Beggar My Neighbour (also known as Strip Jack Naked) can last forever

Here’s an article that discusses this (and also briefly, the probability of Klondike being solvable.)

Obviously have too much time on your hands but i really enjoyed reading it and i like the way you think!
and from now on i’m not going to be wasting my time dealing out the cards in 13 separate piles of 4 but instead just use the pile of 52 cards i have in my hand!

or better still, play classic solitaire instead!

Andrew,

You haven’t taken into account the chance that the judge has bet on you and has detected that you are going to lose. Given you are likely to lose more often than you win, perhaps this could be considered more likely?

If we are taking this sort of issue into account, I would object to being asked to shuffle on completely different grounds. I have wasted enough time getting to the finals of this silly competition, and I wouldn’t be impressed by any delaying tactics that prevent me from getting back to viewing Survivor: Antarctic.

Your random number generator doesn’t provide the full experience; you don’t know how close you would have gotten to winning before having your hopes dashed. Instead, you need to generate four random numbers, mod 52, 51, 50 and 49. These tell you how far up the deck the last king was.

You can then include a clock (configurable for your average play speed) which tells you how much time you would have wasted before winning a game. The actual gameplay can be done by computer much faster, saving you time in which you can watch Survivor:Antarctic.

On a different note, I must agree with your friends on the “shuffling halfway through” issue; there is a small but non-zero probability that the reason you are being offered a shuffle is that the person offering it has detected that you are going to win, but has bet on your opponent. Your analysis, as you note, is correct if you trust everyone involved.