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The Magic Cafe Forum Index » » Magical equations » » Probability question in "Penny For Your Thoughts" (0 Likes) Printer Friendly Version

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LobowolfXXX
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On 2009-01-30 17:56, S2000magician wrote:
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On 2009-01-30 17:49, LobowolfXXX wrote:
Good point; my example carried the unspoken assumption that I would choose either die with equal probability when double sixes come up. If that's the case, then it's 10-1 against.

In bridge if you're following to a trick and you hold, say, both the queen and the jack in the suit led, you can play either one with equal effect (on that trick). Many beginners in that situation will always play the jack - the lower card. If this tendency is recognized by their opponents it can be used profitably: when both the queen and the jack are missing and that player contributes the queen, his opponent knows with certainty that he does not also hold the jack. The beginner learns to play the queen and jack randomly (with equal probability) in those situations; he learns quicker if he's playing for money.

On the other hand...in a normal restricted choice sort of set-up, if he plays the queen and jack with equal probability, his opponent will be right 2/3 of the time regardless of which card he plays, by assuming that his partner has the other one.

If he always plays the jack from QJ, even if his opponent knows it, the declarer will be right 100% of the time he plays the queen, but only 50% of the time he plays the jack (twice as often), for the same over 2/3 success rate (100+50+50)/(3 cases with equal probability of occurrence).
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
S2000magician
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On 2009-01-30 18:03, LobowolfXXX wrote:
Quote:
On 2009-01-30 17:56, S2000magician wrote:
Quote:
On 2009-01-30 17:49, LobowolfXXX wrote:
Good point; my example carried the unspoken assumption that I would choose either die with equal probability when double sixes come up. If that's the case, then it's 10-1 against.

In bridge if you're following to a trick and you hold, say, both the queen and the jack in the suit led, you can play either one with equal effect (on that trick). Many beginners in that situation will always play the jack - the lower card. If this tendency is recognized by their opponents it can be used profitably: when both the queen and the jack are missing and that player contributes the queen, his opponent knows with certainty that he does not also hold the jack. The beginner learns to play the queen and jack randomly (with equal probability) in those situations; he learns quicker if he's playing for money.

On the other hand...in a normal restricted choice sort of set-up, if he plays the queen and jack with equal probability, his opponent will be right 2/3 of the time regardless of which card he plays, by assuming that his partner has the other one.

If he always plays the jack from QJ, even if his opponent knows it, the declarer will be right 100% of the time he plays the queen, but only 50% of the time he plays the jack (twice as often), for the same over 2/3 success rate (100+50+50)/(3 cases with equal probability of occurrence).

What a rarity: meeting someone here who truly understands bridge.

I cringe every time I see a magician deal a perfect bridge hand, and the cards are in order: A, 2, 3, 4, . . ., J, Q, K.
LobowolfXXX
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On 2009-01-30 18:14, S2000magician wrote:
I cringe every time I see a magician deal a perfect bridge hand, and the cards are in order: A, 2, 3, 4, . . ., J, Q, K.

lol The problem with knowing anything about a subject is that it really ratchets up that ol' cringe factor when you see that subject portrayed in other contexts (usually movies, but I know what you mean about magic, too).

I used to own a bridge club in California, and I've also directed tournaments for the American Contract Bridge League from the local level up to a few nationals. Also done some teaching, lecturing, etc. I stopped directing when I went to law school, but even now that I'm practicing, I still have a few students on the side. Love watching that light go off in the ones who are really interested in learning more about the different facets of the game. (Of course, I also like having some side money for those student loans!)
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
JasonEngland
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I cringe every time I see a magician deal a perfect bridge hand, and the cards are in order: A, 2, 3, 4, . . ., J, Q, K.

I do this all the time for non-Bridge players. It's an aesthetic choice that makes sense theatrically. If you see me at the Castle, this is almost always the way I'd present it.

If you see me in front of any serious Bridge players or at the local Bridge club doing the same demonstration (something I've only done once before), then I assure you the Ace will follow the King.

Jason
Eternal damnation awaits anyone who questions God's unconditional love. --Bill Hicks
S2000magician
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On 2009-01-30 19:28, JasonEngland wrote:
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I cringe every time I see a magician deal a perfect bridge hand, and the cards are in order: A, 2, 3, 4, . . ., J, Q, K.

I do this all the time for non-Bridge players. It's an aesthetic choice that makes sense theatrically. If you see me at the Castle, this is almost always the way I'd present it.

If you see me in front of any serious Bridge players or at the local Bridge club doing the same demonstration (something I've only done once before), then I assure you the Ace will follow the King.

There's a big difference between someone (such as you) doing it consciously, and those who haven't a clue.

I once saw an extremely well-known magician perform a gambling routine, finishing with four perfect bridge hands; it was clear from his patter that the gentleman knew nothing about the game. His audience might not have cared, but he should have cared.

Sigh.
sean_mh
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On 2009-01-09 15:41, Lemniscate wrote:
Knowledge doesn't change probabilities. Could you explain this some more? The only thing I can assume you are referring to is that the exposed choice cannot be the prize. If the prize is exposed (and out of play) the probability does, in fact, change but knowledge of the location, as long as the prize is not exposed, changes nothing.

Probability is not a function of knowledge.


Prior knowledge does indeed change probabilities. This is the basis of the concept of Conditional Probabilities: P(A|B) (The probability that the event A will occur, GIVEN THAT we know event B has occurred). If knowledge of event B does NOT change the probability of A occurring, ie. P(A|B) = P(A), events A and B are said to be INDEPENDENT. The problems in this thread are all examples of conditional probabilities. In fact, when I teach this topic in my Probability and Stats courses, we always analyse the Monty Hall problem Smile

Sean
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