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Neyak wrote:... Except the first one, which doesn't matter where it goes (assuming you don't tell them to put the "reds left and the blacks right", but just tell them to put the cards into two piles). So for ten cards it's only a 1 in 2^9 chance, that's 1 in 512.

Ah, but if you look back at Mikey's earlier post:

Mikey.666 wrote:Ok I'll try to be a bit more specific... There is a red and black marker card...

So I guess the first card does matter.

Yours pedantically,
Keith

It all depends too, on whether you tell the spec how many black and red cards you have.
If, for example, you take 10 cards (9 black and 1 red) and you tell the spec that 9 of them are black and 1 is red, then the odds on the spec placing the cards correctly are only 1 in 10 as they know that they need 9 cards in the black pile and 1 in the red pile, so they just need to find the one red card (1 in 10 chance).
If you take the same 10 cards (9 black and 1 red) and don't tell the spec how many of each colour there are - the odds shoot up (I haven't worked this one out yet though ) as there are alot more possible permatations and combinations.
It also depends how many of each colour there are.
If we assume that you do tell the spec how many of each colour there are, then if there are 6 black and 4 red, the odds increase to 1 in 210 (6/10 x 5/9 x 4/8 x 3/7 x 2/6 x 1/5 = 1/210).

I think EVERYTHING in life is 50/50.

Either they will separate them correctly or they will not. There's only two possibilities.

neyak wrote

The psychological factor is hardly quantifiable

Not true, it's very quantifyable, and I might add extreamly important when designing patter for such an effect. Go for the "over a thousand" line instead of "1 in 1024" and some may think crikey in the thousands (ie 2000/3000/etc). Strange thing is your telling the truth both times but in general the audience as a whole will think the proberbility is higher with the first line. You also have the advantage of using a low number (ie comprihendable) to make them think of large numbers (uncompriheadable). This in itself will add to the intelectual confusion.
With manipulating figures to your best advantage with language, just look at the media , politics or advertising.

Given that 84.26% of statistics are made up , I'd say that it doesn't really matter as long as what you say sound plausible to your audience.

I recall reading in the blurb to one of the OOTW effects that the chances of turning a whole deck over and correctly predicting red or black was 4.2 billion to one (may be Cosmos).

Correct or not (and I also wasn't anywhere near to the top of the math class ), it sounded impressive and I've always used this when performing OOTW without anyone ever questionning it.

dat8962 wrote:I recall reading in the blurb to one of the OOTW effects that the chances of turning a whole deck over and correctly predicting red or black was 4.2 billion to one (may be Cosmos).

I was feeling bored so I thought I'd try and work it out (yes, I really was THAT bored ).

If we assume that there are 2 red and 2 black markers (as in the standard OOTW routine), leaving us with 24 red and 24 black cards to try and correctly place, the odds that we place them correctly are:

24/48 x 23/47 x 22/46 x 21/45 x 20/44 x 19/43 x 18/42 x 17/41 x 16/40 x 15/39 x 14/38 x 13/37 x 12/36 x 11/35 x 10/34 x 9/33 x 8/32 x 7/31 x 6/30 x 5/29 x 4/28 x 3/27 x 2/26 x 1/25 = errmmm ....

.... approx 1 in 32 000 000 000 000

I'm not too sure how to actually read this number lol . I think a billion is a thousand million, in which case the result reads as approx 1 in 32 thousand billion. Jeez, it might be better to say to your specs that the odds on them placing all the cards correctly are VERY high instead of confusing them .

hacker wrote:I guess you have a 50/50 chance on having the two piles of red and black cards but sometimes its just bad luck.

Unless once the card has been picked it is placed back in the deck this will not be the case.

Jeeps Moonbeam

That's way beyond my reckoning and those figures are almost magical in themselves

A billion is one thousand million although I think that the US calculate it as being 100 million.

Those are pretty impressive odds

moonbeam wrote:... approx 1 in 32 000 000 000 000

dat8962 wrote:A billion is one thousand million although I think that the US calculate it as being 100 million.

I'm pretty sure a billion is one thousand million and I'm in the US. I don't think it changes between UK and US. Our number system is the same.

I'm also pretty sure that the number moonbeam came up with is 32 TRILLION.

Well im not super statistic man but the order of cards doesnt bother much if you want 5 red and 5 blue. So im inclined to think that 2 xponent 5 would give you the right probability to get 5 of each.

Altho lying a bit on this subject should not bother much as almost nobody will be abble to calculated the probability themself while your doing the trick. Unless yo ask em to bring a calculator in your show and you feed em with time for calculations!

1 chance on 100 or 1000 should be convincing enuff imh.

Indeed Mr Pudding, I wasn't reading the post properly. My most humble apologies.

So yes, 1 in 2^n without any -1s.

However, if they know that they're sorting cards into colours, then they also know that not all cards are black or all are red, so they will distribute them slightly differenlty, so all calculations need to be reconsidered again because they're not dividing them up perfectly randomly. I think by now I agree with just make something up that sounds vaguely plausible.

I was always lousy at probability in maths lessons, but I think Yorkshire Pudding got the right answer.

I'm not actually sure if it matters if they know there are five of each colour, or not. I think that would be different, from a psychological point of view, if they didn't have an even split. Then the premise of the effect (card sorting) would suggest that some cards should be red, making it pretty much impossible for anyone to get them all right.

my OOTW patter goes something like "in scientific circles these tests are measured by percentage. 50% is seen as average, 75% as luck and anything, anything over 75% is seen as psychic." sometimes the numbers are different but you get the idea. i just love it when people nod knowingly at the made up rubbish and accept that scientists generally believe in luck and psychic ability.

Thanks for the help people.

I think I'll stick to "The odds of getting all these correct are just over 1 in a thousand"

Numbers are horrible, haha.

Thanks again.

Josh Clarke wrote:I'm pretty sure a billion is one thousand million and I'm in the US. I don't think it changes between UK and US. Our number system is the same.

I'm also pretty sure that the number moonbeam came up with is 32 TRILLION.

Not so, the US billion is much SMALLER than the UK billion! In the US, one billion is one thousand million (i.e., it has 9 zeros and equals 1,000,000,000). In the UK, one billion is one million million (i.e., it has 12 zeros and equals 1,000,000,000,000

However since all good things started out in Britain, I can clear up the argument by saying that we are right. God bless America.

Russ
www.smartmagic.co.uk