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Paul Jester Special user UK 759 Posts |
Yep, I'm hip to that! Spot on MagicJuggler!
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Pengnome New user 57 Posts |
If you are sure on the odds you should offer a wager. You will either improve your understanding of odds or get rich.
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55john55 Regular user 137 Posts |
You did a wonderful job with the explanation. It was a pleasure to see it.
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Turk Inner circle Portland, OR 3546 Posts |
One math occurrence that always has intrigued me is this:
From two randomly shuffled decks of cards, if you simultaneously turn over the cards in order, (i.e., firs turn over card # 1 of each deck, then the new top card (card #2), then the new top care (card #3), etc.), the odds are very high that somewhere in that dealing/turnover sequence, you will get a match of a card in the two decks (i.e., maybe the QH at card # 27 or the KC at card # 43, etc.) Stated simply, somewhere in two randomly shuffled decks of cards will appear the identical card at the identical card location position. This doesn't work all the time and sometimes you have to repeat the process. (I sometimes have to go through the decks twice; in my lifetime I've had to only go through the deck a 3rd time about 5 times to get a match; I've never had to go through the decks four times to get a match. Does anyone know how to calculate the odds for that occurrence on a first deal run-through and the odds for requiring a 2nd or a 3rd re-deal in order to achieve the match? I've contemplated using this as a prediction effect using a nail ****er but, procedurally, the process risks having to be very long, and, unless you are doing something of a weird voodoo nature at a private sitting or a small private intimate party, I cannot see how an audience's interest can be maintained (during a long process of re-deals, for instance)--particularly in the event of a 2nd re-deal or a 3rd re-deal. But, that said, the occurrence of the match (same card at same location) has always intrigued me. Best, Mike
Magic is a vanishing Art.
This must not be Kansas anymore, Toto. Eschew obfuscation. |
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Jon_Thompson Inner circle Darkest Cheshire 2404 Posts |
Nice video!
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Turk Inner circle Portland, OR 3546 Posts |
Nice video, Paul. Very well (and professionally) explained. Even tho we math neophytes might struggle with our "assumptions" (i.e., our hunches or what we think we "know"), math is math. The real key point in the presentation is not what is the probability of the AS being chosen in two decks. Rather, it is what is the probability that the same card (any random card) will be chosen in both decks. That distinction gave me an "ah-ha!" moment.
Magic is a vanishing Art.
This must not be Kansas anymore, Toto. Eschew obfuscation. |
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Ihop Inner circle Glen Spey, NY 1604 Posts |
That was well explained. Short & simple
Ihor Quote: On 2012-05-15 16:54, Paul Jester wrote:
Ihor
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MagicJuggler Inner circle Anchorage, AK 1161 Posts |
Quote:
One math occurrence that always has intrigued me is this: I'm not exactly sure what the initial odds are, but for each subsequent suffle and deal the odds are the same. So long as you're randomizing the deck each deal through is it's own event, just like the flip of a coin whose odds remain 50/50 for each toss no matter how many times you get head or tails.
Matthew Olsen
I heard from a friend that anecdotal evidence is actually quite reliable. |
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danhughes Regular user Champaign, IL 115 Posts |
Quote:
On first blush, the odds seem to be very close to 50-50 that you will turn up one match in your run-through. Here's why: Turn the left card first. You have 1 in 52 chances that the right card will match. You do this 52 times. So it seems that you have a 1 in 52 chance each time, and when you repeat the trial 52 times, you should on average end up with one match. BUT.... The monkey wrench is that the above explanation works only if you had all 52 cards in the right-side pile every time. But you remove one card from the rightside pile each time you turn over a pair. For example, if your first turn gives you the 6H in the left pile and the 5D in the right pile, then when you later hit the 5D in the left pile there is no way you can also hit the 5D in the right pile, because it is already gone. And each time you turn over a pair without a match, there is one more card gone from the right pile that would have matched a card deeper in the left pile. So the odds you'll get a match in the first try is 1 in 52, but the odds you'll get a match the second try is 1 in 52 UNLESS the second left card is the same as the first right card, which is already gone so in that case there is NO chance of a match. And as you keep eliminating right cards, the chances are higher that the left card mate is already gone. Okay, here's where I get off. This is beginning to sound like a puzzle only Sam Loyd could solve.
---Dan, http://danhughes.net
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Hideo Kato Inner circle Tokyo 5649 Posts |
I once calculated the probabilty of occurence of at least one matching pair appears in two shuffled decks. It is about 64%.
Tom Boyer discovered this principle and written a trick using the principle in May 1940 issue of "Sphinx". The name of the trick is 'The Frequent Miracle'. George Kaplan created a wonderful trick using the principle. It is written in "My Best"(published in 1945). The name of the trick is 'Conincidence? No Prevision? Yes'. If you deal two decks face up simultneously, the probability of same cards appear at same moment is about 95%. (Sometimes one of them appear on the dealt cards and the other on the face of the undealt packet, though). Hideo Kato |
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Tamariz New user 45 Posts |
Quote:
On 2012-06-21 03:15, Hideo Kato wrote: I'd love to see the math calculation/proof for this. Very interesting. |
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saysold1 Eternal Order Recovering Cafe addict with only 10795 Posts |
Mark Elsdon has a nice PDF effect called "The Inevitible" which directly deals with the probablities of two randomly shuffled decks having a match card at the same place at each deck.
http://www.themagiccafe.com/forums/viewt......orum=218
Creator of The SvenPad Supreme(R) line of aerospace level quality, made in the USA utility props. https://svenpads.com/
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Philip Busk Loyal user 229 Posts |
Nicely done. Hated my probability class in school and the stuff still gives me a headache.
Philip Busk
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