# In Bridge, When and Why Do People Sacrifice Overtricks to Be Sure of Making Game?

Most players I've seen will often sacrifice potential overtricks in "rubber" bridge to be sure of making game. Apparently, that's not the case in "duplicate." Why is that?

-
I'm always amazed how so many people start playing games without understanding the scoring system (and thus, what you need to do to win). The best Bridge book I ever read started with the scoring, and only introduced bidding and playing and stuff a few chapters in! Essentially: in rubber bridge the scoring heavily rewards you for making games, and barely rewards you for overtricks. In duplicate, the scoring is ALL about squeezing out the last possible (or even impossible) overtrick. There's no mystery here, it is the very core of these two respective games. – thesunneversets Jun 8 '11 at 21:11
@thesunneversets: I "knew" that in "rubber," you score "points," and in duplicate, you score "match points." But I never understood the difference until I "did the math" (see below.) The difference between 420 and 450 is 7% in rubber. Not a big deal. The match point difference for "30 points" might be 40%-60%. (OK if you get 0 it's 100% but that's extreme.) Few people would risk game for an "odds on" chance at an extra 7% (rubber). Many would do so for +50% in match points. – Tom Au Jun 11 '11 at 17:12

It is a risk vs reward situation.

In duplicate, which is normally played as matchpoints, where your score is compared with other pairs which held the same hands. You get 1 point for every pair you beat and 1/2 for every pair you equal.

Suppose you are playing matchpoints with 11 tables. You are in 4S. Assume the hands are so simple to bid, that you are pretty sure every other pair will be in 4S.

Now you have a shot of making an overtrick, or going down (and expect others to be in the same position). Say, making the overtrick has 75% chances, and the other 25%, you will go down.

Now suppose x of the remaining declarers decide to take the risk too.

75% of the time, you expect to win x/2 + (10-x) = 10-x/2 matchpoints.
25% of the time, you expect to win x/2 matchpoints.

So your expectation is 7.5 - x/4. Which in the worst case is average (5 points)!

Now imagine you don't take the risk and always play safe.

75% of the time you expect to win: 5-x/2
25% of the time you expect to win: 5+x/2

So your expectation is 5 - x/4: At best you get an average!

Now if the chances of the overtrick were < 50%, it turns out that you should actually play safe.

At matchpoints, the usual strategy when taking an action is to look at how frequently that action will win.

In fact, nowadays at IMPS too, I have seen good players talk about trying for overtricks when the chances are > 93% or so, but there are a lot of other factors, like how strong the opposing team is, what the current score is (which you cannot be sure of), how long the match is etc.

In rubber bridge which is total points, you really need a very very low risk in order for the overtrick shot to be worthwhile (harder to compute, I suppose). Of course it depends on the contract you are in and how many overtricks are at stake, where you are in the rubber etc.

-
In rubber, the 30 point difference between 450 and 480 is 7%. Big deal. In duplicate, the 30 point difference makes a larger percentage difference, because of where you stand on the curve. Right? – Tom Au Jun 9 '11 at 17:55
@Tom: It is not 450 vs 480. It is 480 vs -50 and the potential loss of the rubber etc. Don't understand what you mean by: "where you stand on the curve". – Aryabhata Jun 9 '11 at 18:30
@aryabatta: "where you stand on the curve." The difference between say, 5 match points and 7-8 (out of ten). I'd risk a set for a 40%-60% increase in match points, but not the 7% value of an overtrick in rubber. – Tom Au Jun 9 '11 at 18:36
@Tom: Doesn't that ignore the potential loss? THere might be a 1% chance of an overtrick for a 100% increase in matchpoints, but is it really worth it? – Aryabhata Jun 9 '11 at 19:04

There are three popular methods of scoring, each of which treat overtricks with different value:

Rubber - Here the priority is making game (or multiple partscores) to finish the rubber. Points earned for your contract go "below the line", and count towards winning the game and the rubber. All other points (setting contracts, slam bonuses, hundred honors, etc) go "above the line", and do not count towards ending the rubber. Since ending the rubber is worth 500 or 700 points depending on whether or not your opponents scored a game or not, you can see how sacrificing a 20-30 point bonus trick could be worthwhile.

Matchpoint Duplicate - This is the form of the game most often played at bridge clubs in partnerships. Here, you score one point for each other partnership's score you beat when they played the same hands. Since the scoring here is more absolute, there is value in winning an overtrick if you think the rest of the partnerships playing this hand would not. For example, if you are in 4S, but feel that most people might be in 3NT making 4, you're going to want to try to make 5. If you do, your 450 will beat everyone else's 430, and you'll get the maximum amount of points on that board. Conversely, if you only make 4, you'll only score 420 on the hand, and your score will be worth nothing. Since your 4S making 4 is worth nothing, you can see that 4S going down would also be worth nothing, so in this case it is worthwhile to risk the contract to get the overtrick.

International Matchpoints (or IMPs) - This is the form usually played in teams, where you and another partnership play against another foursome, and your results are compared directly. Much like in rubber, in IMPs overtricks are not worth a whole lot. (see the scoring chart for the ugly details) If you score an overtrick that your opponents do not, you get 1 IMP. On the other hand, if you fail to make game while your opponents do, you lose 10-12 IMPS. Here, securing the contract is priority #1.

-