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 Probability Discussions of probability theory

 03-21-2019, 01:42 PM #1 ybot newbie   Join Date: Jan 2014 Posts: 36 prior knowledge on roulette You are at a roulette wheel and see slot defects. You decide to bet on 12 numbers which you believe they would hit better than 12/37 as it should be. You take 1000 trials and numbers you picked hit 361 times(+2,5 standard deviations) What is the chance that these 12 numbers hit +2,5sd knowing a defect on the wheel?
 03-21-2019, 04:07 PM #2 Yoshi63 old hand     Join Date: Jan 2007 Location: sandstorm Posts: 1,937 Re: prior knowledge on roulette Your question isn't very clear. What are you asking exactly?
 03-21-2019, 04:37 PM #3 statmanhal Pooh-Bah   Join Date: Jan 2009 Posts: 4,492 Re: prior knowledge on roulette This almost seems like a trick question if I interpreted it correctly. If you are knowledgeable enough to calculate the standard deviation, I would think you are familiar with normal distribution probability theory, for 1000 samples allows for such theory to apply. But, I agree with the previous poster that the question is unclear. Anyway, observing a sample mean 2.5 deviations above the population mean has probability of 0.6%. So, if the sample data were to be used to determine if the table is biased, you would reject the hypothesis that it was not biased.
 03-21-2019, 05:15 PM #4 ybot newbie   Join Date: Jan 2014 Posts: 36 Re: prior knowledge on roulette It might be a real example. Someone says a section will hit the most. After a 1000-trial-test these numbers hit the most. What is the probability that this man actually knew that these numbers would hit the most ? In the case this man made an hipotesis before this trial which said these 12 numbers would hit +1sd or more, does the next 1000-trial-test doublechek my hipotesis and gives a high likelihood that another 1000 trails would show similar results? Whay about a regular man who does not make an hipotesis? They are not in the same scenario, aren't they?
 03-21-2019, 05:59 PM #5 NewOldGuy Pooh-Bah   Join Date: Mar 2009 Location: In the wires Posts: 5,640 Re: prior knowledge on roulette I think you want to know the chance the player just got lucky with his prediction, yes?
03-21-2019, 07:13 PM   #6
browni3141
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Join Date: Aug 2015
Location: South Florida
Posts: 3,366
Re: prior knowledge on roulette

Quote:
 Originally Posted by statmanhal This almost seems like a trick question if I interpreted it correctly. If you are knowledgeable enough to calculate the standard deviation, I would think you are familiar with normal distribution probability theory, for 1000 samples allows for such theory to apply. But, I agree with the previous poster that the question is unclear. Anyway, observing a sample mean 2.5 deviations above the population mean has probability of 0.6%. So, if the sample data were to be used to determine if the table is biased, you would reject the hypothesis that it was not biased.
This is a cross post from "Other Gambling Games" where he mentioned Bayes'. Since casinos have an interest in providing and unbiased wheel, a 2.5 standard deviation result is actually rather meaningless. It's far, far more likely that the result was due to luck than the player actually possessing an edge. I would argue it depends on the nature of the observed flaw, though. If it is easy to spot then it's likely nothing. If it is extremely difficult to spot then it is more likely to be meaningful.

 03-22-2019, 11:45 AM #7 ybot newbie   Join Date: Jan 2014 Posts: 36 Re: prior knowledge on roulette Hello, a 1000-trial-test with the best 12 numbers rating +2,5 standardar deviations is not great deal. In case you picked these 12 numbers beforehand and hit more than 360 times whereas it should hit 324 happens 71/10.000 by chance. For the player who make the hipotesis it is a confirmation, for another player who takes data it is a regular record. @newoldguy, yes. And different subjective points with the same event.
 03-26-2019, 10:23 AM #8 ybot newbie   Join Date: Jan 2014 Posts: 36 Re: prior knowledge on roulette So, can a bayesian viewer detect n advantage before a frequentist at this scenario?
 03-27-2019, 06:43 PM #9 asymbacguy journeyman   Join Date: Jun 2015 Posts: 319 Re: prior knowledge on roulette Imo gambling problems like this should be solved by an hypothesis made prior of the "post hoc" assumptions. In actual times we have no means to state that a roulette could produce biased outcomes as they are constantly monitored by casinos. Independent hugely taxed (2.7% or 5.26%) outcomes remain just independent unbeatable outcomes. Even though they are slight biased.
 04-07-2019, 08:24 PM #10 ybot newbie   Join Date: Jan 2014 Posts: 36 Re: prior knowledge on roulette Can you provide an example?
 04-08-2019, 06:09 PM #11 asymbacguy journeyman   Join Date: Jun 2015 Posts: 319 Re: prior knowledge on roulette Knowing the actual conditions, the only way to win at roulette is by visual skills (you have to bet when the rotor features a very low speed and when the ball is up to the final 4-5 revolutions). Naturally wheels must get a huge slot edge and a fair ball's weight. A thing that is not happening anymore besides of certain automatic wheels where max limits are ridicolous. Do not waste your time and money at roulette, you can win a lot more at baccarat where cards are there and nothing can alter the actual distribution.

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