bucky310 wrote:

insomniac392 wrote:

I agree, it was most definitely just a coincidence. Assuming that every spectator randomly selects one card,* then the probability of them selecting the force card is 1/52, which is about 2%. Thus, you could expect this to happen about once every 50 times you perform this trick.

~ Kyle

* As people are more prone to picking more recognizable cards, such as the ace of spades or hearts, as opposed to say the 4 of clubs, I doubt the distribution is truly random. Consequently, if your force card is an ace or king, chances are that the probability would be slightly higher than 1/52.

The first section works out, of course, only if you keep using the same card

Strangely enough, although counter-intuitive at first, this is actually not the case -- you could choose a different force card

*every time* and, assuming the spectators' choices are truly random, the probability remains the same. This is because the probabilities of each event are independent (i.e. each individual outcome has no influence on past/future events). Thus, regardless of the choice of the force card, one could expect a random spectator to choose it about 2% of the time.

Another way of looking at the problem is to consider the following related problem. Suppose we randomly shuffle a 52 card deck and predict that the top card will be the ace of spades. Because the shuffle is random, the probability that the top card will be the ace of spades is 1/52... but there is nothing special about the ace of spades -- the probability that any given card will be on top is 1/52. So the probability that

*any* card we choose will end up on top is 1/52, and hence we should expect this to happen about 2% of the time.

~ Kyle

P.S. Curiously enough, in the above exercise, there is nothing special about the position of the top card either... we could change our chosen position and the outcome would remain the same!