Great question! I actually looked into this recently using simulations of 200,000 turns per card type.
Short answer:
roughly 1 turn in 2,000 can end the game on the spot, so rare enough that most players will never see it, but not astronomically rare either. If you play, say, 10 turns a session with 4 players, a group would expect to see one roughly every 50 sessions. So "I've seen one already" is totally plausible and not that lucky!
A few nuances though:
- My simulations assume optimal play: an experienced player who knows when to push their luck and when to bank their score. Casual players would have a lower chance (see this post for more context).
- Only a handful of cards can even produce a 6,000+ score: the Pirate card (doubles everything, the biggest contributor), and the Coin or Diamond cards (which give you a 9th die, opening the door to a 9-of-a-kind for instant win), and the After the Storm card (only coins and diamonds score, but doubled, so a lucky all-coins-and-diamonds roll can go very high). All other cards are simply capped below 6,000 no matter how lucky the roll. All other cards are simply capped below 6,000 no matter how lucky the roll.
If you're curious, you can see the full score distributions for every card here:
score distributions chart. Hover over any bubble to see how likely each score is. The Pirate card row is a good one to look at to understand why it's the main path to a one-turn win.
