Doge is set along the canals of Venice, and pits the players in a political competition to build houses in the different districts. Those are ultimately converted into palazzos, the final victory condition. By the standard of many modern games, Doge has shockingly simple rules. You can teach it in less than 5 minutes, and play it in 30-45. There are really just a few mechanisms in the game... one of which works very well (and deserves to be reused in another game), and one of which makes the game nearly unplayable to my modern eye.
The winning element is the voting system used to establish control of districts each round. All players have 7 identical "voting chips" valued at 0, 1, 1, 2, 2, 3, and 3. In a round of voting, each player chooses between one and four of those chips to place somewhere on the board, along with the card representing their secret choice of where to place the chips. Once everyone chooses, the districts are revealed while the votes themselves remain hidden. The process then repeats twice more, until all chips are placed and each player has voted in three (or sometimes only two) districts. Votes are then tallied district by district, establishing a winner (and second place player) who gains houses and a bit of extra voting power to wield in another district.
There's a lot of play within that simple system. Watching people gradually expend their voting chips creates fun "double bluff" scenarios. Next round, can you go to that district everyone else is ignoring... or will the other players also seize upon the fact that it sits empty? Did your opponent who went big with four chips make a huge play for one district... or are they bluffing you with low value chips? How few votes can you get away with in a district to pull off a useful second place finish?
Unfortunately, this compelling system is in service of a game that's decided in the first two rounds. The system for converting houses into game-winning palazzos is even simpler than the voting: the first palazzo in a district is built as soon as one player has 3 houses there; the next takes 4 houses; the next 5; and so on. To win the game, a player needs to get one palazzo in each of the six districts along the canal... or add an additional palazzo for each district they're missing. (That is, seven palazzos in five districts, or eight in six.)
Through clever play or sheer luck (or both), one player usually succeeds in creating at least two palazzos by the end of the second round. With the rising costs of subsequent palazzos, this is enough to create an insurmountable lead. Players can plot openly about where to try to block the leader, but there's a little too much flexibility in moving houses around, cheaply picking up second place bonuses, and exploiting competition between your rivals. I think this game is essentially decided 5 to 10 minutes in, even though it's likely to last a half hour more. Even for a rather short game like this is, that's not really a fun situation.
The designer of Doge, Leo Colovini, has had many popular and well-received designs over the years, including sequels and re-releases. But Doge has never been revisited, and I'm now pretty sure I know why. But I also think there's a real gem of a mechanic here, paired with an unfortunate victory/scoring system... a gem that I truly hope Colovini himself (or some other designer with a clever twist) revisits some day.
Balancing those two extreme elements, I think I'd call Doge something like a C+ in the grand scheme of my game collection. I intend to hang onto it as a reminder, as potential inspiration... even though I wouldn't be surprised if I never actually played it again.
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