Main     Study 8J21 by Richard Pavlicek    

Positional Advantage

Which hand should be declarer?

As virtually all bridge players are aware, it sometimes matters which hand declares the partnership’s final contract — the difference being the opening lead, which may have a greater impact from one defender than the other. Most of the time it doesn’t matter, but when it does, it’s nice to have the positional advantage of declaring from the right side.

It is widely accepted, in general, that the stronger hand should be declarer, the logic being that its high-card abundance is spared from an immediate lead-through. This is the foundation for Jacoby transfers and various other conventions, such as the negative diamond response to forcing club bids so the weak hand will not be the first to name a major or notrump. But how much of an advantage is it? Is hand pattern also an issue? And how often does it matter? This study will provide answers.

Game in NotrumpSlam in NotrumpGame in a MajorSlam in a SuitHonor Holdings
All statistics were derived from my database of 10,485,760 random solved deals. Partnerships of 21-35 HCP were appraised in two ways: (1) Notrump relevant if either hand is balanced or if longest fit is only eight cards, or (2) Suit relevant if both hands are unbalanced or if an 8+ card fit exists.* Note the overlap, so some partnerships were appraised both ways. Partnerships of 21-28 HCP were considered for game bidding (3 NT or four of a major), and partnerships of 29-35 HCP for slam bidding (6 NT or six of a suit).

*Where multiple fits exist, the longest was deemed to be trumps (even if play in another suit could win more tricks). In the event of a tie, the higher ranking was picked to emulate the usual practice of preferring a major.

Another factor that affects trick production and game or slam chances is the apportionment of a side’s HCP. Are the HCP evenly distributed? Or are they lopsided? To investigate this influence, each HCP total is not only shown in full but also broken down into its constituents, e.g., 25 HCP is shown for 13-12, 14-11, …, 24-1, 25-0.*

*Extreme divisions of course are rare, so statistics based on small samples are less likely to be accurate in theory.

TopMain

Game in Notrump

The following tables show the positional advantage of declaring 3 NT for partnerships of 21-28 HCP. Sided shows the percent of cases in which the declaring hand matters. Stats for the declaring hand are shown in four categories: Fixed = same declarer throughout, which is effectively an average; Stronger = played by the hand with more HCP; Tamer = played by the more balanced hand; Utopian = always played from the better side, which of course is unattainable in practice.

Each declaring category shows two numbers: (1) Average tricks won, which is the main concern at matchpoint scoring, and (2) the percent of cases 3 NT makes, which is the main concern at IMP scoring. Play by both sides is double-dummy, however, past studies have shown this to be in close proximity to actual play.

An interesting observation is that, on average, it is better to choose the tamer (more balanced) hand as declarer than the stronger hand. As the HCP disparity increases, the advantage of the stronger hand also increases and eventually overtakes that of the tamer hand.

Perhaps the most astounding revelation is the effect of apportionment. For instance, with 24 HCP your chance of making 3 NT (assuming a fixed declarer) is 40.13 percent if the HCP are split 12-12, but only 25.12 percent if the HCP are split 21-3. We all know why this is true, but the difference of 15 percent is remarkable. The obvious implication is not to stretch for game when partner opens 2 NT or the like.

21 HCPCasesSidedFixedStrongerTamerUtopian
All ways14565378.916.555.136.575.226.575.306.615.63
11-103209318.956.615.806.625.816.635.976.676.34
12-92954508.946.605.646.615.706.615.846.656.19
13-82565418.876.595.376.605.486.605.566.645.91
14-72082538.966.565.126.585.266.585.306.615.62
15-61486568.966.514.526.534.676.534.706.574.99
16-51021168.776.464.066.484.216.474.206.514.47
17-4646198.856.413.666.443.806.433.766.474.01
18-3346868.686.323.196.353.366.343.326.373.48
19-2155868.766.222.466.262.506.232.496.282.62
20-170908.706.182.696.222.766.192.746.232.81
21-026097.866.233.226.283.456.243.336.283.45

22 HCPCasesSidedFixedStrongerTamerUtopian
All ways13689589.637.0811.577.0911.767.0911.897.1412.61
11-111504549.587.1412.957.1412.957.1613.267.2014.10
12-102871619.727.1212.647.1312.717.1412.997.1813.78
13-92577139.587.1212.427.1212.597.1312.807.1813.56
14-82171569.637.1011.917.1212.167.1212.267.1613.00
15-71689179.747.0611.127.0911.457.0811.417.1312.12
16-61178899.647.0110.117.0310.417.0210.377.0711.03
17-5783909.686.979.206.999.556.989.507.0310.05
18-4482579.236.918.256.958.586.938.516.978.94
19-3251159.696.817.146.847.486.827.296.877.79
20-2111879.486.745.796.786.056.755.916.796.27
21-150069.376.645.496.695.716.665.536.705.79
22-017138.586.615.146.665.606.635.496.675.72

23 HCPCasesSidedFixedStrongerTamerUtopian
All ways123721710.377.5922.447.6022.817.6122.967.6624.21
12-1126359810.437.6524.327.6524.417.6724.857.7126.19
13-1024493510.447.6323.937.6424.157.6524.497.7025.78
14-921348510.417.6223.437.6323.807.6424.007.6925.28
15-817329610.307.6022.757.6223.247.6223.297.6724.56
16-713190610.377.5621.407.5821.977.5821.927.6323.12
17-68944610.327.5019.537.5320.147.5219.997.5721.15
18-55750010.367.4618.217.5018.927.4818.657.5319.75
19-43413110.187.4016.407.4417.207.4216.807.4617.85
20-3172909.757.2813.477.3214.167.3013.957.3414.62
21-273219.837.2312.477.2712.917.2512.817.2913.36
22-1323310.057.1010.187.1510.707.1110.217.1610.92
23-0107611.347.149.677.2010.227.1510.047.2010.32

