what is the math of this ? - Page 2 - Beginning Poker Questions

See: https://en.wikipedia.org/wiki/Bayesian_inference

I don't know about you, but I would update my distribution assumption after witnessing an alleged 1 in 2^100 event. That would be harder than winning the Powerball jackpot 3 times in a row.

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06-15-2019 , 09:41 PM

#27

ad hoc

journeyman

Join Date: Aug 2010 Posts: 225

Quote:

Originally Posted by heehaww

What do rigged coin flips have to do with poker and the math thereof?

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06-15-2019 , 10:48 PM

#28

madlex

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Join Date: Jan 2009 Posts: 17,428

If you lose 50 times in a row with QQ to AK, you might want to question if everything is alright with that game.

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06-16-2019 , 12:13 AM

#29

ad hoc

journeyman

Join Date: Aug 2010 Posts: 225

You're looking for this thread:

https://forumserver.twoplustwo.com/2...dition-255990/

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06-16-2019 , 12:14 AM

#30

Didace

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Join Date: Nov 2009 Posts: 19,877

ad hoc,

Try to follow along.

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06-16-2019 , 07:02 PM

#31

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

Quote:

Originally Posted by ad hoc

What do rigged coin flips have to do with poker and the math thereof?

It admittedly has nothing to do with the thread, but I wasn't going to leave your false idea of gambler's fallacy unchallenged. In theory, with full certainty that a coinflip is fair, you're right that the 101st flip is 50/50. But in the real world, fairness is only an assumption, therefore to update the likelihood is not a fallacy.

Your original reply to Mr. Big Stack was right: the OP was asking about the beforehand probability.
P(lose next two 80/20 races) is a different question than P(next 80/20 race | lost previous one).
The answer to the first is .2^2 while the answer to the second is .2

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06-16-2019 , 10:21 PM

#32

the_spike

old hand

Join Date: Jul 2009 Posts: 1,615

Quote:

Originally Posted by madlex

We don’t even have to go to 100. Probability for tails 20 times in a row is under 0.0001%. At that point it’s already fair to assume something might be “wrong” with the coin or environment and you can safely bet on tails on the next throw.

In the real world it's something to think about, but on the other hand if you're dealing with large numbers, for example casinos that see millions of events per year, then it's different. If the number of trials is large enough, then it's a virtual certainty that you'll get 20 tails in a row at some point. The only thing that would be weird with a fair coin is if it never happened.

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06-17-2019 , 07:41 AM

#33

madlex

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Join Date: Jan 2009 Posts: 17,428

Quote:

Originally Posted by the_spike

20 times in a row is roughly a one in a million shot, so that certainly happens sometimes somewhere.

I used that example because it’s a number that people can still visualize. The 100 times example isn’t. That number is so large that everyone is like “that’s a lot of zeros”. Statmanhal posted the number in this thread, it’s 1.3 followed by 29 zeros. The number of atoms in the universe is estimated at 10^80.

Even with a fake coin that lands on tails 95% of the time, we’re talking about <.6% for tails 100 times in a row.

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06-17-2019 , 08:32 AM

#34

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

Quote:

Originally Posted by the_spike

In the real world it's something to think about, but on the other hand if you're dealing with large numbers, for example casinos that see millions of events per year, then it's different.

Only if:

a) You have access to the historical results that you didn't observe, or
b) You have testimony from other players about their observations, or
c) You can safely assume others would have noticed something fishy by now.

Even that doesn't rule out the possibility that the abnormal behavior only just began recently, but of course that hypothesis would be a reach.

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