Main     Study 9X29 by Richard Pavlicek    

Actual Play vs. Double-Dummy

How does actual play compare with double-dummy play? The question has often been asked, but concrete answers are rare because “actual play” is difficult to define. Clearly it implies imperfection to some degree, but exactly how much is unclear. Whatever the case, if both sides are equally imperfect, the errors should tend to cancel out in the long run, approaching the double-dummy state.

This study compares actual play from four major annual team events — Vanderbilt, Spingold, U.S. Championship and World Championship — with double-dummy play. The database from vugraph archives 1996-2014 consists of 80,138 results from 72 events, however 196 passouts are removed to leave 79,942 contracts. The playing field of “expert versus expert” is an ideal setting for comparison.

General CaseAfter the Opening LeadConclusion
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General Case

The first table shows various contract groups and the number of times each occurred. The remaining columns show the number of times made, percent made and average tricks won, both in actual play and at double-dummy. Corresponding values are placed side-by-side for comparison. The second table does the same for the 35 specific contracts. Rows tinted gold show contracts in which double-dummy play surpassed actual play in both percent made and average tricks won.

The overall picture is that actual declarer play does slightly better than double-dummy play except at the slam level where double-dummy play has a slight edge. The reason is apparent: The opening lead gives the defense a considerable advantage at double-dummy; e.g., the perfect lead will sometimes bury a contract before declarer has a chance. As the contract level increases, the opening lead tends to be less crucial, so the advantage tapers off, disappearing entirely from 5 NT upward. The narrow exception with 4 H in the second table is probably a fluke that would reverse in a larger sample.

Contracts by Group
GroupTimesTimes MadePercent MadeAverage Tricks
PlayedActualDDActualDDActualDD
All contracts79,94251,44849,58564.3662.039.289.21
Notrump22,68915,62114,51768.8563.988.728.56
Suit57,25335,82735,06862.5861.259.509.47
Major suit42,13027,31626,78064.8463.579.509.47
Hearts19,40112,60212,47764.9664.319.589.57
Spades22,72914,71414,30364.7462.939.439.39
Minor suit15,1238511828856.2854.809.509.47
Clubs71683912384354.5853.619.539.51
Diamonds79554599444557.8155.889.479.43
Partscore29,50018,14417,06261.5157.848.087.96
Game not slam44,49529,35928,46165.9863.969.759.71
Slam (6 or 7)59473945406266.3468.3011.7111.77
1 level57863925354667.8461.297.116.84
2 level11,7717715735665.5462.497.957.84
3 level25,84416,52815,55863.9560.208.948.85
4 level24,31216,20216,03066.6465.939.939.93
5 level62823133303349.8748.2810.3110.27
6 level51523434350366.6567.9911.6311.68
7 level79551155964.2870.3112.2612.37
1 of suit85158356068.5165.807.257.10
2 of suit10,3146889662466.7964.228.007.91
3 of suit10,4595783547255.2952.328.588.52
4 of suit23,97615,91915,75766.4065.729.929.92
5 of suit62653123302249.8548.2410.3110.27
6 of suit46903095315365.9967.2311.6111.66
7 of suit69843548062.3268.7712.2012.32

Specific Contracts
ContractTimesTimes MadePercent MadeAverage Tricks
PlayedActualDDActualDDActualDD
1 C45252855.5662.226.536.53
1 D72393154.1743.066.746.38
1 H23015315366.5266.527.297.23
1 S50436634872.6269.057.387.20
1 NT49353342298667.7260.517.096.79
2 C84750548459.6257.147.847.72
2 D138591486065.9962.098.017.91
2 H32972233218767.7366.338.067.98
2 S47853237309367.6564.647.997.89
2 NT145782673256.6950.247.597.39
3 C23031315127157.1055.198.628.59
3 D25631527147359.5857.478.718.66
3 H27041437132953.1449.158.498.42
3 S28891504139952.0648.438.518.41
3 NT15,38510,74510,08669.8465.569.199.07
4 C78237436047.8346.049.369.25
4 D70234732849.4346.729.329.26
4 H10,4067154720468.7569.2310.0010.03
4 S12,0868044786566.5665.089.929.91
4 NT33628327384.2381.2510.6810.57
5 C21101050102749.7648.6710.2810.26
5 D21241059102349.8648.1610.3210.30
5 H118352949044.7241.4210.1910.08
5 S84848548257.1956.8410.5510.50
5 NT17101158.8264.7110.5910.76
6 C95658259560.8862.2411.5611.62
6 D94462162765.7866.4211.6511.71
6 H137194595868.9369.8811.6611.70
6 S141994797366.7468.5711.5611.63
6 NT46233935073.3875.7611.7911.87
7 C125617848.8062.4011.9112.14
7 D1659210355.7662.4211.9312.04
7 H21015115671.9074.2912.4012.45
7 S19813114366.1672.2212.4012.53
7 NT97767978.3581.4412.6512.69

