3 4 9 0

How to run a match proposition (prop)

It is basically assumed that you are familiar with The Rules of Backgammon and the most common Backgammon Glossary.

[ 1. Money game props | 2. Match props | 2.1 An example ]

1. Money game props

Money game props are a common (and sometimes expensive) way of settling a dispute over which checker play or cube action is best. It is always started by writing up the position at which the dispute was.

• If the dispute is on a checker play or a double/take vs. no double/take you agree on a money rate and then play each side a predetermined number of games with your preference on the checker play or cube action. Some like to switch sides with each game since the position type will become better known. This fact can have different value on each side of the board.
• The easiest type of prop is a beaver-prop. It is easy because you by claiming that a position is a beaver just think that you are a favorite (owning the cube). Your opponent claiming that the position is not a beaver think that you are not. The way to settle this dispute is just to play the position a number of times.
• For the remaining cube disputes there are a special way of settling matters. If you preferred double/drop to double/take you play the doubling side and pay 1 point per game you play with your opponent owning the cube at 2. If you preferred no double/drop (too good) to double/drop you play the no doubling side and pay 1 point per game you play with the cube at 1 (owned by you). The reasoning behind this can be found in my doubling strategy article.

The latter way of settling cube disputes is the most common type of prop and is used in some Chouettes.

2. Match props

Matters are not as simple when you run match props since some points are more important than others. The way to handle this is first to agree on a match equity table. From this match equities can be calculated (normally MWC are given in match equity tables rather than match equities).

The way to calculate an equity at a given score you simply pick a side (I usually pick the one who has the turn at the dispute) and lookup the match winning chance (MWC) at the score and use the following formula.

It can be a good idea to calculate all relevant match equities if the match is not too long. After this you can simply do the same as in a money game prop (with the match equities rather than e.g. 1 point for an undoubled single game, 4 points for a doubled gammon etc.) and all the correct actions in the match will still be correct in the match prop (given that the match equity table is correct).

2.1 An example

Take a look at the following position:

Match to 5, Blue leads 2 to 1
Blue on roll. Cube Action?

163
131
(Position ID: 4NvBADHMbuApAA)

Here you can find take-points, doubling-points and some gammon prices. I think that most experts would say that this position is a double/drop (?). Likewise I think that most computer programs (GNU and Snowie) say that the position is a no double/drop (too good). Now how do you and an opponent settle a dispute? Of course the answer is that you can play the position as a prop (alert: the better player will probably win regardless of what side he plays in a complex prop like this).

Let us say that you think that the position is a no double/drop and your opponent (as I) think it is a double/drop. You will then play the blue checkers.

At the score 2 away 4 away (the score if the position is double/dropped) Snowies match equity table says that you have MWC=66.4% corresponding to a match equity of 2 * 66.4% - 1 = 0.328. This means that your opponent by believing the position is a double/drop think that it is 0.328 match equity points worth to have the blue checkers (you think it is even more match equity points worth). In a normal money game he would have thought it was 1 point worth and would receive 1 point per game for playing the white checkers. At this score you will pay him 0.328 match equity points per game for playing the blue checkers.

Now if you win 1 point in the game the score 2 away 4 away is reached and your opponent will have to pay back the 0.328 points that he received for taking the white checkers. If you win 2 points (1 away 4 away by a gammon or a single doubled game) Snowie's match equity says that you are a 81.9% favorite in the match corresponding to 0.638 match equity points. Your opponent will have to pay you that amount of points. Finally if you win the match (backgammon?) your opponent pay you 1 match equity point.

If you lose a single point (3 away 3 away) corresponding to 0 match equity points you will pay him nothing besides the fee of 0.328 that you already payed him for playing the blue checkers. If you lose 2 points (3 away 2 away) you pay your opponent 0.188 match equity points. If you lose 3 points (3 away 1 away by backgammon!) you pay your opponent 0.496 match equity points. Finally if you lose the match (4 points) you pay your opponent 1 match equity point.

The relevant match equity points can be summed up in the following table:

All of the above match equity points have to be multiplied with the rate you agree on from the start. Have fun!

Copyright © 2002 by Peter Max Friis Jensen