Game Propositions
Suppose you're playing a game and your opponent doubles. You grab the cube and snicker "What an awful double!" Or you're kibbitzing and the player doubled drops and you say "No way! That's a take." And suddenly you hear a voice say "For how much?"
You've just been challened to a proposition. In effect the two players are expressing a difference of opinion as to the proper action - and backing it with money.
Consider the second case. In effect, you are saying that the equity in the game is greater if you accept the double than if you drop. So you might set the board up and agree to play the game out ten times for a certain stake. Since you feel the game is a "take" - you play the side that has been doubled. So you would start with the cube at 2 on your side, and your opponent giving you one point per game - because your opponent is saying that this position is so bad that even with the cube on your side, he would be willing to pay a point rather than have to play on.
Propositions are very common at tournaments - because backgammon players love to gamble, and they love to argue.