I hope this question fits the site, if not feel free to flag.
In the place I live there's a simple game of cards that you play on your own. Cards are 40, let's say A1 ... A10 , B1 ... B10 , C1 ... C10 , D1 ... D 10. The game goes as follows:
You dispose all of the 40 cards on the table, with their face down. You have to create a 4x10 matrix, like below. Mentally, you assign each row to a type (A, B, C or D) and each column to a number (1...10).
cols: _ 1 _ 2 _ 3 _ 4 _ 5 _ 6 _ 7 _ 8 _ 9 _ 10 row A | row B | HERE YOU HAVE THE 40 CARDS FACE-DOWN row C | row D | X
Note that each card now, like the one I checked with a X, in addition to having its value (which you can't see because it's down) is strictly connected to another card through its position:
Xcan identify the value
D2with its position.
You choose one card randomly, let's say
You flip it and see its real value, let's say
You move to position
B7and flip that card,
cols: _ 1 _ 2 _ 3 _ 4 _ 5 _ 6 _ 7 _ 8 _ 9 _ 10 row A | row B | Y row C | row D | B7
You win if you manage to flip all the cards. You lose if at some point the value on the card you just flipped, points to a position which is already turned up. For example, you would lose immediately if
Y has value
D2 (it happens).
What is the probability one is going to lose?
This is probably a question one could solve with just some basic notions, but I don't have any.