Probability Odds

[EuanC]

Don't know if this is the appropriate section for this...... A local pub runs a quiz & at the end it has it's own version of "Play Your Cards Right". The aim is to go through 14 cards saying if the next will be higher or lower. Nobody ever seems to manage. I was just wondering if anyone knows what the odds would be to predict 14 [higher/lower] correctly.

[pldcav]

I don't know if there's an exact answer, but I'd say less than 1%. At each card, the chance of making the right choice will vary between 0.94 (with an Ace or a King, there are 48 out of 51 cards higher/lower) and 0.47 (with a 7, there are 24 out of 51). Taking account of the cards already dealt will alter the odds somewhat, but suppose you had a 0.7 chance each time.  The chance of guessing right 13 times would be 0.7 ^ 13 which is about 0.009.

I reckon the pub's money is safe for a year or so!