Release 2.19n
Results with Commentary

Here is the link to the Common Game page with commentary for our game results:

Common Game Double Dummy Results

The Common Game uses the ACBLmerge program to compute its double dummy results.  This shows all contracts that can be made if all players knew all four hands and bid and played perfectly. Since real bridge players do not see all the hands and therefore must bid and play based on the ensemble of hands consistent with the bidding and play up to that point, double dummy results must be taken with a healthy dose of skepticism. The double dummy line of play may require dropping an offside singleton king, underleading an ace, eschewing a simple 50% finesse for a low probability squeeze requiring exactly the right lay of the cards, and other plays that work on the given board but which would not be the percentage bid or play. Many new players look at the double dummy results and feel they have done something wrong if they do not match the computer generated result. This is a serious misconception. To some extent, double dummy results are shown because double dummy analysis is a well defined and solvable problem, requiring only a few seconds on average for each board running on a modest computer using efficient software. Determining what should happen on a board is much more complicated and even then would involve assumptions about bidding systems, aggressiveness, and so forth, which vary.

The ACBLmerge double dummy results are complete. Every denomination is tested from each seat. By contrast the Deep Finesse results shown on Dealmaster generated recap sheets are usually incomplete. In the default setting, Dealmaster only computes the double dummy results for “likely” contracts. Sometimes it misses a good, or even optimal, contract. Usually this happens when the trump fit is poor, e.g. a 4-3 or 5-1 fit with strong cards. Thus, a dash on a Dealmaster recap sheet does not always mean the contract fails.

On the ACBLmerge output, a result such as 4♠ means that the contract can be made regardless of direction. A result like 3/4 means North (or East) can make 3 and South (or West) can make 4. A dash, as in -/1 means only South (or West) can make anything in hearts. Smaller indications in light blue such ♠5, with the number after the denomination, show the number of tricks that can be taken. Thus, ♠5 means 2♠ would fail by three tricks. Sometimes one actually cares to know just how many tricks a low level contract can be set. For example suppose you are vulnerable against not and the auction proceeds 1♣ - 1♠ to you. Holding ♠KJ83  AT5  KQ72 ♣J4, you debate passing and hoping that partner reopens with a double, but decide to bid 3N directly instead. After you collect +660, you begin to wonder if defending 1♠X would have been more profitable. ♠3 would tell you that +800 had been possible.

Explanation of Par Score

The par score is the raw score for the contract beyond which neither side can bid further to improve the score for their side. The par score is shown from the perspective of N-S, i.e. it is negative if E-W are making a contract or N-S must sacrifice. There may be multiple par contracts which achieve the same score. For example, equivalently scoring contracts such as 4♥ and 4♠ will yield the same par score. Likewise 3N and 5♣/♦; however if the opponents can sacrifice profitably in say 4♠ but not 5♠ then only 5♣/♦ would be the par contract. All sacrifice contracts are doubled since that always improves the result for one side. As with makeable contracts, there may be equivalently scoring sacrifices in more than one denomination.

The par score calculation is computed from the double dummy information above and therefore carries the same caveats. Accordingly, some authors speak of the par presented here as “absolute par”, reserving the word par for the most realistic result given what each player knows as the hand is bid and played out.

Although par is a straightforward concept, there are some subtleties which the code must handle. First and rather rarely, neither side may have a makeable contract in which case the par score is 0 and the par contract is Pass Out. Thomas’s Bridge Fantasia has an interesting section on these par zero deals. Second, and somewhat more commonly, both sides may be able to make the same maximally scoring contract (often 1NT) from at least one seat. In game theory, this is a “hot” situation where victory goes to the side to get there first. This situation is indicated by the ± sign, e.g. ±90 1NT-EWNS. See Everyone makes 1♠ and Everyone makes [3N] for specific examples. Victor Mollo anticipated such amusements inBridge in the Menagerie, where Oscar the Owl, his chief kibitzer, remarks, “Curious hand, both sides can make four hearts”, one by drawing trump and establishing a side suit, the other by cashing outside winners and then crossruffing. However, 4♥ is probably not the par contract on that hand.