Trix itself is a very wide game, being able to be played in various different ways depending on how you want to. You can read up about it in any search result that comes up when you hit Trix Complex on Google. I'm only going to discuss about the Trix - Complex - Partner version, easily the most widely played and best. The other boring versions are for people who chose not think, count, and use their mind a little bit more to make it more interesting. And that is actually not a very bold statement to be making here, it really is that amazing!
"The best of card games are played by 4 players." - Me
I say 4 players because there are 4 suits, and here each player gets 13 shuffled cards so that uses the entire deck and gives you the most out of it. For those who are really new to this, let me brief you up. We use a standard 52 card deck (without extra Joker cards) which comprises of four suits, namely Spades, Hearts, Clubs, and Diamonds (as seen on your background). Each suit has 13 cards: A-K-Q-J-10-9-8-7-6-5-4-3-2 (descending order).
The objective is to have total positive points at the end of the game (4th kingdom). Trix is played in kingdoms, each player gets one kingdom comprising of 2 rounds in it, namely Trix (yes, the in-game round is also called Trix which gives you positive points), and Complex (negative points).
In the first round of the kingdom, the player gets to look at only their own hand and choose the game they want to play (Trix or Complex), and next they play the other and complete their kingdom. Repeat four times, or three, if the score of one team is too low to come back from in one kingdom.
POINTS - Each round contains an exact total of 500 points. Positive in Trix, and negative in Complex.
In Trix, the cards do not have individual points. It's just a matter of who finishes their hands first while following the rules of the game.
1st - 200 points
2nd - 150 points
3rd - 100 points
4th - 50 points
Breakdown: 200+150+100+50 = 500 no matter who gets which rank. You share 500 points between the 2 teams.
In Complex, the cards themselves have points as you collect them. They are as follows:
King of Hearts: -75 points
All the Queens: -25 points each
Every Diamond card: -10 points each
Every hand that you collect: -15 points each
In the end you count the total of all the hands collected by the team.
Breakdown:
13 Collections x 15 points = 195
13 Diamonds x 10 points = 130
4 Queens x 25 points = 100
1 King of Hearts x 75 points = 75
195+130+100+75 = 500 Points in total
While counting, always count all the cards one team has taken (including the doubled values) and then only give positive points if the opponents have taken doubled cards in that round. 25 for each Q and 75 for the King of Hearts. It's important to not mess it up with the positive and negative points. Do not give yourself +50 for giving them a doubled Queen, or +150 for giving them the doubled King.
For example, if you took a doubled Q and a normal Q but gave them the other 2 Queens and a doubled King, you count for yourself the negatives first. Count -25 for the normal one and -50 for the doubled Q you took. Finally add a +75 only to your score because they took the doubled King. No other additions as counting both teams scores might get confusing.
I call it mathematically brilliant because of how it was designed to be always pivoted around 500 points. In each round you either get 500 positive or 500 negative points, making the total score sum of (both teams) each kingdom as Zero. Try to count the score of one team in a round, and the other team will automatically be the remaining amount from 500. Positive or negative, depending on Trix or Complex respectively.
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