Partner opens one heart. You raise to two holding nine points and three small trumps. Partner comes back with three hearts, which in bridge means "I have extra, do you?" And there you sit, adding your points a second time, hoping they grew.
They did not. Nine is nine. You still have to choose.
This decision shows up more often than slams, squeezes, or anything else players spend their study time on. Most of us resolve it by feel, bid it or pass it, then never find out whether the feel was any good.
What the game bonus is actually buying
Four hearts bid and made, not vulnerable, scores 420. Three hearts taking those exact same ten tricks scores 170. Identical cards, identical play, 250 points of difference for nothing but naming the higher contract. Vulnerable the gap gets wider: 620 against 170.
Which is why the old rule survives. Bid a game that will make roughly half the time. When it comes home you bank the bonus, and when it fails you hand over 50 or 100, and across a long session the good days pay for the bad ones with room to spare. Vulnerable you can shade below fifty percent, since the bonus is bigger. Not vulnerable, you want a shade better than a coin flip.
That is the arithmetic. Then you sit down at an actual table and the scoring method quietly rewrites the question.
Matchpoints asks something else entirely
Playing IMPs or rubber, you are playing against the odds. Bid the percentage game, accept the occasional minus, finish ahead. Clean and mostly correct.
Matchpoints does not care how big your score is. It cares whether you beat the people who held your cards. So the question stops being "will this make?" and becomes "what will everybody else do?" If the entire field bids four hearts and it goes down, joining them costs you nothing, because you all share the same bottom. Stop in three, take ten tricks, and your 170 is a top only if the others actually bid game and failed. Otherwise it is a near zero against their 420.
The practical version: at matchpoints, follow the field on genuinely close hands, and save your independence for the hands where you know something the field does not. The way IMPs and matchpoints pull strategy in different directions reaches further into ordinary auctions than most club players expect.
A partscore is not a failure
Improving players develop a strange guilt about stopping low. Bid three, make four, groan about the missed game. But plus 170 is a fine result when the field could not make ten tricks either, and it beats minus 50 every single time.
Some hands belong in a partscore. Two flat hands with 23 points between them and no fit worth the name are not going to produce game because you wanted it badly enough. Fighting hard for the small contracts is real bridge, not a consolation prize, and partscore battles decide more sessions than anyone gives them credit for.
The hands that outrun their point count
High card points are a rough proxy for trick-taking power, and they are wrong in predictable directions.
They undervalue shape. A nine count with four trumps and a doubleton will produce more tricks than a nine count sitting in 4-3-3-3, because ruffs generate winners that no honor card ever pays for. They undervalue aces and kings in the suits partner has bid. They badly overvalue queens and jacks stranded in the suit the opponents opened, where they are likely sitting under the strength and taking nothing at all.
Two hands, both nine points. The first is an ace, a king, four hearts and a singleton club. The second is three queens and a jack scattered across a completely flat hand. Same number on the scorecard. Not remotely the same hand. Accept the invitation with the first one and pass the second, and you will be right far more often than the point count alone would make you.
Trump length deserves special mention. That fourth trump is worth roughly an extra ace in a raise, and it is the single most reliable signal that a borderline hand is stronger than it looks.
The part you cannot settle by yourself
Every one of these decisions has a correct answer that stays invisible at the table. You bid the game, went down one, and partner does that thing with the eyebrows. Was the bid wrong? Or was it right, and the trumps broke four-one? One outcome from one deal cannot tell you, and arguing about it after the fact just means the louder player wins.
Comparison is the only thing that closes that gap. When your table's result sits next to the results of other people who held those same cards, the borderline game stops being a matter of opinion. Playing pre-dealt hands with your usual four at home and scoring them properly against other tables, which is what Bridge@Home is built to do, turns "should we have bid it?" into something with an actual answer. Eleven pairs took the push, seven of them made it. Now you know, and so does partner.
The takeaway
Count the shape, not just the points. Weight the fourth trump heavily and discount the queens sitting in front of the opponents' strength. Then let the format break the tie: at IMPs, bid the close game and take your medicine when it fails, because the bonus is worth the risk. At matchpoints, do what the room is doing unless your hand tells you something the room does not know.
And whatever you decide, find out afterwards whether it worked. Bridge rewards small edges applied consistently, and the invitation you got right last Tuesday is the same invitation you will face again next month.