'One, Two, Three' is a cooperative game for 2 or more players that requires no
equipment whatsoever, and can last anywhere from 30 seconds (a very quick game)
to hours, the average being maybe 5 minutes. This makes it ideal to play during
car journeys, waiting for the bus, etc. etc.

So how do you play?

With just two players, the game goes as follows:

Each player thinks of a word or phrase - some idea or object. For example: 'Christmas', 'Grass', 'The Statue of Liberty', 'Australia', 'Isaac Newton',
'Postmodernism', etc. etc. etc. For simplicity this entry uses the word 'word' to refer to these things, though bear in mind they don't need to be single words.

When each player has thought of a word, they both together say "One, two, three,"
and then together say their word. We now have two words. Next, the
players each try to think of a new word that somehow links the
two ideas - something that word-associates with the two starting words. When both players have thought
of something, they again together say "One, two, three,"
and then together say their new word.

Two things can have happened at this point, either:

1. The two new words are the same! Everyone wins!¹...or:
2. We have two different words.

If we get 2. (which is most likely) then again the players try to think of a new word to link the two latest ideas. And so we continue, trying to converge at some point to the same word.

A couple of extra rules: No word used previously in a game can be used again, and
usually the new word should link to the current two words - words from further back are irrelevant.

Convergence in the Space of Words?

One way to think about what's going on when playing 'One, Two, Three'
is that there is some abstract 'space of words' floating around inside
the players' shared culture and knowledge. Two words are 'near' to each
other in this 'space' if there is some link between the concepts they are
labels for. As the players play the game, they are navigating in this 'space',
jumping to nearby words, trying to jump to a place in between the two previous
words, and hoping that the other player lands there as well (or at least nearby).
If they do, the paths have converged and the players win!

One, Two, Many

This is a variant for more than 2 players. The start is the same - two people think of words and say them
together. Next everyone tries to think of a word to link the words. When someone thinks of a word, they say
"One", when someone else thinks of a word they say "Two", then those two try to converge. If they converge
the game is over, everyone wins!² If not
then as in the two player version there are two new words, and again everyone tries to think of words
to link the new words. In larger groups you might try a rule that when two people try to converge, they
are 'out' for thinking up the next words (to make sure everyone gets a chance).

'One, Two, Many' has the nice feature that people can drift in and out of the game anytime they want, without
disrupting it.

History

'One, Two, Three' was invented in 1992 by some counselors at Camp Winnarainbow, a circus camp north of San Francisco. From there it has spread through puzzle groups - The variant 'One, Two, Many' was invented by a group of people at the 2002
National Puzzlers League convention in Vancouver, British
Columbia, the name coined by someone known as 'Codex'.

Strategies

Well, not so much strategies as the sorts of things that can happen. There are very often multiple
obvious links, and no good way to choose between them. The words can get very close as a result, but not
actually converge, for example, 'ocean' and 'sea' are almost the same concept, and its a matter
of judgement on whether or not that's a convergence. Coming up with those words doesn't have the same sense
of satisfaction as when both people
say precisely the same words at once, so maybe that doesn't really count as convergence. Even if its not
that close, you might get to 'sea' and 'water' which are certainly close but not the same concept.
Here, there is no obvious place to go linking the two, and the players can jump around the general idea of water
without actually converging. The rule that you are not allowed to reuse words means that eventually all the
water related ideas are gone, and the game has to move off somewhere else. Using alternate meanings of words
is very useful to get out of traps like this.

Getting too close means that there are too many choices for where to go next, so the players are unlikely to choose the same one. Being too far away makes it difficult to think of any sensible place to go at all, so you have to think of some word that isn't really that near to at least one of the old words. Ideally you want to be between these two cases, so that there is one sensible answer that both players will go to³.

Be careful not too get too obscure, unless you know someone else playing knows about the words you're using.
Otherwise nobody else will know anything about your word, and in particular will be unable to think up a
new linking word. Obscure words are also going to be less likely to be thought of by both people, so are
less likely to be a convergence, though if they are, it is extra satisfying. Sometimes there are certain
linking words that are just right, and no matter how obscure they are they just have to be said. And
then explained to everyone else. Of course its not very good form to use words that come up in the explanation
of why someone chose a word as a new linking word...

Example games

1. Christmas / Grass
2. Green / Green (a very fast game - 2 round games are surprisingly common.)

1. Shark / Sun
2. Ray / (something else) (this wasn't actually the end of a game, but it would have been a great ending if it was. Wonderful use of alternate meanings.)

1. Consumption / San Francisco (a standard random start to a game)
   
2. Electricity / Rice-a-roni (Rice-a-roni is a kind of food popular in San Francisco - danger of being too obscure here)
   
3. Cooking / Stove (almost...but now we're too close)
   
4. Baking / Hotplate (still too close)
   
5. Oven / Pan
6. Heat / Pizza (trying to get away from cooking)
   
7. Insulation / Burn (insulation as in keeping your pizza hot while it is being delivered)
   
8. Bandage / Protection
9. Dressing / Cast
10. Injury / Net (a net is the first layer put on when making a cast)
    
11. Dolphin / Tennis (oh no! They're miles away from each other!) (dolphins get injured by fishing nets, tennis involves nets and injuries)
    
12. Ball / Ball (Yay!) (dolphins play with balls, as do tennis players)