things like that in those days, now "money plays" is a bar near the Rio for off duty dealers and music lovers). So I rolled a fourth seven and the C-note guy walked away saying " made a believer out of me". Then the stick turned to me and said "You shot yourself in the foot" since, just having learned the Don't Pass bet, I had been shooting from the Don't.
Four sevens in a row and it cost me money.
Sometimes I wish I had learned my lesson that day. I didn't Probably never will.
And as for all those "yo's".... I'd still probably bet against them quite promptly.
Quote: FinsRuleHere's the real question. If the dice kept coming yo - yo - yo - yo... on and on. At what point would you start betting yo? Everyone would start at some point, right? I think I'd start at about 5.
I'd bet it after 18.
you forgot to mention that is the probability over just the next 3 rolls.Quote: RomesOdds of seeing 3 7's in a row = .1667^3 = .00463... so just under half of a percent.
What it is (the truth)
is
the average number of attempts it takes to get 3 7s in a row, and each attempt is NOT 1 roll in length.
1 / 0 .1667^3 = 216 ATTEMPTS (not rolls)
this has been pointed out many times B4, especially on the WoV and by BruceZ, btw so...
https://wizardofvegas.com/forum/questions-and-answers/math/8141-on-average-how-many-trials-will-it-take-to-see-a-streak-of-8-qs-for-fun/
216 attempts and each attempt is 1.194444444 rolls in lengthQuote: RomesSo out of 'about' every 200 roles you should (variance happens) see a string of 3 in a row.
(1 + p + p^2, where p = 1/6,so 1+0.166666667+ 0.027777778)
*****
average number of rolls to SEE 3
7s in a row = 216 * 1.194444444(rounded) = 258
as expected
(1/p+1/p^2+1/p^3, p=1/6)
6+36+216=258
http://www.wolframalpha.com/input/?dataset=&equal=Submit&i=(1%2Fp%2B1%2Fp%5E2%2B1%2Fp%5E3,+p%3D1%2F6)
Sally
KU rules!
wildcat power
but EVERY Craps player knows that when you SEE 3 7s in a row
it (The 7) should be going to sleep (I mean Duh!)
unless shooter is real good at rolling winner 7s
Place across and working!
Quote: mustangsally
Sally
KU rules
wildcat power
I thought these were some new math concepts I had to learn about then I recalled "rock chalk Jayhawk, KU".
Quote: FleaStiffI thought these were some new math concepts I had to learn about then I recalled "rock chalk Jayhawk, KU".
Not Kansas - "Wildcat power" - I think she went to One-and-done (er, Kentucky).
Yes UK = wildcats (yes, there R other wildcats too)Quote: ThatDonGuyNot Kansas - "Wildcat power" - I think she went to One-and-done (er, Kentucky).
like my KittyG - super wildcat!
my friend went to KU(?) never been there
(I kid her about it all the time. she got no degree and no husband from there)
they BOTH won NCAAB yesterday
Yahoo!
Sally
The odds of 4 rolls IN THE FUTURE all being 7s are 1 in 6 times 1 in 6 times 1 in 6 times 1 in 6, or 1 in 1296.
But if three sevens have already rolled, then the odds of four rolls being seven UNDER THE CONDITION that three of them in the past are already seven is 100% * 100% * 100% * 1 in 6, or just 1 in 6.
One other side note I learned from online video games is that people tend to say something isn't random when in fact they just encountered proof that it is. Most people would prefer for things to be uniform, for example that if they lost $100 then they'd soon win $100. The fact that players can win win win or lose lose lose is actually proving things are random, instead of uniform as they would like.
What about us players who can only lose, lose, lose? Don't we get to prove anything?Quote: gamemaster3000. The fact that players can win win win or lose lose lose is actually proving things are random, instead of uniform as they would like.
Seriously, those who know of the recent results may or may not realize they are irrelevant. Just as irrelevant as the un-observed rolls that have gone on when players held the dice for hours. Admitedly though, when the dice come to me I never expect to be rolling my way into the history books, I just want to roll long enough to reach the plus column.
For minibacc you look at chip piles or these new tote boards. No longer do you have to do your paper work.
The fact that it is all BS is obvious but casinos will do anything to get your money on the table. Point-SevenOut all night long yet there can be hordes of moths who will flock to the candle at any suggestion of having an edge
I don't think it hurts anyone. Triple zero, maybe a little. Otherwise, better than throwing it in a slot machine.Quote: Lucca3927Once upon a time roulette wheels didn't have that tote board that showed the last 20 or so numbers that had come up. When they introduced them and the people saw long streaks of reds and blacks, odds and evens, their roulette revenue shot way up. That rise in revenue is the basis of gamblers fallacy. Blackjack notwithstanding, the past does not decide the future. Whoever thought of that tote board was a genius. Maybe it would work for craps too. Nothing but 7 outs have happened for the last 5 shooters so it's time for the new shooter to to make the point so up your bet, right?.
(Well, it does help the casino).
Yeah, that is why they do it. Saw one jerk berating some sweet young thing for forgetting to hit the button on her baccarat tote board. Floor came over and sent her on break. Should have told the middleaged player to grow up.Quote: Lucca3927(Well, it does help the casino).
