tournament dilemma: what would you do?

Do you switch?

  • switch

    Votes: 10 43.5%

  • don't switch

    Votes: 13 56.5%
  • Total voters
    23
mikepage

mikepage

AzB Silver Member
Silver Member
hypothetical poll just for fun.

So you pay your big entry fee and enter a hypothetical IPT qualifier. While drawing up match assignments, the TD says to you,

"Here are three face-down slips of paper with first-match assignments.
One of them is Efren. *One is Archer. *And one is an AZBilliards C PLAYER. * And (grinning) I know which one is the C player! *Go ahead and select one, but don't turn it over yet."

You select the first paper, thinking this is a little unusual but figuring
you have a one third chance of sailing unscathed through your first
match. Then the TD does something unexpected. *He says

"I'm going to turn over one of the other slips of paper to reveal a world-beater" and he turns over the third slip revealing Archer. *He then looks you straight in the eye and says,

"For 20 bucks, I'll let you switch your slip for the second slip."

"Do you want to switch your choice to the second slip? *Or do you want to
stay with what you've got?"

mike page
fargo
 
pltrgyst said:
Jeez, Mike, Marilyn vos Savant's been dining out on that old chestnut for many, many years...

-- Larry
Click to expand...

It's true, this is a very old exercise in probability. One option (switch or don't switch) has twice the probability of drawing Efren than the other option does. I won't give away the answer yet, though, in case there are any aspiring mathematicians reading this who haven't already heard this problem and want to try to figure it out.

-Andrew
 
pltrgyst said:
Jeez, Mike, Marilyn vos Savant's been dining out on that old chestnut for many, many years...

-- Larry
Click to expand...

Yes, and Martin Gardner before that.

mike page
fargo
 
i didn't know that monty hall is directing tournaments now. maybe the ipt made him a better deal. okay, i'll stop.
 
mikepage said:
Yes, and Martin Gardner before that.

mike page
fargo
Click to expand...
As I recall, von Savant got it wrong. Or she got it right (you should switch) and was then assailed by mathematicians saying, incorrectly, that she got it wrong. Either way, you should switch.

The key is that our director cannot flip over the card showing one of the two goats (ER and JA). Therefore, anytime you pick a goat to begin with, the director will flip over the other goat, and so you'll win by switching. If you pick the right card to begin with, then you'll lose by switching.

2/3 of the time you initially pick a goat and win by switching.

1/3 of the time you pick the C player and lose by switching.

So the strategy "always switch" wins 2/3 of the time.

The strategy of "never switch" wins 1/3 of the time.

The strategy of "heads I switch, tails I don't" wins .5*(2/3) +.5*(1/3) = 50% of the time.

Your $20 cost of switching complicates it. Is it worth $20 to increase your odds of not playing ER or JA from 1/3 to 2/3? For me, probably not, because I'm still not gonna make the money in an IPT qualifier.

Cory
 
mikepage said:
hypothetical poll just for fun.

So you pay your big entry fee and enter a hypothetical IPT qualifier. While drawing up match assignments, the TD says to you,

"Here are three face-down slips of paper with first-match assignments.
One of them is Efren. *One is Archer. *And one is an AZBilliards C PLAYER. * And (grinning) I know which one is the C player! *Go ahead and select one, but don't turn it over yet."

You select the first paper, thinking this is a little unusual but figuring
you have a one third chance of sailing unscathed through your first
match. Then the TD does something unexpected. *He says

"I'm going to turn over one of the other slips of paper to reveal a world-beater" and he turns over the third slip revealing Archer. *He then looks you straight in the eye and says,

"For 20 bucks, I'll let you switch your slip for the second slip."

"Do you want to switch your choice to the second slip? *Or do you want to
stay with what you've got?"

mike page
fargo
Click to expand...

Ah, the ol' Montey Hall problem. Statistically, there's a 66.67% chance that the other slip is the C player so you should pay youer $20 and get the other slip.
 
mikepage said:
Yes, and Martin Gardner before that.
Click to expand...

Yes, but Gardner was a terrifically complex and interesting person, IMO one of the greatest minds of my lifetime, along with e.e.cummings and a few others. MvS couldn't carry his jock.

Well, I mean technically she *could*, but the picture would look really strange in Parade magazine.

-- Larry
 
Why would I want to take a chance that I might play Efren when I already know I will be playing a world class player. :confused:
I would love to play either one of them :cool: , even if it means my tournament may be a little short...
 
i would say YES! go for the other paper. your there to gamble anyway why not go fo the gusto! if it does'nt go your way be as slow, crazy and obnoxious as possible ( within reason ) and hope to take the player off his game.
 
Steve Lipsky said:
For anyone with a LOT of time on his hands, have fun with this thread, from the CCB.

http://www.billiardsdigest.com/ccbo...&Number=28755&page=&view=&sb=&o=&fpart=1&vc=1
Click to expand...

steve,

i only had time to read the first two pages of that thread. i never knew how patient you are!

there is one minor point worth mentioning (and i apologize if it was brought up in the last four pages). for the probability to be 1/3 for sticking and 2/3 for switching, the host must open a door randomly amongst the remaining two for the case that the contestant chooses the correct door in the first place.

granted that if the contestant chooses a wrong door initially, the host's choice is restricted as to which door she opens (which is the "extra" information that a lot of people don't get). but when the host has no restriction (i.e. when the contestant happens to choose the winner), the host must choose randomly which of the remaining two doors to open. contrast this to the case that the host always opens the lowest numbered (or leftmost) door (of the remaining two) when the contestant chooses the winner. then, the probability is 0 for sticking and 1 for switching if the highest numbered (or rightmost) door is opened by the host. and if the lowest numbered (or leftmost) door is opened by the host, the probability becomes 1/2 for either sticking or switching. (of course if you ignore which door the host opens, then it's the same as random and is 1/3, 2/3.)

i know this is minor, but i think you'd appreciate it.

william
 
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