niuniuking
niuniuking
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Mission146
January 18th, 2021 at 1:13:41 PM permalink
Does anyone want to solve this?

Say in Keno you draw 1, 3, 9, 5, 6, 15, 30, 33. By itself the probability of drawing these eight numbers is 1 in one billion. Anyone who receive this set of numbers is going to say to receive this set of numbers is so improbable cheating must have occurred!

Yet if you realize for any draw you are bound to receive one set of of this numbers. So for Any result you are going to say cheating Must have occurred since the chance of getting this set of numbers is one in a billion.

How you resolve this conundrum
Wizard
Administrator
Wizard
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January 18th, 2021 at 1:24:28 PM permalink
There are 80!/(8!*72!) = 28,987,537,150 ways to pick 8 numbers out of 80 without replacement. In other words, if you let the game pick your 8 numbers randomly, the chances of any given set of numbers are about 1 in 29 billion.

I'm not sure why you ask about this set of numbers in particular. Maybe that they are all 33 or less. The chances of that are 1 in 2088.

I hope this helps, but I'm not not sure what the conundrum is.
It's not whether you win or lose; it's whether or not you had a good bet.
rsactuary
rsactuary
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January 18th, 2021 at 1:30:33 PM permalink
Quote: niuniuking

Does anyone want to solve this?

Say in Keno you draw 1, 3, 9, 5, 6, 15, 30, 33. By itself the probability of drawing these eight numbers is 1 in one billion. Anyone who receive this set of numbers is going to say to receive this set of numbers is so improbable cheating must have occurred!

Yet if you realize for any draw you are bound to receive one set of of this numbers. So for Any result you are going to say cheating Must have occurred since the chance of getting this set of numbers is one in a billion.

How you resolve this conundrum



If I understand what you're getting at, the flaw is in your thinking that an extremely low probability of something happening is evidence of cheating. That's simply not the case. As you state, if you're going to draw 8 numbers from 80, it has to be one combination. So determining whether cheating is happening should be done on the basis of whether the draw mechanism was fair, not if the outcome was fair.
niuniuking
niuniuking
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January 18th, 2021 at 1:36:24 PM permalink
The conundrum is this. Someone who receives this or any result is going to say" Hey it's so improbable to receive this numbers. There must have cheating going on for you to receive this numbers against the odds!

In Another thread I posted a question about how 7 different casinos each independently had a 1 in 500 odds outcome opened. Forumers replied cheating Must have occurred since the odds of casinos independently having 1 out of 500 each is 1/500^7, more than 1 in one Trillion!

Yet if you think carefully about it, EACH casino will deliver one result yes? say A roulette outcome of 36 twice. The other casino an outcome of 15 twice etc. So practically to ANY result you are then going to accuse this result to having occurred as a result of cheating.

Counter this allegation
niuniuking
niuniuking
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January 18th, 2021 at 1:49:51 PM permalink
In this thread and in another thread many posters unanimously conclude cheating has occurred. In many life situations the improbability of the events speaks something about the fishiness of the event or some oddity of it. Say if there is going to be only 1 in a million chance that nerd gets that hot girl, you are going to reason it cant be, you mistaken it for someone else, or literally if you win lotto, you are going to say it cant be! I have mistaken my eyes!. So here we have an it cant be, cheating Must have gone on to receive such improbable result! Yet There MUST be a result any to ANY result you have to accuse cheating!

https://wizardofvegas.com/forum/questions-and-answers/math/31513-niu-niu/13/#post791582

Quote: rsactuary

If I understand what you're getting at, the flaw is in your thinking that an extremely low probability of something happening is evidence of cheating. That's simply not the case. As you state, if you're going to draw 8 numbers from 80, it has to be one combination. So determining whether cheating is happening should be done on the basis of whether the draw mechanism was fair, not if the outcome was fair.

TomG
TomG
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January 18th, 2021 at 3:10:13 PM permalink
Quote: niuniuking

Does anyone want to solve this?

Say in Keno you draw 1, 3, 9, 5, 6, 15, 30, 33. By itself the probability of drawing these eight numbers is 1 in one billion. Anyone who receive this set of numbers is going to say to receive this set of numbers is so improbable cheating must have occurred!

Yet if you realize for any draw you are bound to receive one set of of this numbers. So for Any result you are going to say cheating Must have occurred since the chance of getting this set of numbers is one in a billion.

How you resolve this conundrum



The chance of drawing eight numbers is 100%.

When looking at past numbers drawn, do they pass tests for randomness? When seeing new numbers drawn, is there any predictable patters to them? The answers to those questions resolve the conundrum.
niuniuking
niuniuking
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January 18th, 2021 at 7:58:44 PM permalink
You missed the point.

The chance of getting this particular set is 1 in 1 trillion. Also, say you get only 1 draw so you cannot compare. A person may reason to get this particular set is extremely improbable. Which is why this conundrum exist. Yet we must have a particular result.
ThatDonGuy
ThatDonGuy
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January 18th, 2021 at 8:46:00 PM permalink
Quote: niuniuking

The conundrum is this. Someone who receives this or any result is going to say" Hey it's so improbable to receive this numbers. There must have cheating going on for you to receive this numbers against the odds!

In Another thread I posted a question about how 7 different casinos each independently had a 1 in 500 odds outcome opened. Forumers replied cheating Must have occurred since the odds of casinos independently having 1 out of 500 each is 1/500^7, more than 1 in one Trillion!

Yet if you think carefully about it, EACH casino will deliver one result yes? say A roulette outcome of 36 twice. The other casino an outcome of 15 twice etc. So practically to ANY result you are then going to accuse this result to having occurred as a result of cheating.

Counter this allegation


You don't specify in the "seven casinos" version under what conditions the 1 in 500 events happened.

If it is a case of "each one picked a number from 1 to 500," then yes, each had a 1 in 500 event occur, but that's an expected result in this case as every possible outcome is seven separate 1 in 500 results.

On the other hand, if it is seven specific events stated in advance - say, "If the number 123 is chosen, all player bets lose," and all seven casinos just happened to have their next number be 123, then there is legitimate reason to suspect the randomness of the selections.
niuniuking
niuniuking
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January 18th, 2021 at 9:28:04 PM permalink
There is still the conundrum isn't it? The 1 in 500 result. What's the probability that there is this specific one in a trillion result? Yet there Must be a result and Any result is one in a trillion
TomG
TomG
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January 18th, 2021 at 9:45:31 PM permalink
Quote: niuniuking

You missed the point.

The chance of getting this particular set is 1 in 1 trillion. Also, say you get only 1 draw so you cannot compare. A person may reason to get this particular set is extremely improbable. Which is why this conundrum exist. Yet we must have a particular result.



It seems like your point is that the probability of an improbable event is 100%. If you find that to be an unresolvable conundrum, that is on you. The rest of us have accepted it.

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