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 That's single player blackjack with 52 instead of 21, innit?
@christianp Since the deck is shuffled you can transpose the "look at the next card" and "remove the required number of cards" steps. This means it's equivalent to drawing cards from the top until they either sum to 52 (success) or higher (failure).
This doesn't really give a full answer, only simplifies the problem a little.
@timorl ah, that's a useful insight, thanks
@timorl is it?