24 HCPCasesSidedFixedStrongerTamerUtopian
All ways107092411.198.1037.718.1238.228.1338.388.1840.18
12-1211290811.278.1740.138.1740.138.1940.838.2442.61
13-1121949411.358.1640.058.1740.248.1940.728.2442.56
14-1019830511.218.1439.288.1539.628.1639.998.2241.82
15-916582211.208.1338.718.1439.218.1539.348.2041.17
16-813179911.198.1037.418.1238.168.1238.118.1739.94
17-79709911.218.0535.458.0836.388.0736.178.1337.92
18-66409810.988.0033.638.0334.668.0234.268.0736.04
19-53966010.807.9431.057.9832.197.9631.768.0133.34
20-42302510.667.8928.517.9329.957.9129.037.9630.80
21-31142710.837.7825.127.8226.467.8025.837.8427.06
22-2462910.637.6921.997.7423.097.7122.457.7623.66
23-1201410.877.5818.027.6519.077.6118.477.6619.41
24-06449.017.5917.557.6319.257.6017.707.6419.25

25 HCPCasesSidedFixedStrongerTamerUtopian
All ways88956612.078.6254.998.6455.548.6455.728.7057.80
13-1218324212.288.6857.188.6857.238.7057.978.7660.01
14-1117432012.188.6757.038.6857.248.7057.758.7659.79
15-1015024112.118.6556.188.6756.648.6856.868.7458.98
16-912303812.098.6355.378.6556.038.6556.098.7158.20
17-89468711.848.6054.528.6255.358.6255.198.6857.31
18-76843211.988.5452.188.5853.378.5752.998.6355.06
19-64342311.698.4949.908.5351.048.5250.668.5752.71
20-52635911.758.4347.528.4849.158.4648.448.5250.52
21-41444411.328.3745.228.4246.898.3945.848.4548.01
22-3702011.988.2640.668.3142.588.2941.618.3443.60
23-2290912.558.1536.348.2138.438.1737.168.2339.33
24-111269.598.0732.688.1334.468.0933.138.1434.81
25-03258.007.9928.628.0329.548.0028.628.0329.54

26 HCPCasesSidedFixedStrongerTamerUtopian
All ways70702212.919.1370.299.1570.819.1670.979.2272.94
13-137278012.979.1871.859.1871.859.2172.599.2774.38
14-1214134113.019.1971.939.1972.019.2272.599.2874.51
15-1112775712.979.1871.719.1971.999.2172.349.2774.26
16-1010948013.119.1570.859.1771.409.1871.619.2473.55
17-98643212.919.1270.179.1570.879.1570.829.2272.89
18-86479812.749.0969.439.1270.259.1270.039.1872.08
19-74460712.699.0668.309.0969.399.0868.969.1470.98
20-62803412.778.9665.309.0066.658.9966.099.0568.20
21-51651612.538.9363.968.9765.438.9664.669.0266.74
22-4871711.718.8361.148.8963.358.8662.048.9264.31
23-3413611.708.7156.048.7658.128.7356.878.7959.14
24-2162211.168.6452.968.6954.508.6653.398.7155.24
25-162911.928.4243.088.5144.838.4643.408.5245.15
26-01739.258.5647.988.6549.138.6147.988.6549.13

27 HCPCasesSidedFixedStrongerTamerUtopian
All ways53810213.659.6681.949.6882.389.6982.579.7684.15
14-1310893013.859.7182.929.7182.949.7483.529.8185.03
15-1210119913.919.7082.639.7182.909.7383.359.8084.86
16-119016413.819.6982.369.7082.669.7282.929.7984.52
17-107508613.609.6882.479.7082.919.7183.109.7884.64
18-95743913.379.6481.729.6782.419.6782.389.7483.97
19-84147613.539.6081.249.6481.999.6381.839.7083.49
20-72799613.419.5680.459.6081.419.5981.049.6682.79
21-61722013.019.4978.789.5479.879.5179.369.5881.18
22-5977612.789.4277.709.4879.359.4578.479.5280.29
23-4511811.869.3275.269.3776.779.3475.979.4077.53
24-3240112.499.2172.399.2874.599.2573.479.3075.39
25-290813.339.0969.169.1671.159.1269.829.1971.81
26-130413.168.9763.499.0264.478.9863.169.0365.13
27-08510.599.0261.189.1165.889.1165.889.1165.88

28 HCPCasesSidedFixedStrongerTamerUtopian
All ways38821913.9110.1889.4210.2089.7610.2189.9210.2891.04
14-143963314.1410.2490.0610.2490.0610.2790.5010.3591.57
15-137577014.0110.2389.9310.2490.0510.2690.3710.3391.45
16-126867514.1210.2189.6110.2289.8010.2490.1310.3291.21
17-115904913.9210.2089.7710.2290.0310.2390.3710.3191.33
18-104796013.8410.1989.4610.2289.9610.2189.9510.2991.11
19-93548514.1610.1488.9110.1889.5410.1789.4910.2590.74
20-82533113.2710.1288.9510.1589.5610.1489.3910.2290.57
21-71633813.1710.0688.7510.1189.4210.0989.1510.1690.35
22-6968913.4510.0087.3810.0588.2810.0387.9310.1089.21
23-5554413.989.9286.339.9987.649.9687.0910.0388.44
24-4282712.919.8786.709.9387.809.8986.849.9688.61
25-3129114.189.7083.279.7785.139.7484.439.8086.13
26-245613.169.5678.739.6179.829.5879.179.6480.70
27-11374.389.5180.299.5581.029.5381.029.5581.02
28-03414.719.1270.599.1573.539.1270.599.1573.53

TopMain

Slam in Notrump

The following tables show the positional advantage of declaring 6 NT for partnerships of 29-35 HCP. Sided shows the percent of cases in which the declaring hand matters. Stats for the declaring hand are shown in four categories: Fixed = same declarer throughout, which is effectively an average; Stronger = played by the hand with more HCP; Tamer = played by the more balanced hand; Utopian = always played from the better side, which of course is unattainable in practice.

