Par Score and Par Contracts

Board 2
East Deals
N-S Vul
♠ 5
A K 4
A K J 10 8 2
♣ A 4 3
♠ K J 8 7 6
7 6 5
♣ K Q 6 2
♠ A Q 4 2
Q 10 3
9 7 6 3
♣ 10 5
♠ 10 9 3
J 9 8 2
Q 5
♣ J 9 8 7

EW 3♠; NS 3; NS 4; NS 2N; NS 2♣; Par +100: EW 4♠×−1

When the Board→Double Dummy command has been used, BridgeComposer also shows the par score (in makeable contracts, grid [2 rows], and grid [4 rows] formats) and the par contract(s) (in makeable contracts and grid [4 rows] formats). (See Makeable Contracts and Double Dummy Analysis).

The Encyclopedia of Bridge defines par as “the result on a hand if both sides have done as well as possible.” This implicitly includes both bidding and play. As described following, BridgeComposer uses the double dummy analysis to determine the par score for a deal.

The PBN standard says (slightly rephrased):

"The par score is the number of points of a deal based on the trick score of the par result, with open cards (double dummy). This result is computed by comparing all possible (doubled) contracts, including all passes. The number of tricks for a certain contract—and hence the corresponding score—may be derived from the double dummy analysis."

Note: The standard refers to this as the optimum score rather than the par score, but (as used therein) it is the same concept.

In other words, a par contract has been reached when neither side can improve their score by bidding again (assuming double-dummy play results).

See also Wikipedia: Optimum contract and par contract.

Determining the Par Score and Par Contract

Best contract: Suppose the makeable contracts on a deal (nobody vulnerable) are: NS 4; NS 3N. The duplicate bridge score for 4 is 420 and for 3 NT it is 400. Thus the par score is the higher of the two, +420, and the par contract is the corresponding contract (i.e., NS 4=).

But if 3 NT can always make four on this deal (4N would be shown in the makeable contracts), then the par contract would be NS 3N+1 (three notrump, making with one overtrick) and the par score would be +430.

Sacrifices: Sacrifice bids also come into consideration. If the makeable contracts (nobody vulnerable) are NS 4; EW 3, then East/West will do best by bidding 4 over 4 and taking the penalty for down one. For calculating the par score, all sacrifice bids are considered to be doubled, since that is how the out-bid side can do their best. The score for EW 4 doubled down one (non-vulnerable) is NS +100, so that would be the par score on this deal.

Competitive bidding: Now suppose that the makeable contracts on a deal (both vulnerable) are: NS 4N; NS 5; EW 3. NS would bid 3NT and, with everyone playing their best, would score +630 if allowed to play it. But, EW, doing their best, would sacrifice in 4, which would be EW −200 for down one doubled. NS could then bid 4NT for +630 again, and EW would bid 5, doubled down two for −500. Finally, NS would bid 5, making for +600. (EW would not bid 6, because down three doubled is −800 which is worse than −600.) The upshot is that even though NS 4N makes on this deal, the par score is nonetheless +600, not +630. Competitive bidding has pushed NS from notrump into the lower-scoring minor suit game.

Similarly, competitive bidding can force a contract making with overtricks to a higher level in the same strain. For example, NS making 11 tricks at notrump is usually NS 3N+2. But if EW are able to make a contract, or sacrifice profitably, in a suit at the 4 or 5 level, the par contract would be raised to 4N+1 or 5N=, respectively. Note that such a change in the par contract does not affect the par score: it remains +460 (or +660 when vulnerable).

Additional Details

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