{"id":177,"date":"2021-01-17T13:38:42","date_gmt":"2021-01-17T12:38:42","guid":{"rendered":"https:\/\/www.bolukan.nl\/?p=177"},"modified":"2021-01-17T15:30:29","modified_gmt":"2021-01-17T14:30:29","slug":"the-crew-kosmos-game-statistics","status":"publish","type":"post","link":"https:\/\/www.bolukan.nl\/?p=177","title":{"rendered":"The Crew (Kosmos) – game statistics"},"content":{"rendered":"\n

In this article I record the calculated game statistics for The Crew if played with 4 players.<\/p>\n\n\n\n

The Crew<\/a> is a cooperative card game by designer\/author Thomas Sing and artist Marco Armbruster, published by Kosmos. The game was awarded the Kritikerpreis 2020<\/a>.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Number of card distributions is 1,2 * 10^21<\/strong><\/p>\n\n\n\n

For one color the number of distributions is:
#players ^ #cards<\/code>
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<\/code>
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.<\/p>\n\n\n\n

With the restriction of each player starting with 10 cards, the possible distributions is limited to
#cards! \/ #cardsperplayer! ^ #players<\/code>
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.<\/p>\n\n\n\n

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).<\/p>\n\n\n\n

Distribution of one color<\/strong><\/p>\n\n\n\n

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.<\/p>\n\n\n\n

# cards<\/th>#<\/th>%<\/th><\/tr><\/thead>
0<\/td>19.683<\/td>7,5%<\/td><\/tr>
1<\/td>59.049<\/td>22,5%<\/td><\/tr>
2<\/td>78.732<\/td>30,0%<\/td><\/tr>
3<\/td>61.236<\/td>23,4%<\/td><\/tr>
4<\/td>30.618<\/td>11,7%<\/td><\/tr>
5<\/td>10.206<\/td>3,9%<\/td><\/tr>
6<\/td>2.268<\/td>0,9%<\/td><\/tr>
7<\/td>324<\/td>0,1%<\/td><\/tr>
8<\/td>27<\/td>0,0%<\/td><\/tr>
9<\/td>1<\/td>0,0%<\/td><\/tr><\/tbody>
TOTAL<\/td>262.144<\/td>100,0%<\/td><\/tr><\/tfoot><\/table>
Number of color cards a player can expect to start with<\/em><\/figcaption><\/figure>\n\n\n\n

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%.<\/p>\n\n\n\n

Players<\/th>#<\/th>%<\/th><\/tr><\/thead>
9-0-0-0<\/td>4<\/td>0,0%<\/td><\/tr>
8-1-0-0<\/td>108<\/td>0,0%<\/td><\/tr>
7-2-0-0<\/td>432<\/td>0,2%<\/td><\/tr>
6-3-0-0<\/td>1.008<\/td>0,4%<\/td><\/tr>
5-4-0-0<\/td>1.512<\/td>0,6%<\/td><\/tr>
7-1-1-0<\/td>864<\/td>0,3%<\/td><\/tr>
6-2-1-0<\/td>6.048<\/td>2,3%<\/td><\/tr>
5-3-1-0<\/td>12.096<\/td>4,6%<\/td><\/tr>
4-4-1-0<\/td>7.560<\/td>2,9%<\/td><\/tr>
5-2-2-0<\/td>9.072<\/td>3,5%<\/td><\/tr>
4-3-2-0<\/td>30.240<\/td>11,5%<\/td><\/tr>
3-3-3-0<\/td>6.720<\/td>2,6%<\/td><\/tr>
6-1-1-1<\/td>2.016<\/td>0,8%<\/td><\/tr>
5-2-1-1<\/td>18.144<\/td>6,9%<\/td><\/tr>
4-3-1-1<\/td>30.240<\/td>11,5%<\/td><\/tr>
4-2-2-1<\/td>45.360<\/td>17,3%<\/td><\/tr>
3-3-2-1<\/td>60.480<\/td>23,1%<\/td><\/tr>
3-2-2-2<\/td>30.240<\/td>11,5%<\/td><\/tr><\/tbody>
TOTAL<\/td>262.144<\/td>100,0%<\/td><\/tr><\/tfoot><\/table>
Distributions of cards over 4 players<\/em><\/figcaption><\/figure>\n\n\n\n

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.<\/p>\n\n\n\n

 <\/td># rounds<\/td> <\/td> <\/td><\/tr>
# cards<\/td>0<\/td>1<\/td>2<\/td><\/tr><\/thead>
9<\/td>100%<\/td>0%<\/td>0%<\/td><\/tr>
8<\/td>100%<\/td>0%<\/td>0%<\/td><\/tr>
7<\/td>100%<\/td>0%<\/td>0%<\/td><\/tr>
6<\/td>78%<\/td>22%<\/td>0%<\/td><\/tr>
5<\/td>56%<\/td>44%<\/td>0%<\/td><\/tr>
4<\/td>38%<\/td>62%<\/td>0%<\/td><\/tr>
3<\/td>26%<\/td>62%<\/td>12%<\/td><\/tr>
2<\/td>17%<\/td>54%<\/td>29%<\/td><\/tr>
1<\/td>12%<\/td>88%<\/td>0%<\/td><\/tr>
0<\/td>100%<\/td>0%<\/td>0%<\/td><\/tr><\/tbody><\/table>
Chance all players can follow suit, if a player starts with a number of cards<\/em><\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"

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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-177","post","type-post","status-publish","format-standard","hentry","category-esp8266"],"_links":{"self":[{"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=\/wp\/v2\/posts\/177","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=177"}],"version-history":[{"count":6,"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=\/wp\/v2\/posts\/177\/revisions"}],"predecessor-version":[{"id":184,"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=\/wp\/v2\/posts\/177\/revisions\/184"}],"wp:attachment":[{"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bolukan.nl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}