Each declaring category shows two numbers: (1) Average tricks won, which may be of concern at matchpoint scoring, and (2) the percent of cases 6 NT makes, which is the main concern at IMP scoring. Play by both sides is double-dummy, however, past studies have shown this to be in close proximity to actual play.

A curious observation is that the percent of sided cases (choice of declarer matters) peaks at 13.91 percent with 28 HCP then drops quite abruptly to only 0.52 percent with 35 HCP. Apparently, the super abundance of HCP leaves fewer weak spots and fewer resources for the opponents to avail an attack. Hence, declarer position is less important for slam bidding than for game — a concept that seems strange, since we tend to remember most the wrong-sided slams over the years.

29 HCPCasesSidedFixedStrongerTamerUtopian
All ways27055113.6810.7025.6010.7226.1510.7226.2610.8028.24
15-145337013.9310.7527.1310.7627.3410.7827.8610.8630.07
16-135033314.1210.7326.6310.7426.9010.7627.2610.8429.49
17-124452913.7810.7226.2210.7326.6210.7426.8610.8228.96
18-113732213.6610.7125.5810.7326.1710.7326.1510.8128.21
19-102924713.5710.6925.3210.7326.3910.7226.1910.8027.97
20-92138613.2410.6624.2810.7025.2410.6924.9410.7626.73
21-81466913.2210.6223.3910.6724.4110.6524.1010.7225.54
22-7916812.9910.5822.3310.6323.1010.6122.7510.6824.09
23-6539613.0310.5421.7810.5922.7910.5622.1510.6323.41
24-5286712.0710.4719.1510.5320.2010.4919.9910.5520.72
25-4135912.2110.3116.3410.3717.5910.3416.9210.4017.81
26-358711.5810.1913.8010.2314.4810.2114.4810.2714.65
27-22239.8710.0614.8010.1416.1410.1215.7010.1516.14
28-17410.8110.0516.2210.1116.2210.0716.2210.1116.22
29-0219.529.574.769.714.769.674.769.714.76

30 HCPCasesSidedFixedStrongerTamerUtopian
All ways17640412.4611.1942.4811.2143.2111.2143.3611.2846.02
15-151737712.7911.2143.2111.2143.2111.2343.8511.3046.84
16-143380912.6311.2243.5911.2343.9611.2444.5811.3147.40
17-133102512.8611.2143.6311.2344.1111.2444.4711.3147.41
18-122666212.9111.2243.7411.2344.6211.2444.6411.3147.54
19-112162512.2411.1942.6211.2243.5411.2243.5311.2845.99
20-101665511.8211.1841.8711.2142.8211.2042.5411.2745.06
21-91171111.9211.1541.1211.1942.3011.1842.1511.2444.32
22-8775612.0711.1140.0211.1541.4811.1340.8611.2043.18
23-7471411.9011.0437.3811.0939.0111.0738.6111.1440.37
24-6264510.8910.9833.8811.0335.9511.0035.0511.0736.94
25-5134810.6810.9531.8211.0233.3810.9832.3411.0434.05
26-466410.6910.8028.1610.8529.8210.8329.3710.8730.12
27-329713.4710.6828.6210.7629.2910.7128.9610.8029.63
28-2776.4910.6124.6810.7525.9710.7425.9710.7525.97
29-13010.0010.2010.0010.2010.0010.2010.0010.2010.00
30-090.0010.3311.1110.3311.1110.3311.1110.3311.11

31 HCPCasesSidedFixedStrongerTamerUtopian
All ways10966110.1811.6361.8711.6562.7311.6562.7611.7165.63
16-152137110.1211.6663.2511.6763.3711.6863.9811.7366.97
17-142018910.2311.6663.0311.6763.5611.6864.0511.7467.07
18-131798310.2911.6563.0011.6663.8311.6763.7511.7266.74
19-121484110.5011.6362.1611.6563.2611.6663.4011.7166.20
20-111198010.4411.6261.3011.6462.5411.6462.2011.7065.15
21-1087999.7311.6061.0411.6262.3511.6161.8011.6764.66
22-959599.9511.5959.8111.6261.0511.6060.5111.6662.98
23-838479.6711.5758.1811.6159.8611.5958.9611.6461.66
24-723279.0211.5357.0711.5758.6611.5557.5411.6059.82
25-6127810.8011.5054.2311.5656.9611.5455.8711.5857.75
26-56249.9411.3648.5611.4250.8011.3849.8411.4351.44
27-428710.1011.2848.0811.3050.1711.3049.1311.3551.92
28-31166.9011.2744.8311.3045.6911.2944.8311.3145.69
29-2407.5011.0840.0011.1842.5011.1342.5011.1842.50
30-11723.5310.4111.7610.6517.6510.5917.6510.6517.65
31-030.0011.3333.3311.3333.3311.3333.3311.3333.33

