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What Kind of Chance?

DeletedUser8152

lemur said:
If "5% chance" does not refer to the probability of an individual event, then to what does it refer?
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It does refer to the probability of an individual event. But it doesn't require that the outcome of that individual event is independent of other events that may have occurred before.

Suppose that before picking your ticket, you saw that the person picking before you did not pick the winning ticket - what is your chance of picking the winning ticket now? Does this in any way change your answer to the first question?
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Well yes, now the chance of drawing the wining ticket is 1/19. But I think a better analogy would be, say there are 20 tickets in a hat, one of which is a winner. An unknown number (but less than 20) of people may have drawn tickets from the hat already, and one of them might have won already. You don't have any information about that. Nonetheless, what is your chance of winning if you draw one ticket? It is still 5%, based on the knowledge available.
 

DeletedUser3679

jaelis said:
Well yes, now the chance of drawing the wining ticket is 1/19. But I think a better analogy would be, say there are 20 tickets in a hat, one of which is a winner. An unknown number (but less than 20) of people may have drawn tickets from the hat already, and one of them might have won already. You don't have any information about that. Nonetheless, what is your chance of winning if you draw one ticket? It is still 5%, based on the knowledge available.
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Not clear on this. You may think your odds are 5%, but in fact they are not. If the ticket has been drawn, your odds are 0. If the ticket has not been drawn, your odds are better than 5%, and dependent on the number of tickets still in the hat.

Reminds me of the game show that has door #1, #2, and #3 (Price is Right?). One door has something valuable, the other two do not. After the contestant has picked a door, the MC opens one of the two remaining doors to show that it does not contain the valuable prize. Then the MC asks the contestant if he or she wants to change their choice to the other door, or keep their original choice. What is the right thing to do?

Is sticking with the original choice is the best thing, because that pick is still in the running, and there is only 1 other left? Or maybe it doesn't matter either way as there is a 50/50 chance no matter what you do? Nope, both are wrong. The proper choice is to always switch.

Here's why - the first pick has a 1/3 chance of being correct, but switching gives you the valuable prize 2/3 of the time. So nothing changes the odds of the first pick (1/3), but eliminating one door (the open one) doubles the chance of winning.
 

DeletedUser8152

rostertag said:
Not clear on this. You may think your odds are 5%, but in fact they are not. If the ticket has been drawn, your odds are 0. If the ticket has not been drawn, your odds are better than 5%, and dependent on the number of tickets still in the hat.
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The odds depend on the information you have. If you know that the ticket has been drawn, then you have a 0% chance of winning. If you know 19 people have drawn and nobody won, then you have a 100% chance of winning. If you don't know anything about previous draws, then you have a 5% chance of winning. Probably the easiest way to see that is that if you did the whole lottery over and over again (and again, you never know how many tickets were drawn before you pick yours) then you will win about 5 out of every hundred times. It doesn't matter if you are the first to draw or the last to draw.


Reminds me of the game show that has door #1, #2, and #3 (Price is Right?). One door has something valuable, the other two do not. After the contestant has picked a door, the MC opens one of the two remaining doors to show that it does not contain the valuable prize. Then the MC asks the contestant if he or she wants to change their choice to the other door, or keep their original choice. What is the right thing to do?

Is sticking with the original choice is the best thing, because that pick is still in the running, and there is only 1 other left? Or maybe it doesn't matter either way as there is a 50/50 chance no matter what you do? Nope, both are wrong. The proper choice is to always switch.

Here's why - the first pick has a 1/3 chance of being correct, but switching gives you the valuable prize 2/3 of the time. So nothing changes the odds of the first pick (1/3), but eliminating one door (the open one) doubles the chance of winning.
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Yes, but the difference here is that you know the MC opened a door without the prize. If the MC opened one door in secret and you don't know whether it had the prize or not, then you don't improve your odds any by switching.
 

DeletedUser14197

I think it is more like putting a large number of tickets in a pot, say maybe 200,000. 10,000 of them would be winning tickets.
 
lemur

lemur

Well-Known Member
jaelis said:
It does refer to the probability of an individual event. But it doesn't require that the outcome of that individual event is independent of other events that may have occurred before.
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If the "5% chance" does refer to the probability of an individual event, then the outcome of other events is irrelevant. Otherwise, in some circumstances it wouldn't be 5% anymore — as others have already pointed out.

jaelis said:
The odds depend on the information you have.
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No, your perception of the odds depends on the information you have. You're conflating risk-in-fact with risk perception.
 

DeletedUser8152

Nope, you just seem to have a nonstandard idea of what probability means. Which is cool, just don't get too riled up about how other people use the term.
 

DeletedUser10076

You can get lost in the weeds with probability with this event. I find its best to simply play pot odds.

20% is worth the risk at 75 cups
10 is worth the risk at 150 cups
5% is worth the risk at 300 cups

its really 50, 100, 200 but i like a little extra cushion. I've won 5k+ on 4 worlds playing this way, and thats with not playing much last week.
 

DeletedUser20367

Walrusking001 said:
You can get lost in the weeds with probability with this event. I find its best to simply play pot odds.

20% is worth the risk at 75 cups
10 is worth the risk at 150 cups
5% is worth the risk at 300 cups

its really 50, 100, 200 but i like a little extra cushion. I've won 5k+ on 4 worlds playing this way, and thats with not playing much last week.
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Yup, playing 6 worlds pretty much like this and am between 9k & 11k on all of them.
 

DeletedUser9433

During the World Cup event I won several neighborhood cups, none so far this year. :(
 

DeletedUser20367

lemur said:
What a joke.
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It's not a joke. If Monty Hall had been allowed to play the game he could have won the new car every day since he knew which door it was behind. The contestants had (at the start of the game) only a 33% chance of winning because they didn't know which door the new car was behind.

I'm guessing that you are saying that the odds of the game 'when played as intended' don't depend on how much information you have and that is correct since if you have enough information to change the odds you are not 'playing as intended'.
 
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