talkmagic.co.uk

Just lie! And make the lie a bit bigger than it actually is. The specs are not going to sit down and work out the actual odds.

For what it is worth

1. In practical terms the UK has come around to the US view that a billion is 1000 million. We do not yet have the word trillion.

2. Trying to quote probabilities is a real problem unless you are an expert. A Mum recently spent years in jail in the UK because an expert witness said that the probability of two cot deaths was 1 in 'huge figure', whereas is was in fact several orders of magnitude less. The expert had had no statistical or mathematical training.

Much better to keep it vague ('One in a thousand') than invent something which is downright wrong, at least if you want to keep credibility with those who do understand such things. If on the other hand, you are indifferent, make the figures up.

Bigtone53 wrote:In practical terms the UK has come around to the US view that a billion is 1000 million. We do not yet have the word trillion.

That decision was a sad legacy of, I believe, a previous Labour Government. There existed at the time, and still exists today, a perfectly good English word to describe one thousand million - Milliard. I guess the devaluation of one million million comes under the heading of 'progress'

Mandrake wrote:I guess the devaluation of one million million comes under the heading of 'progress'

Wait for the devaluation of those other fine big numbers, google and googleplex. But one number cannot be touched. It is the biggest known number with a real purpose, Skewes' Number.

Next thing you know, they'll be devaluing infinity and there will we be ?

in (something else)

The probability that the spectator get OOTW right (without the magician exercising his magical powers) depends on the spectators behavior.

If the spectator always deals piles of slightly uneven size, s/he would of course NEVER get a correct red/black separation.

If the spectator uses a coin to determine where to put each card, the spectator is correct with probability (1/2)^n where n is the number of cards to be guessed.
It is curious, but it is irrelevant how many red and black cards there are in the deck from the start.

The probability the spectator guess each of the 52 cards colors correct is (1/2)^52 which is 1 : 4.503.599.627.370.496

If each person in the world tried the experiment and were doing it for 10 years it is still unlikely anyone would get it right.

Assume that we randomly place 10 cards from a deck of cards into two piles with 5 cards in each. Then the probability that all 5 cards in the left pile are red and all cards in the right pile are black is 42! (26!)^2) : 52! (21!)^2 which is close to 1 : 923 (not 1 : 1024 like a rough calculation would suggest).

It we use a coin flip to guess the color of each of the 10 cards, the probability that we guess them all correct is 1 : 1024

Different versions of OOTW have slightly different probabilities of being correct (assuming of course that the magician turns off his magical powers).

The classical version with 4 divider cards it is correct with probability (1/2)^48

Including the mental force (p=25% if no forcing skills) Derren Browns version is correct with probability (1/2)^52 i.e with a probability that is roughly 4 times as unlikely as the classical version.

Including the mental force (p=50% if no forcing skills) my version of OOTW (see secret section) is correct with probability 48 x (1/2)^48 i.e. it is roughly 50 times as unlikely like the classical version.

Willards and Falkensteins version does not involve any mental force and is roughly 12 times as unlikely as the classical version.

Other versions (e.g. Ammar's suggestion of two spectators selecting a special card in advance) appear less likely than the ordinary version of OOTW (since it appear very strange that the two selected cards end up in the wrong section). However, objectively speaking this happens with exactly the same probability as the classical OOTW.