32 HCPCasesSidedFixedStrongerTamerUtopian
All ways638517.4212.0079.7012.0180.4412.0280.4412.0582.88
16-1662277.1812.0280.9212.0280.9212.0381.4012.0783.91
17-15122497.7112.0280.8812.0381.2112.0481.5712.0884.24
18-14110067.4112.0280.5012.0381.0912.0381.2712.0783.73
19-1396227.3512.0180.1912.0381.1212.0381.1212.0783.40
20-1277897.2711.9979.1512.0180.1012.0179.9312.0582.33
21-1160037.9811.9979.3912.0180.8912.0180.5112.0583.06
22-1042707.2611.9979.1812.0079.8112.0079.6512.0481.99
23-929627.2211.9777.4511.9978.5311.9877.9212.0180.18
24-817687.4711.9276.0711.9577.7111.9476.8111.9879.30
25-79895.3611.9175.8311.9377.0511.9176.0411.9578.26
26-65557.0311.8671.7111.9073.6911.9073.1511.9274.23
27-52427.0211.7668.1811.7869.4211.7668.6011.7970.66
28-41089.2611.6966.6711.6967.5911.7067.5911.7468.52
29-34010.0011.5052.5011.5355.0011.5052.5011.5355.00
30-2137.6911.3138.4611.3846.1511.3846.1511.3846.15
31-1616.6710.6716.6710.8316.6710.8316.6710.8316.67
32-020.0012.50100.0012.50100.0012.50100.0012.50100.00

33 HCPCasesSidedFixedStrongerTamerUtopian
All ways351283.9012.3191.9612.3292.3112.3292.3212.3493.61
17-1669213.9912.3191.9512.3192.2312.3292.5212.3493.84
18-1563353.7712.3292.8512.3292.9912.3292.9912.3494.38
19-1457184.0212.3192.2412.3292.3212.3292.6212.3493.90
20-1348253.9812.3392.4112.3392.9912.3392.8512.3594.07
21-1237734.0312.2991.9712.3092.6812.3092.5512.3293.88
22-1127593.9512.3392.0312.3392.4212.3492.2812.3593.48
23-1019543.5312.3290.8912.3290.8912.3290.6312.3492.07
24-912293.7412.2889.8312.2889.9912.2889.9912.2990.97
25-87843.4412.2589.0312.2890.6912.2690.0512.2891.07
26-74453.1512.2790.5612.2891.0112.2890.3412.2991.24
27-61964.0812.2391.3312.2692.8612.2191.3312.2793.37
28-51234.8812.1582.9312.1884.5512.1884.5512.1984.55
29-4410.0012.1287.8012.1287.8012.1287.8012.1287.80
30-32015.0011.8070.0011.8070.0011.7565.0011.8070.00
31-240.0012.25100.0012.25100.0012.25100.0012.25100.00
32-110.0012.00100.0012.00100.0012.00100.0012.00100.00
33-00

34 HCPCasesSidedFixedStrongerTamerUtopian
All ways173031.3412.5697.8512.5697.8712.5697.9012.5698.25
17-1716561.3912.5897.8912.5897.8912.5897.8912.5898.31
18-1632471.3612.5798.1212.5797.8712.5798.0912.5898.58
19-1529930.9412.5798.3612.5798.2312.5798.4012.5898.60
20-1426481.5512.5698.0712.5698.2612.5698.0712.5798.60
21-1321441.0312.5597.5712.5697.7112.5597.6712.5697.95
22-1215661.2112.5698.2112.5698.2112.5698.2112.5798.47
23-1112031.6612.5297.0912.5397.3412.5397.2612.5397.59
24-107591.7112.5398.2912.5398.4212.5398.4212.5498.68
25-95021.9912.5296.2212.5396.6112.5296.4112.5396.81
26-82881.0412.5296.5312.5296.5312.5296.5312.5296.53
27-71692.9612.5395.2712.5396.4512.5395.8612.5496.45
28-6714.2312.3591.5512.3491.5512.3792.9612.3792.96
29-5382.6312.55100.0012.58100.0012.58100.0012.58100.00
30-4120.0011.9283.3311.9283.3311.9283.3311.9283.33
31-360.0011.8350.0011.8350.0011.8350.0011.8350.00
32-20
33-110.0012.00100.0012.00100.0012.00100.0012.00100.00
34-00

35 HCPCasesSidedFixedStrongerTamerUtopian
All ways79300.5212.7499.5312.7599.6312.7499.5712.7599.70
18-1715360.4612.7699.8012.7699.9312.7699.8012.7699.93
19-1614820.4712.7599.3312.7599.3912.7599.3912.7599.46
20-1512350.2412.7599.6012.7599.7612.7599.6812.7599.76
21-149950.9012.7499.3012.7499.4012.7499.4012.7599.70
22-138430.7112.7499.5312.7499.6412.7399.5312.7499.64
23-126830.0012.7799.8512.7799.8512.7799.8512.7799.85
24-114590.2212.7399.5612.7399.5612.7399.5612.7399.56
25-103070.9812.6999.6712.6999.6712.6999.6712.69100.00
26-92050.9812.7099.0212.7199.0212.7199.0212.7199.02
27-8972.0612.6797.9412.6798.9712.6697.9412.6898.97
28-7492.0412.80100.0012.80100.0012.80100.0012.82100.00
29-6310.0012.65100.0012.65100.0012.65100.0012.65100.00
30-560.0012.50100.0012.50100.0012.50100.0012.50100.00
31-420.0012.50100.0012.50100.0012.50100.0012.50100.00
32-30
33-20
34-10
35-00

TopMain

Game in a Major

The following tables show the positional advantage of declaring four of a major for partnerships of 21-28 HCP. Sided shows the percent of cases in which the declaring hand matters. Stats for the declaring hand are shown in four categories: Fixed = same declarer throughout, which is effectively an average; Stronger = played by the hand with more HCP; Tamer = played by the more balanced hand; Utopian = always played from the better side, which of course is unattainable in practice.

