Triumvirate is a 2-player-only trick-taking game. That sounds weird. At least I have not heard of "2-player-only" and "trick-taking" linked together before this. Surprisingly it works quite well. There's no simple way to give a brief overview of gameplay. I will forge ahead and describe the whole thing.
The deck has 27 cards in 3 suits (colours), numbered 0 to 8. At the start of the game all but five cards are dealt out. Like most trick-taking games, the leading player plays a card, and the other player must follow suit if possible. When you win a trick, you don't claim the cards. You just become the next leading player. The trick played remains at the centre of the table, to keep count of how many tricks of each colour has been played. The winning card determines the winning colour. When a colour reaches three tricks at the centre of the table, a hand ends. A disc of the winning colour is placed onto the gameboard. Each player secretly sets aside a card for potential scoring. Cards numbered 3, 5, and 7 are scoring cards. They are worth points if at game end the winning colour (the one with 3 discs placed onto the board) matches them.
So the game is played over a few hands. At the conclusion of each hand, a disc will be added to the gameboard, and two cards will be secretly removed from the game by the players. Players keep their hand of cards. Other cards, including those previously not dealt, are reshuffled and dealt out again, leaving three undealt (as opposed to five in the first hand). This means players can quite easily count cards. They can see all the cards that have been played in the previous hand. There is some uncertainty in those three undealt cards, so you can't be 100% sure of what cards your opponent may be holding. The cards that have been set aside by your opponent are an uncertainty too, but you can try to guess what colour your opponent is going for by his card play. Cards set aside need not be scoring cards. Non scoring cards can be set aside too, just that they won't be worth points, but they can help in manipulating the card pool, and maybe even in confusing your opponent.
When one colour has its third disc placed onto the board, the game ends. Both players reveal their secret cards, and only scoring cards in the winning colour count. Whoever has more points wins.
One special case is the 0 cards. Although they are smallest in their own colours, they trump over all cards of other colours. You can use a red 0 to trump a black 6, even if you have other black cards in hand. This is an important consideration during the game.
The rules are mostly simple, but the implications of your actions are not immediately apparent. The deck size is small so cards are easy to count, if you are willing to put in the effort. The two cards that are set aside at the end of every hand has a big impact to the card pool. It is tempting to set aside many scoring cards of the colour (or colours) you hope will win, but that will weaken the colour. Every round, by watching what cards come out, you can get a good feel of what cards are still in circulation and what cards your opponent have probably set aside for scoring. At least that was the case in my first game. I think at higher skill levels, players can better conceal their scoring cards and also confuse their opponents.
When I played, my approach was mostly quite tactical and short-sighted. I tried to save a scoring card to be set aside every round, and as the game end approached, I tried to push for the colour in which I had the most scoring cards. As I played, I realised that the card pool was greatly impacted by the cards that were set aside, but I never got around to experimenting with manipulating the card pool. I felt I have just scratched the surface of the strategies of this game. I felt there should be tactics in deciding how quickly to let a hand end, so that few cards are revealed. There should be tactics in holding certain cards from hand to hand. There should be tactics in setting aside cards which are not scoring cards. There should also be techniques in guessing what your opponent is trying to do.
I would group Triumvirate with classic games such as Bridge. Rules are minimalistic, but there are many techniques and tactics involved. One thing that turns me off from these games is the effort required to play well. I always feel (but I may be wrong) that these games take significant effort to learn to play well and to better appreciate them. Something like Go, Chess. Triumvirate has luck, like Bridge, but there is much skill involved too. My gut feel is this is a kind of game that can be played competitively, and there are different skill levels that players can achieve. I feel nervous with these games because I always feel I'm not good enough, and I'm too lazy to put in enough effort so that I can get to a "good enough" skill level. It's quite chicken and egg. Compare this to Eurogames, even complex ones, or conflict games. Sure, these boardgames have many more rules, and they have strategy too, but they don't give me this bare, spartan, merciless feeling, like l'm a gladiator facing another gladiator both wearing only loincloths, and armed with short swords and no shields. Hmmm... how did such imagery come out of a little harmless looking card game...
Triumvirate is very different from games like Lost Cities and Jaipur. In these other games, there are tough decisions to make, there is some strategy, but I'd argue that luck is more significant, and the skills involved are not as deep as Triumvirate. These games can be played in a rather relaxed manner, and still be enjoyed. I find that Triumvirate needs to be played in more intense manner to be able to fully appreciate it. It is suitable to be played with a regular opponent, so that both can explore the depth of the game together and play competitively.