The Crew (Kosmos) – game statistics
In this article I record the calculated game statistics for The Crew if played with 4 players.
The Crew is a cooperative card game by designer/author Thomas Sing and artist Marco Armbruster, published by Kosmos. The game was awarded the Kritikerpreis 2020.
The players need to complete 50 different missions. The card deck consists of 4 sets (blue, green, purple and yellow) of 9 cards numbered from 1 to 9 and 1 set of 4 rocket cards (black) numbered from 1 to 4. The black cards are the trump cards. You have to follow suit (play the same color of the first card of each trick) but you can play a low card if you can’t follow suit. The missions are variations of specific cards a specific player needs to win under specific conditions.
Number of card distributions is 1,2 * 10^21
For one color the number of distributions is:#players ^ #cards
For a common color with 9 cards the number of distributions is 262.144 and for the 4 black cards this is limited to 256. For the complete deck the number of all possible distributions of 40 cards to 4 players is also#players ^ #cards
4^40 is equal to 4^4 * (4^9)^4, which is equal to 256 * 262.144^4, which is equal to 1.208.925.819.614.630.000.000.000 = 1,2*10^24. However, this calculation does not restrict the number of cards per player and thus the last calculation is irrelevant for our purposes.
With the restriction of each player starting with 10 cards, the possible distributions is limited to #cards! / #cardsperplayer! ^ #players
This limits the number of possibilites to 4.705.360.871.073.570.000.000 = 4,7*10^21. This is 0,4% of all distributions.
As the player with the highest card (black 4) is the commander and commences the game, the number of possibilities to simulate all card distributions needs to be divided by #players, this is 1.176.340.217.768.390.000.000 (1,2*10^21).
Distribution of one color
A player has most chance (30%) to get 2 cards of a specific color and in 7,5% of the cases starts the game with none.
| # cards | # | % |
|---|---|---|
| 0 | 19.683 | 7,5% |
| 1 | 59.049 | 22,5% |
| 2 | 78.732 | 30,0% |
| 3 | 61.236 | 23,4% |
| 4 | 30.618 | 11,7% |
| 5 | 10.206 | 3,9% |
| 6 | 2.268 | 0,9% |
| 7 | 324 | 0,1% |
| 8 | 27 | 0,0% |
| 9 | 1 | 0,0% |
| TOTAL | 262.144 | 100,0% |
The chance a color can be followed by all players 2 tricks is 11,5% (3-2-2-2 distribution), 1 trick 59,6% and the chance at least one player can’t follow suit is 28,9%.
| Players | # | % |
|---|---|---|
| 9-0-0-0 | 4 | 0,0% |
| 8-1-0-0 | 108 | 0,0% |
| 7-2-0-0 | 432 | 0,2% |
| 6-3-0-0 | 1.008 | 0,4% |
| 5-4-0-0 | 1.512 | 0,6% |
| 7-1-1-0 | 864 | 0,3% |
| 6-2-1-0 | 6.048 | 2,3% |
| 5-3-1-0 | 12.096 | 4,6% |
| 4-4-1-0 | 7.560 | 2,9% |
| 5-2-2-0 | 9.072 | 3,5% |
| 4-3-2-0 | 30.240 | 11,5% |
| 3-3-3-0 | 6.720 | 2,6% |
| 6-1-1-1 | 2.016 | 0,8% |
| 5-2-1-1 | 18.144 | 6,9% |
| 4-3-1-1 | 30.240 | 11,5% |
| 4-2-2-1 | 45.360 | 17,3% |
| 3-3-2-1 | 60.480 | 23,1% |
| 3-2-2-2 | 30.240 | 11,5% |
| TOTAL | 262.144 | 100,0% |
The player with 9, 8, 7 or 0 cards knows not everybody can follow suit. With 1 card you have 88% chance everybody follow suit once. Players with 2 or 3 cards can consider the possibility all players will follow suit two tricks.
| # rounds | |||
| # cards | 0 | 1 | 2 |
| 9 | 100% | 0% | 0% |
| 8 | 100% | 0% | 0% |
| 7 | 100% | 0% | 0% |
| 6 | 78% | 22% | 0% |
| 5 | 56% | 44% | 0% |
| 4 | 38% | 62% | 0% |
| 3 | 26% | 62% | 12% |
| 2 | 17% | 54% | 29% |
| 1 | 12% | 88% | 0% |
| 0 | 100% | 0% | 0% |