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

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.

Quote:niuniukingDoes 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.

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

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

Quote:rsactuaryIf 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.

Quote:niuniukingDoes 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.

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.

Quote:niuniukingThe 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.

Quote:niuniukingYou 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.