Each declaring category shows two numbers: (1) Average tricks won, which is the main concern at matchpoint scoring, and (2) the percent of cases four of a major makes, which is the main concern at IMP scoring. Play by both sides is double-dummy, however, past studies have shown this to be in close proximity to actual play.

Unlike the 3 NT scenario, the tamer hand is not the preferred declarer for game in a major. The stronger hand has a greater advantage for all HCP and splits, barring a few narrow exceptions. The stats run pretty close, however, so there’s little to gain or lose either way.

The percent of sided cases (choice of declarer matters) is much lower for suit contracts than at notrump, peaking at only 8.56 percent (27-28 HCP) versus 13.91 percent for 3 NT. Therefore, seeking to right-side suit contracts is less important, suggesting a rule of golf, “Play ‘em where they lie.”

Note that for the same HCP content, make percents are much higher for major-suit games than for 3 NT. This is because distributional factors are almost always present, sometimes extremely so, creating games out of thin air. Let this be a warning to anyone who evaluates a bridge hand by HCP alone. Distributional points must always be considered to bid accurately in a point-count system. Or as most experts would agree, shape rules as the greatest incentive to be aggressive.

Another difference is that the impact of apportionment is only slight. For instance, with 24 HCP your chance of making four of a major (assuming a fixed declarer) is 68.25 percent if the HCP are split 12-12, and 64.04 percent if the HCP are split 21-3. Quite a difference! A drop of only 4 percent, versus 15 in 3 NT. No doubt this is because ruffing ability often provides the needed communication.

21 HCPCasesSidedFixedStrongerTamerUtopian
All ways14980476.518.9430.508.9530.718.9430.548.9731.31
11-103315726.378.9631.088.9631.138.9631.108.9931.92
12-93048176.478.9530.598.9530.748.9530.618.9831.42
13-82646846.488.9630.898.9731.118.9630.918.9931.72
14-72140396.488.9430.538.9530.788.9430.578.9831.34
15-61522386.648.9330.048.9430.408.9330.128.9630.85
16-51045026.588.9229.768.9330.128.9229.828.9530.55
17-4655226.878.9029.528.9229.948.9129.598.9430.28
18-3352266.838.8728.638.8929.088.8728.708.9029.38
19-2157127.058.8628.458.8828.908.8628.538.8929.19
20-171597.388.8528.198.8828.728.8528.368.8928.83
21-025766.488.8628.658.8929.008.8628.738.8929.08

22 HCPCasesSidedFixedStrongerTamerUtopian
All ways14059436.879.2941.559.3041.839.2941.609.3342.66
11-111549546.839.3142.279.3142.279.3142.279.3543.41
12-102965336.709.3142.099.3142.199.3142.149.3443.20
13-92658726.789.3041.859.3142.089.3041.919.3342.98
14-82227976.919.3041.869.3142.169.3041.899.3442.94
15-71730946.979.2941.409.3041.869.2941.499.3342.56
16-61205317.129.2740.729.2941.169.2740.799.3141.80
17-5800046.939.2640.369.2841.019.2640.439.3041.44
18-4488306.839.2640.259.2840.859.2640.329.2941.32
19-3254477.509.2238.699.2439.299.2238.959.2539.76
20-2112067.679.2038.199.2338.809.2038.299.2439.16
21-149927.079.1937.509.2238.449.1937.869.2238.58
22-016837.909.2137.679.2438.449.2237.859.2538.50

23 HCPCasesSidedFixedStrongerTamerUtopian
All ways12685047.299.6454.369.6554.739.6454.459.6855.76
12-112707877.219.6655.099.6655.149.6655.139.6956.46
13-102528447.189.6554.869.6655.089.6554.929.6956.26
14-92199477.289.6554.789.6655.089.6554.859.6956.17
15-81774267.269.6554.529.6654.949.6554.569.6855.91
16-71350057.369.6354.209.6554.779.6454.269.6755.59
17-6911067.379.6153.189.6353.929.6153.359.6554.59
18-5582147.449.6052.389.6253.229.6052.659.6353.82
19-4341917.709.5951.979.6152.839.5952.279.6353.40
20-3173497.939.5850.799.6051.929.5851.209.6252.43
21-273207.429.5450.409.5751.309.5550.869.5851.64
22-132717.779.5449.539.5750.759.5550.059.5851.02
23-010447.289.5248.189.5649.439.5348.959.5649.52

24 HCPCasesSidedFixedStrongerTamerUtopian
All ways10953157.729.9967.6610.0068.089.9967.7410.0369.22
12-121159237.7010.0068.2510.0068.2510.0068.2510.0469.76
13-112250807.7010.0068.4510.0068.5910.0068.4610.0469.98
14-102039307.7210.0068.3010.0168.5710.0068.3610.0469.84
15-91699367.699.9967.6410.0068.149.9967.7610.0369.27
16-81346027.739.9967.5110.0068.119.9967.6110.0269.10
17-7991227.899.9867.089.9967.789.9867.1810.0268.66
18-6649117.579.9566.399.9767.209.9666.569.9967.93
19-5400767.779.9465.749.9766.619.9565.929.9867.24
20-4230997.719.9465.099.9666.209.9465.379.9866.80
21-3114297.979.9164.049.9465.269.9264.439.9565.70
22-245957.839.8662.399.8963.689.8762.929.9064.03
23-119967.929.8762.789.9264.789.8963.689.9264.88
24-06167.959.8863.319.9365.269.9064.299.9365.42

