Here's more detail on first turn odds, focusing in on reasonable numbers of players.
These are for standard games where the discard pile is seeded, and where the strategy is to draw if neither the tavern nor the discard improve your score by as much as 5. (There's no clear reason why either of these should matter here, but I mention them for completeness.) To get random numbers, I used the Mersenne Twister algorithm as implemented by the TRandom3 ROOT library. "33%" and "67%" really mean that, not 1/3 and 2/3. To find these numbers, I ran as many as 10 billion trials; less than this is sometimes not sufficient to resolve which of consecutive scores is the correct boundary.
| # of players | Sail with ≤ this ⇒ skunked < 1% of the time | Sail with ≤ this ⇒ skunked < 10% of the time | Sail with ≤ this ⇒ skunked < 33% of the time | less ⇒ less than ½; more ⇒ more than ½ | Sail with ≥ this ⇒ skunked > 67% of the time | Sail with ≥ this ⇒ skunked > 90% of the time | Sail with ≥ this ⇒ skunked > 99% of the time |
|---|---|---|---|---|---|---|---|
| 2 | 8 | 15 | 22 | 26 / 27 | 31 | 39 | 49 |
| 3 | 6 | 12 | 18 | 21 / 22 | 25 | 31 | 38 |
| 4 | 6 | 11 | 16 | 19 / 20 | 22 | 27 | 33 |
| 5 | 6 | 10 | 15 | 17 / 18 | 21 | 25 | 30 |