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Bamzai

Bamzai is a bar-game, simple and can be played anywhere where a winner or looser has to be determined fast. Basic idea: all players have three matches, they may take any number of (0,1,2 or 3) in a hand and predict the total of matches in all hands, one after another. No one is allowed to call the same total twice (the last player has the advantage to have more information, but the disadvantage to choose only between the left-over possibilities). When looking for a looser (the one that should pay the bill for instance), repeat the game while winners of earlier rounds do no longer participate (note, some games may not have a winner, so it has to be repeated). Propably the most simple strategy game around. 

(example game: 2 players, player1 holds (secretly) 2 matches, player 2 holds (secretly) one match. Bidding round: first player calls a total of 4 matches (estimating player2 holds 2 matches). Based on this bid player2 can deduct that player1 at least holds 1 match. As he holds himself 1 match he can call for 2 or 3 matches (expecting player1 to hold 1 or 2 matches: he can't choose 4 since player 1 already called for that total) unless the player1 was bluffing and just to have the next round to be the second caller. If he call he call for 3, he wins and player1 pays the round. If he call for 5 of 6 matches, he is sure he will loose, unless his strategy is based on being the first caller the next round (for whatever reason).