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March 19th, 2019, 02:30 PM   #1
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bayes in roulette?

Hello, can you help to solve this problem? to calculate probabilities.

If 2 people go to the casino, 1 of them is blind, the other is not.
When arriving at the table, the sighted person sees that in pockets 0 32 15 19 4 21 2 25 17 34 6 27 there are particles that could obstruct the entry of the ball, the blind man does not see that.
The 2 players decide to play and write down what happened in the roulette. The blind man will play a dozen, the 1st dozen. The other player would also play 12 numbers, but making guesses he would play the next adjacent 6 numbers on the cylinder from this problematic section, the 6 numbers 26 3 35 12 28 7 and 13 36 11 30 8 23(12 numbers)
By scoring and playing 1000 balls results are: the blind man have tied and the other player has won.
Over 1000 balls, the dozen chosen by the blind man came out 334 times, which he did not lose. And the 12 numbers chosen by the sighted player came out 361 times so they came out 28 times more than the 12/36 payment rate and 36 times more than the 12/37 average. For the blind player, he simply analyzes 1000 balls where a sector of roulette has come out based on the +2.5 standard deviations(it is not difficult that ANY 12-number-set of numbers hit + 2,5 standard deviations.
. But, for the sighted player, it happened that the probability of choosing 12 numbers in advance and achieving +2.5 standard deviations happens by chance in 1 test of 1000 every 30 tests of 1000.
That is to say that it has had a very strong streak, or its prediction obeys some previous subjective knowledge. There is a saying that says: "the one who does not know is like the one who does not see"
The blind will go the other day to play another dozen or the same, the other player will apply the same prediction, and its result will have a very high probability of repeating itself.
I think this kind of example has never been raised before. We can use subjectivity, or maybe it's something from Bayes giving A and B some of the assumptions and events in the example.
What do you think?

regards
ybot
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March 19th, 2019, 04:59 PM   #2
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I didn't follow all the details or really understand your question.

But say there's a coin that's landed on heads. Two players try to guess how the coin has landed. One's blindfolded and the other isn't. Clearly the player without the blindfold has strong prior knowledge. He thinks the probability is 100% heads. The blindfold player must necessarily assign probability 50% to heads and 50% to tails.

Is that the point you're making? Can you rephrase your question in a simpler setting?
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March 19th, 2019, 05:09 PM   #3
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Hello Maschke, thanks for you reply.
The point is how much knowledge have these people before this event happens.
Suppose a roulette entire 12-number-section is covered by a cloth. The blind man cannot see it, the other can.
The blind man will bet on any number, the other will play every number but the ones covered.
In this case you can see these 12 numbers are not going to hit. In the example, sighted player had an hipotesis these numbers will not hit as the others.
After taking new data, each player have their own conclusion.
It is more clear now?

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ybot
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March 19th, 2019, 05:20 PM   #4
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Quote:
Originally Posted by ybot View Post
Hello Maschke, thanks for you reply.
The point is how much knowledge have these people before this event happens.
Suppose a roulette entire 12-number-section is covered by a cloth. The blind man cannot see it, the other can.
The blind man will bet on any number, the other will play every number but the ones covered.
In this case you can see these 12 numbers are not going to hit. In the example, sighted player had an hipotesis these numbers will not hit as the others.
After taking new data, each player have their own conclusion.
It is more clear now?
All but the question being asked.
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March 19th, 2019, 05:34 PM   #5
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The original example is more complicated.
I want to know if a subjective probability could infer future events more quickly than a regular frequentist.
Let's go to a coin toss, suppose I am a coin expert and know a certain coin is unfair and has more chances to hit more heads than tails. You do not know it.
You start a test of 1000 trials and head hit 540 times to 460 tails.
500 of 1000 is the average, 540/1000 breaks the 2,5 standard deviations.
At head and tails you have only 2 exclusive options rating 1/2.
The coin expert had created an hipotesis "heads will hit more than tails", this 1000 sample give strength to his hipotesis. With this 1000 sample he could say his hipotesis is true.
The other man sees the same sample which hit one side more than the other, he has no hipotesis.
With the same event you have 2(or more) meanings.
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March 19th, 2019, 05:44 PM   #6
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Quote:
Originally Posted by ybot View Post
The original example is more complicated.
I want to know if a subjective probability could infer future events more quickly than a regular frequentist.
Let's go to a coin toss, suppose I am a coin expert and know a certain coin is unfair and has more chances to hit more heads than tails. You do not know it.
You start a test of 1000 trials and head hit 540 times to 460 tails.
500 of 1000 is the average, 540/1000 breaks the 2,5 standard deviations.
At head and tails you have only 2 exclusive options rating 1/2.
The coin expert had created an hipotesis "heads will hit more than tails", this 1000 sample give strength to his hipotesis. With this 1000 sample he could say his hipotesis is true.
The other man sees the same sample which hit one side more than the other, he has no hipotesis.
With the same event you have 2(or more) meanings.
Of course prior knowledge makes a difference in how you evaluate probabilities. Is that the question?

Last edited by Maschke; March 19th, 2019 at 05:49 PM.
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March 19th, 2019, 05:54 PM   #7
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The question is: what are the chances to test a new 1000 coin tosses which head hit 530 to 540 times again?
What does regular man conclude about this 1000 tosses?
Is there a difference between the 2 players in decision making for the next test?
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March 19th, 2019, 07:26 PM   #8
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Quote:
Originally Posted by ybot View Post
The question is: what are the chances to test a new 1000 coin tosses which head hit 530 to 540 times again?
What does regular man conclude about this 1000 tosses?
Is there a difference between the 2 players in decision making for the next test?
The person who knows the coin is biased can use that information. The person who doesn't, must conclude that the odds are still 50-50 and that the 530 result was due to chance.

Now a good question is, what kind of results would give you what confidence level that a coin is biased. That's a question for someone who knows more probability than I do.
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March 19th, 2019, 07:35 PM   #9
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We could have confidence this coin is unfair with another 1000-test which results were 540/460 to heads because 2,5sd happens very very few times by chance.
At this coin toss example which you have a 50/50 theorical probability it becomes easier than in roulette with 37 slots
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March 19th, 2019, 07:48 PM   #10
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Quote:
Originally Posted by ybot View Post
We could have confidence this coin is unfair with another 1000-test which results were 540/460 to heads because 2,5sd happens very very few times by chance.
That can be exactly quantified by people versed in probability theory, which I'm not.

Besides, incredibly unlikely things happen all the time. The fact that you or I exist as the people we are is, before the fact, extremely unlikely. Yet here we are. Which is why there's something fundamentally wrong with the philosophy of probability theory. We live in an extremely unlikely world. Perhaps the only such world in the universe. What are the odds! And if not ... where are the aliens? This is the Fermi paradox. Which is way off topic, but still. How do you know the flip of a coin five minutes from now wasn't entirely determined at the instant of the big bang? People say quantum physics is random, but that's only an interpretation. The physics itself is agnostic on interpretations.

Are you asking a quantitative question about probability? Or a philosophical one?


Quote:
Originally Posted by ybot View Post
At this coin toss example which you have a 50/50 theorical probability it becomes easier than in roulette with 37 slots
Ok. That's why I mentioned coins. Easier to visualize.

Last edited by Maschke; March 19th, 2019 at 07:53 PM.
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