EW 3♠; NS 3♥; NS 4♦; NS 2N; NS 2♣; Par +100: EW 4♠x-1
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).
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 4N 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.
In grid format, this situation is indicated by showing the same par score for both N/S and E/W. For example:
In makeable contracts format, if the vulnerabilities are the same, the "±" notation is used. But if the vulnerabilities differ, the par scores for both sides are shown (for example, "Par +2220/−1520").
In grid format, the respective par scores are shown for both N/S and E/W. For example,
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