I got hooked on Piraten Kapern! (known in French as Mille Sabords!, which I prefer) a while back and, out of pure curiosity about how the game actually works, ended up building a solver that computes the mathematically optimal strategy for every possible situation in a turn: which dice to keep, which to reroll, and when to stop.
The goal here is not to "cheat" (in a live game you cannot consult this in real time anyway...).
It is more about satisfying a genuine curiosity: what does perfect play actually look like? And what does it tell us about the game itself?
You can try it yourself with this web app!
How it works
At any point in a turn you face a decision: keep these dice, reroll those, or stop. The solver finds the choice that maximises your expected score, which you can think of as follows: if you played that exact situation 1,000 times and averaged your score across all of them, which choice gives the highest average? The solver finds that answer for every possible situation, using an algorithm called value iteration.
The result is exact, not an approximation or a simulation.
Source code for those interested
Expected score per fortune card
**SPOILER**
The list below shows, for each fortune card, the average score a perfect player would get across many turns. Cards are sorted from strongest to weakest.
Score distributions
The expected score is a useful summary, but it hides a lot. For more details, see the full score distributions for all fortune cards (unfortunately I cannot attach the image here as the board quota has been reached already).
Each row is one card, sorted by expected score. Each circle represents a 100-point scoring range: bigger means more likely under optimal play. The triangle marks the average.
Two things stand out when looking at all 15 cards together. First, every card has a genuinely distinct shape: Zombie is nearly binary (two circles, 0 or 1,200), Pirate spreads wide to the right, Pirate Ship (4 swords) has a spike on the negative side. Each card feels different to play, and the distributions make that concrete. Second, despite all this variety, the expected scores are spread fairly evenly with no huge gaps and no obviously broken or pointless card. That is not easy to achieve across 15 mechanically distinct cards, and it says a lot about the quality of the design.
Using the web app
At any point in a turn, click the lightbulb button to see the optimal move, or open the full strategy table to see the expected score for every possible state from your current position. Note that you can also "edit" manually the dice and the fortune card (click the "pencil" button at the top, enter your dice combination, then go back to "play" mode by clicking on the "game boy" button to enable the "hint" button).
Curious to know the community's opinion on these findings? What do you find most surprising in these numbers? e.g. does the Guardian ranking match your intuition?
The goal here is not to "cheat" (in a live game you cannot consult this in real time anyway...).
It is more about satisfying a genuine curiosity: what does perfect play actually look like? And what does it tell us about the game itself?
You can try it yourself with this web app!
How it works
At any point in a turn you face a decision: keep these dice, reroll those, or stop. The solver finds the choice that maximises your expected score, which you can think of as follows: if you played that exact situation 1,000 times and averaged your score across all of them, which choice gives the highest average? The solver finds that answer for every possible situation, using an algorithm called value iteration.
The result is exact, not an approximation or a simulation.
Source code for those interested
Expected score per fortune card
**SPOILER**
The list below shows, for each fortune card, the average score a perfect player would get across many turns. Cards are sorted from strongest to weakest.
- Pirate (score x2): 1,158 pts
- Guardian (reroll one skull once per turn): 905 pts
- After the Storm (one reroll only; coins and diamonds score x2; no Skull Island): 805 pts
- Coin (extra die, starts as a coin): 784 pts
- Diamond (extra die, starts as a diamond): 784 pts
- Animals (monkeys and parrots form one combined combo): 735 pts
- Treasure Island (held dice score even if you bust): 680 pts
- No card (baseline): 579 pts
- Peace (any sword at the end: -1,000 pts per sword): 521 pts
- Pirate Ship, 2 swords (hit quota: +300 pts; miss: -300 pts): 443 pts
- Zombie Attack (5+ swords: 1,200 pts; else 0): 436 pts
- Skull x1 (starts with 1 extra locked skull): 346 pts
- Pirate Ship, 3 swords (hit quota: +500 pts; miss: -500 pts): 249 pts
- Skull x2 (starts with 2 extra locked skulls): 113 pts
- Pirate Ship, 4 swords (hit quota: +1,000 pts; miss: -1,000 pts): -156 pts
- Pirate at 1,158 pts is the strongest card, as most players probably expect. The multiplier compounds on top of already-good dice, which is very powerful.
- Guardian at 905 pts is the one that surprised me the most. A single skull reroll sounds like a minor perk, but it dramatically extends how long you can safely push your luck.
- Pirate Ship (4 swords) is the only card with a negative expected score. Even perfect play cannot save you on average. The -1,000 penalty is just too punishing given how hard the quota is to hit.
Score distributions
The expected score is a useful summary, but it hides a lot. For more details, see the full score distributions for all fortune cards (unfortunately I cannot attach the image here as the board quota has been reached already).
Each row is one card, sorted by expected score. Each circle represents a 100-point scoring range: bigger means more likely under optimal play. The triangle marks the average.
Two things stand out when looking at all 15 cards together. First, every card has a genuinely distinct shape: Zombie is nearly binary (two circles, 0 or 1,200), Pirate spreads wide to the right, Pirate Ship (4 swords) has a spike on the negative side. Each card feels different to play, and the distributions make that concrete. Second, despite all this variety, the expected scores are spread fairly evenly with no huge gaps and no obviously broken or pointless card. That is not easy to achieve across 15 mechanically distinct cards, and it says a lot about the quality of the design.
Using the web app
At any point in a turn, click the lightbulb button to see the optimal move, or open the full strategy table to see the expected score for every possible state from your current position. Note that you can also "edit" manually the dice and the fortune card (click the "pencil" button at the top, enter your dice combination, then go back to "play" mode by clicking on the "game boy" button to enable the "hint" button).
Curious to know the community's opinion on these findings? What do you find most surprising in these numbers? e.g. does the Guardian ranking match your intuition?
