{"id":117165,"date":"2017-05-01T10:00:30","date_gmt":"2017-05-01T08:00:30","guid":{"rendered":"https:\/\/mygaming.co.za\/news\/?p=117165"},"modified":"2017-05-01T11:24:37","modified_gmt":"2017-05-01T09:24:37","slug":"terra-mystica-blew-my-mind-so-i-did-the-maths","status":"publish","type":"post","link":"https:\/\/mygaming.co.za\/news\/entertainment\/117165-terra-mystica-blew-my-mind-so-i-did-the-maths","title":{"rendered":"Terra Mystica blew my mind, so I did the maths"},"content":{"rendered":"

I recently picked up a copy of Terra Mystica, a highly rated board game that has stubbornly remained in Board Game Geek’s all-time top five<\/a><\/strong> for years.<\/p>\n

The base game supports 2-5 players and includes 14 factions, each with a unique set of abilities.<\/p>\n

As a game geek, I wondered how you play-test something with so many combinations.<\/p>\n

This led to the question: How many faction combinations are there in the game?<\/p>\n

For those who know binomial coefficients, calculating the answer might sound simple – but Terra Mystica throws a spanner in the works.<\/p>\n

When you choose a faction, you eliminate another<\/h3>\n

Terra Mystica has 14 factions, or, more accurately, 7 pairs of factions.<\/p>\n

Each couple is a denoted by a colour, and when you choose one faction, you eliminate the other in the couple.<\/p>\n

The implementation is simple – double-sided print. To choose a faction, players must take a board which has their faction\u2019s features printed on one side.<\/p>\n

The other faction in the couple is printed on the other side of the board.<\/p>\n

The factions and their colours are:<\/p>\n

    \n
  1. Yellow:<\/strong> Fakir, Nomads<\/li>\n
  2. Red:<\/strong> Chaos Magicians, Giants<\/li>\n
  3. Blue:<\/strong> Swarmlings, Mermaids<\/li>\n
  4. Grey:<\/strong> Dwarves, Engineers<\/li>\n
  5. Brown:<\/strong> Halflings, Cultists<\/li>\n
  6. Black:<\/strong> Alchemists, Darklings<\/li>\n
  7. Green:<\/strong> Auren, Witches<\/li>\n<\/ol>\n

    For the mathematics, this choose-one-eliminate-one mechanic complicates things somewhat.<\/p>\n

    \"Terra<\/a><\/p>\n

    \n

    The maths<\/h3>\n

    The first player to choose a faction has a selection of 7 faction boards, the next player 6, and so on.<\/p>\n

    Multiplied together, this gives you the number of permutations.<\/p>\n

    When you multiply incrementally-decreasing numbers,\u00a0you get a factorial. There are seven factorial (7!) total permutations of the faction boards. This equals 5,040 permutations.<\/p>\n

    \"Terra<\/a><\/p>\n

    \n

    However, you don\u2019t have seven players in a game. Four players, for example, results in 7 \u00d7 6 \u00d7 5 \u00d7 4.<\/p>\n

    To get rid of 3 \u00d7 2 \u00d7 1 in the original calculation, divide by 3!. This equals 840 permutations in a four-player game.<\/p>\n

    \"Terra<\/a><\/p>\n

    \n

    This is what the permutation calculation looks like written as a formula.<\/p>\n