Everything boardgames
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Everybody submits up to 3 games. Once all the votes are in everybody gets to veto a single game out of all the submissions. And then random pick from the remaining ones.
Another way: everybody submits 3 games and then do an approval vote between all the options. This means that everybody can vote for as many games as they want (no ranking, just a list of games they approve of) and then simply count the approvals for each game.
Give everyone a paper list of the games on offer.
Everyone anonymously scores each game from zero to five stars, zero means don't wanna play today and five means really wanna play today.
It's OK to mark a bunch of zeroes and just one five, it's OK to give all kinds of scores, it's OK to have several fives or several threes or whatever. It works anyway.
Then gather up these ballots. For each game, count up the stars. For the two games with most total stars, look at all the ballots again but now instead of looking at the number of stars, count the amount of ballots where one of the two games has strictly more stars than the other.
For example let's say Ticket to Ride has 30 stars, Carcassonne has 25, Uno has 24, Caylus has 18, and Dixit has 5. The two finalists are Ticket to Ride and Carcassonne. And then let's say there are three ballots where Carcassone has more stars than TtR, one ballot where TtR has more stars than Carcassonne, and four where they are tied. Carcassonne won.
That actually sounds very interesting!
Usually some people bring games to the table.
We talk about what we think of each one (in terms of how much we want to play them and maybe some pros and cons why the group might like it). Games that no one liked (for this evening) are out.
People can say if they do not want to play certain games. They are out as well.
By then we either have only one game left or people start vetoing some more or express strong preferences. As everyone is at least okay with the remaining games, this can be very quick.