[fmlclzwx] experiencing e

Euler's game of coincidence (previously) as a solitaire game involving no skill:

separate out the clubs into one pile and diamonds into another pile.  (the rest of the cards will not be used.)  shuffle at least one of the two piles well, and place both piles face down next to each other.  simultaneously flip the top card of each pile and examine if the numbers (ranks) match.  if they match, you have lost and the game is over.  if not, keep flipping successive pairs.  if you make it through all 13 pairs without matching, you have won.

the probability of winning is approximately 1/e = 0.368 .  counterintuitively, the probability does not change with larger decks; it converges asymptotically very quickly to 1/e.  the exact probability with 13 pairs is a rational number which differs from 1/e by less than one part in 14! ~= 10^11.  (it would therefore take roughly 10^22 deals to estimate 1/e to that precision: not an efficient method of computing e.)

it is also counterintuitive that only one of the piles needs to be shuffled.  the other pile could even be in rank order.  you could skip this pile and simply say the ranks in order while dealing out the shuffled suit.  however, I think it's easier to visually detect a match using two piles.

repeatedly playing the game always shuffling the same suit will cause cards in that suit to become more worn than the other suits.  this may be problematic if the cards will also be used in other games.  perhaps rotate among suits.

we use suits of different colors so that if a card should accidentally migrate between piles, it will be easy to spot.  we start with piles face down then flip cards so that there are fewer face-up cards to look at, less distractions that might cause missing a match.  (we could have started with piles face up.)

what is a good way to shuffle just 13 cards?  riffle shuffle is hard to do with so few cards.

add a joker to each suit to make it 14 pairs of cards.

did a play test with only 7 pairs and it also worked fine.