25 HCPCasesSidedFixedStrongerTamerUtopian
All ways9069798.1710.3279.3610.3379.7310.3279.4110.3680.85
13-121876748.3010.3379.6610.3379.7310.3379.7010.3781.13
14-111786368.1310.3479.9610.3480.1410.3479.9810.3881.39
15-101538878.0210.3379.7910.3480.0710.3379.7810.3781.23
16-91256728.1910.3279.4210.3379.8510.3279.4610.3680.92
17-8960148.1210.3179.0410.3279.5810.3179.0810.3580.54
18-7693008.3410.3178.8210.3379.6110.3178.9810.3580.45
19-6435838.1210.2878.2110.3079.0410.2878.2910.3279.79
20-5264308.2010.2777.5310.3078.4110.2877.6910.3179.13
21-4145467.9310.2777.9010.3078.8310.2877.9710.3179.41
22-369978.2710.2375.6510.2576.7610.2375.8210.2777.49
23-228228.0410.1774.4510.2075.6610.1874.8110.2176.26
24-111056.7010.1672.4910.2074.3010.1873.2110.2074.39
25-03138.3110.2875.0810.3176.6810.2875.7210.3277.32

26 HCPCasesSidedFixedStrongerTamerUtopian
All ways7186598.4210.6488.3410.6588.6110.6588.3810.6989.49
13-13743438.3910.6588.5310.6588.5310.6588.5210.6989.59
14-121442388.4410.6688.6110.6688.6810.6688.6210.7089.73
15-111301838.5110.6688.5710.6788.7510.6688.6510.7089.71
16-101120078.3410.6488.5510.6588.8010.6588.5810.6989.66
17-9878038.3610.6488.2610.6588.6310.6488.3410.6889.43
18-8654018.2410.6388.1710.6588.6010.6488.1810.6889.35
19-7450708.5610.6387.8910.6588.4010.6387.9410.6789.10
20-6280938.5010.6187.5810.6388.3110.6187.6410.6588.90
21-5164858.4910.6287.5210.6488.1510.6287.5010.6688.63
22-486388.5210.5986.8410.6187.7110.5987.0110.6388.23
23-340518.6410.5685.6310.5986.6010.5685.4910.6086.79
24-215638.5110.5584.3310.5885.3510.5684.6410.5985.73
25-161510.0810.5385.0410.5886.3410.5484.8810.5986.50
26-01695.3310.6485.8010.6686.9810.6485.8010.6686.98

27 HCPCasesSidedFixedStrongerTamerUtopian
All ways5434858.5610.9694.0010.9794.1910.9694.0411.0094.80
14-131108688.5710.9794.1410.9794.1910.9794.1711.0294.92
15-121028288.4510.9694.0610.9794.1610.9694.1111.0094.86
16-11914008.7710.9794.1910.9794.3210.9794.2511.0194.99
17-10759338.5810.9694.0810.9894.3110.9794.0911.0194.83
18-9576778.5510.9594.0510.9794.2610.9594.0311.0094.82
19-8414008.4010.9493.9310.9694.2410.9493.9310.9894.72
20-7280268.4610.9493.6410.9694.0810.9493.6710.9894.46
21-6171868.6210.9293.4010.9493.8710.9293.5510.9694.32
22-596648.3610.9093.0910.9393.7810.9193.2510.9594.06
23-449598.5510.8892.4410.9193.2410.8992.7210.9293.57
24-322957.8910.8491.9810.8792.5510.8592.2910.8892.94
25-287911.9510.8091.9210.8592.8310.8191.2410.8693.29
26-12866.9910.8390.5610.8691.6110.8491.2610.8691.96
27-0843.5711.0096.4311.0297.6211.0297.6211.0497.62

28 HCPCasesSidedFixedStrongerTamerUtopian
All ways3905988.5611.2697.2211.2697.2811.2697.2011.3097.65
14-14401318.6411.2797.2911.2797.2911.2797.2211.3197.67
15-13766438.5711.2797.3011.2797.3211.2797.3311.3197.71
16-12691528.6111.2697.3011.2797.3011.2697.2811.3197.70
17-11598828.7911.2697.2411.2797.2811.2697.2111.3197.70
18-10482128.5011.2697.2811.2797.3911.2697.2411.3197.71
19-9355238.4611.2497.0811.2597.1811.2497.0611.2897.55
20-8253598.2511.2497.0211.2697.2311.2497.0711.2897.50
21-7162498.3911.2597.3211.2797.5111.2597.2711.2997.78
22-694968.5711.2196.6811.2496.9411.2296.6711.2697.27
23-553828.3611.1996.8411.2197.0811.1996.8611.2397.31
24-427447.5811.2196.4311.2496.6811.2296.5011.2597.05
25-312278.3111.1896.1711.2196.5011.1995.8411.2296.74
26-24319.0511.1596.2911.1997.2211.1696.7511.2097.22
27-11336.0211.1396.9911.1296.9911.1196.9911.1496.99
28-0345.8811.18100.0011.21100.0011.21100.0011.21100.00

TopMain

Slam in a Suit

The following tables show the positional advantage of declaring six of a suit for partnerships of 29-35 HCP. Sided shows the percent of cases in which the declaring hand matters. Stats for the declaring hand are shown in four categories: Fixed = same declarer throughout, which is effectively an average; Stronger = played by the hand with more HCP; Tamer = played by the more balanced hand; Utopian = always played from the better side, which of course is unattainable in practice.