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After the Opening Lead

The next two tables show a comparison after the actual opening lead. That is, double-dummy play begins with the first play from dummy. (This reduced the database to 77,406 contracts, because some results did not include the play or opening lead.) Essentially, this removes the defensive advantage of the first strike, so double-dummy play surges to the front in each category — except for 1 D (obviously unreliable based on little data) and 2 D in percent made only, a curious mystery but probably a fluke. Another way of looking at it is that the actual declarer loses the advantage of a favorable lead; he may still get one but so will the double-dummy declarer.

Contracts by Group
GroupTimesTimes MadePercent MadeAverage Tricks
PlayedActualDDActualDDActualDD
All contracts77,40649,81052,47364.3567.799.289.44
Notrump21,95515,11315,76968.8471.828.728.92
Suit55,45134,69736,70462.5766.199.509.65
Major suit40,79826,44727,97664.8268.579.509.65
Hearts18,80912,22213,03664.9869.319.589.75
Spades21,98914,22514,94064.6967.949.429.57
Minor suit14,6538250872856.3059.569.509.63
Clubs69433795405654.6658.429.549.67
Diamonds77104455467257.7860.609.479.60
Partscore28,56017,56218,11661.4963.438.088.17
Game not slam43,12928,44930,15765.9669.929.759.96
Slam (6 or 7)57173799420066.4573.4711.7111.91
1 level55733788383267.9768.767.127.15
2 level11,3917471771265.5967.707.958.05
3 level25,09116,02116,78963.8566.918.949.13
4 level23,54715,69716,72266.6671.029.9310.12
5 level60873034321849.8452.8710.3110.44
6 level49493301364666.7073.6711.6311.84
7 level76849855464.8472.1412.2612.40
1 of suit82056056568.2968.907.257.29
2 of suit99966682687566.8568.788.018.11
3 of suit10,1685611585355.1857.568.588.69
4 of suit23,22015,42216,44166.4270.819.9210.11
5 of suit60703024320649.8252.8210.3110.43
6 of suit45042974328866.0373.0011.6111.82
7 of suit67342447663.0070.7312.2012.35

Specific Contracts
ContractTimesTimes MadePercent MadeAverage Tricks
PlayedActualDDActualDDActualDD
1 C42242857.1466.676.606.83
1 D70373452.8648.576.716.51
1 H21914514866.2167.587.277.37
1 S48935435572.3972.607.377.41
1 NT47533228326767.9268.747.107.13
2 C81849351560.2762.967.867.95
2 D134188587566.0065.258.018.11
2 H31882159226067.7270.898.058.17
2 S46493145322567.6569.378.008.09
2 NT139578983756.5660.007.597.68
3 C22341270133656.8559.808.628.75
3 D24961492155959.7862.468.728.84
3 H26331396144853.0254.998.488.59
3 S28051453151051.8053.838.508.59
3 NT14,92310,41010,93669.7673.289.199.44
4 C75135837147.6749.409.379.39
4 D67733434849.3451.409.339.40
4 H10,1006950749868.8174.2410.0010.22
4 S11,6927780822466.5470.349.9210.11
4 NT32727528184.1085.9310.6610.87
5 C20521023109649.8553.4110.2810.43
5 D20541014108949.3753.0210.3110.45
5 H114651752645.1145.9010.2010.26
5 S81847049557.4660.5110.5510.66
5 NT17101258.8270.5910.5911.00
6 C92456763361.3668.5111.5711.77
6 D91160266466.0872.8911.6711.89
6 H1321909100168.8175.7811.6611.85
6 S134889699066.4773.4411.5611.77
6 NT44532735873.4880.4511.7912.04
7 C122607749.1863.1111.9112.16
7 D1619110356.5263.9811.9412.09
7 H20214615572.2876.7312.3912.48
7 S18812714167.5575.0012.4112.56
7 NT95747877.8982.1112.6412.74

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Conclusion

The overriding impact of the tables is that actual play versus double-dummy is pretty close, so analyses based on double-dummy play should generally be on track. The henchmen below don’t buy any of this, so please leave the building quietly and don’t make any quick moves.

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© 2013 Richard Pavlicek