Playing with the pack of cards on my desk, something just happened that I didn't expect!
Look at the deck with the cards face-up. Here's a rule: look at the top card. Draw that many cards from the deck. Repeat until the deck is empty.
I did this, and dealt out exactly the right number of cards (at the end, I had 3 cards left and the top card was a 3).
What's the probability of this happening?
@christianp If each card appears randomly with replacement (magically?) and you reach a pile with k cards left, let P_k = probability you won. P_k = 0 if k < 0 (you ran out of cards in last draw), P_0 = 1 (you won!), and otherwise P_k = sum_{i=1}^13 P_{k-i}/13. A quick computational experiment shows that for large k like k=52, P_k appears to converge to 1/7.
Quick question: how do you consider the effect that you only have 4 suits for every card?
@sojournTime @christianp I'm not considering it. That's what I meant about "with replacement". It's an assumption that makes the mathematics easier but also less accurate for the actual problem.