Each declaring category shows two numbers: (1) Average tricks won, which may be of concern at matchpoint scoring, and (2) the percent of cases six of a suit makes, which is the main concern at IMP scoring. Play by both sides is double-dummy, however, past studies have shown this to be in close proximity to actual play.

Stats for declaring six of a suit are pretty much as would be expected. The importance of sided consideration is reduced (as with 6 NT) and dwindles rapidly as the HCP total increases. Like major-suit games, the stronger hand is a better declarer choice than the tamer, high-card apportionment matters little, and make percents run high because of the likely distributional factors. Bid ‘em up!

29 HCPCasesSidedFixedStrongerTamerUtopian
All ways2700458.1411.5453.2511.5553.7711.5453.3911.5855.59
15-14536508.1511.5554.1511.5654.3011.5654.3011.6056.50
16-13506688.3811.5553.8511.5554.0611.5553.8411.5956.23
17-12445128.0611.5452.9411.5553.5011.5453.1511.5855.40
18-11371368.2911.5453.2311.5553.7611.5453.2911.5855.56
19-10291598.0911.5453.3511.5654.1711.5553.5811.5855.76
20-9211987.8211.5352.6711.5453.6111.5352.9111.5754.94
21-8145318.1811.5252.0711.5452.9911.5252.2111.5654.28
22-789698.1211.5051.2111.5252.1511.5051.3811.5453.36
23-652897.7511.5151.8111.5353.1311.5252.3011.5554.04
24-527937.1611.4951.3811.5252.6711.5051.8111.5353.28
25-412977.5611.4851.1211.5052.5811.4951.8111.5253.12
26-35545.9611.4048.1911.4249.1011.4148.5611.4349.28
27-220510.7311.3845.3711.4146.8311.4046.3411.4347.32
28-1653.0811.5247.6911.5447.6911.5147.6911.5447.69
29-0195.2611.4757.8911.5357.8911.5357.8911.5357.89

30 HCPCasesSidedFixedStrongerTamerUtopian
All ways1744577.4311.8166.9811.8267.4711.8167.0511.8569.42
15-15172517.2311.8166.8011.8166.8011.8166.6611.8569.14
16-14338577.3511.8267.3011.8267.5011.8267.3711.8669.76
17-13308347.7011.8267.3111.8267.6111.8267.3511.8669.88
18-12264167.4511.8267.4811.8268.0511.8267.4911.8569.97
19-11212807.6311.8167.1411.8167.7911.8167.2111.8469.59
20-10164027.0711.8166.9411.8267.6511.8167.1011.8569.21
21-9113627.2311.8066.6911.8267.6611.8066.8011.8469.05
22-875347.9411.7865.7411.8066.6411.7965.9011.8268.37
23-746507.0511.8066.6711.8267.5311.8166.9911.8468.80
24-625787.5611.7463.3411.7664.6211.7563.7311.7865.71
25-512676.9511.7664.0111.7865.1111.7864.5611.8066.14
26-46367.3911.7361.1611.7562.7411.7361.1611.7663.52
27-32838.1311.7159.7211.7462.1911.7160.0711.7662.90
28-2717.0411.6861.9711.7063.3811.6863.3811.7063.38
29-1283.5711.6857.1411.6857.1411.6857.1411.6857.14
30-080.0012.0087.5012.0087.5012.0087.5012.0087.50

31 HCPCasesSidedFixedStrongerTamerUtopian
All ways1075536.1412.0578.8312.0679.2612.0678.8912.0980.96
16-15211116.2312.0679.0512.0679.1212.0679.0612.0981.14
17-14198886.0912.0779.1712.0779.4412.0779.2712.1081.36
18-13176966.1712.0679.2712.0679.6012.0679.3012.0981.43
19-12145596.3612.0578.4912.0579.0512.0578.7112.0880.75
20-11116766.1512.0578.4912.0679.1412.0578.5512.0880.68
21-1086496.0212.0478.4812.0579.1912.0478.4412.0780.54
22-958246.1512.0578.8812.0679.7412.0578.7612.0880.98
23-837435.7212.0478.3112.0679.2412.0478.4112.0780.26
24-722275.8412.0478.1312.0578.5812.0478.1312.0779.61
25-611915.7112.0478.9312.0579.6012.0478.8412.0780.18
26-55725.4211.9573.7811.9874.8311.9673.9511.9875.35
27-42605.3811.9877.3111.9978.4611.9877.3112.0179.23
28-31006.0012.1583.0012.1986.0012.1784.0012.2086.00
29-2395.1311.7969.2311.8271.7911.8571.7911.8571.79
30-11513.3311.5346.6711.6753.3311.6046.6711.6753.33
31-030.0011.3333.3311.3333.3311.3333.3311.3333.33

32 HCPCasesSidedFixedStrongerTamerUtopian
All ways621955.0912.2787.7812.2788.1012.2787.7812.2989.36
16-1661515.2312.2787.5312.2787.5312.2787.5112.2989.06
17-15120865.0312.2888.2512.2888.5012.2888.2012.3090.00
18-14107994.6912.2887.9212.2888.1512.2887.9512.3089.42
19-1393525.0712.2788.0112.2788.1612.2787.9512.3089.48
20-1275885.0512.2787.2612.2787.6012.2687.1912.2988.72
21-1158105.5212.2687.5712.2788.2312.2687.7812.2989.33
22-1040825.3212.2688.0512.2788.4612.2687.9512.2889.64
23-927905.0512.2687.7412.2787.9912.2687.5612.2889.00
24-816925.6712.2386.2912.2487.3512.2386.5812.2688.30
25-79564.9212.2788.8112.2889.8512.2688.7012.2990.48
26-65046.5512.2085.9112.2287.5012.2187.1012.2388.29
27-52304.7812.2086.9612.2087.8312.2086.9612.2287.83
28-4965.2112.2586.4612.2687.5012.2486.4612.2787.50
29-3402.5012.2082.5012.2082.5012.2082.5012.2082.50
30-2110.0011.9154.5511.9154.5511.9154.5511.9154.55
31-160.0011.6766.6711.6766.6711.6766.6711.6766.67
32-020.0012.50100.0012.50100.0012.50100.0012.50100.00

33 HCPCasesSidedFixedStrongerTamerUtopian
All ways336853.7012.4793.5712.4793.7812.4793.6812.4994.48
17-1665983.8212.4793.5012.4793.5912.4793.6012.4994.39
18-1561253.1812.4894.2712.4894.4212.4894.2212.4995.05
19-1455033.4212.4693.2812.4693.5112.4693.4812.4794.15
20-1346173.6812.4693.5212.4793.6512.4793.6512.4894.41
21-1236203.8712.4693.4312.4693.7012.4693.6512.4794.56
22-1126693.7812.4893.5912.4993.9312.4993.9712.5094.79
23-1018594.5712.4993.1112.4993.3312.4993.0112.5193.92
24-911863.6312.4693.5112.4693.5112.4693.1712.4894.01
25-87374.4812.4594.1712.4794.9812.4694.4412.4795.12
26-74174.8012.4492.0912.4492.5712.4492.0912.4693.29
27-61844.8912.4493.4812.4694.5712.4492.9312.4794.57
28-51105.4512.4991.8212.5193.6412.5193.6412.5394.55
29-4370.0012.4694.5912.4694.5912.4694.5912.4694.59
30-31915.7912.1689.4712.2189.4712.1684.2112.2189.47
31-2425.0012.0075.0012.0075.0012.0075.0012.0075.00
32-10
33-00

34 HCPCasesSidedFixedStrongerTamerUtopian
All ways164832.6112.6396.7812.6396.8112.6396.7712.6497.17
17-1716062.6812.6497.2012.6497.2012.6497.3212.6597.51
18-1630932.7212.6496.9312.6496.7712.6496.8612.6597.22
19-1528502.2112.6497.0512.6496.8812.6496.8812.6597.23
20-1425393.3512.6296.4612.6396.5712.6296.2212.6497.12
21-1320372.9912.6196.3712.6296.6112.6296.3712.6396.81
22-1215102.2512.6397.0912.6397.0912.6397.2212.6497.42
23-1111242.4912.6196.6212.6296.8912.6296.8912.6397.15
24-107071.5612.6596.4612.6696.7512.6696.8912.6697.17
25-94692.7712.6095.9512.6096.3812.6096.1612.6196.38
26-82691.4912.6597.4012.6597.4012.6597.4012.6797.40
27-71542.6012.6697.4012.6698.0512.6798.0512.6798.05
28-6700.0012.5394.2912.5394.2912.5394.2912.5394.29
29-5372.7012.65100.0012.68100.0012.68100.0012.68100.00
30-4110.0012.5590.9112.5590.9112.5590.9112.5590.91
31-360.0012.6783.3312.6783.3312.6783.3312.6783.33
32-20
33-110.0012.00100.0012.00100.0012.00100.0012.00100.00
34-00

35 HCPCasesSidedFixedStrongerTamerUtopian
All ways74522.2812.7598.3212.7698.3612.7698.4212.7798.64
18-1714602.3312.7798.9012.7899.0412.7898.9012.7999.18
19-1614082.5612.7497.9412.7497.8012.7497.9412.7598.22
20-1511812.2012.7598.3112.7698.3912.7698.3112.7698.48
21-149502.5312.7698.0012.7598.0012.7598.2112.7798.53
22-137763.0912.7898.8412.7898.9712.7899.1012.8099.36
23-126241.7612.7698.4012.7698.2412.7698.5612.7798.56
24-114201.1912.7198.5712.7198.5712.7198.5712.7298.81
25-102811.0712.7497.8612.7598.2212.7497.8612.7598.22
26-91871.6012.7596.2612.7696.7912.7697.3312.7797.33
27-8863.4912.7497.6712.7697.6712.7697.6712.7697.67
28-7440.0012.82100.0012.82100.0012.82100.0012.82100.00
29-6273.7012.6396.3012.6396.3012.6796.3012.6796.30
30-550.0012.80100.0012.80100.0012.80100.0012.80100.00
31-420.0013.00100.0013.00100.0013.00100.0013.00100.00
32-310.0013.00100.0013.00100.0013.00100.0013.00100.00
33-20
34-10
35-00

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Honor Holdings

I thought it would be interesting to examine the specific honor holdings in each case that was sided (choice of declarer matters). The data source seems large enough for this to provide a meaningful ranking of the positional value of each holding. More specifically, the frequency in which a holding appears in the optimal declaring hand would be a grading scale; the more frequent, the greater its positional value.

I decided to limit the scope to notrump cases, not only because positional values are more prominent there but to eliminate ruffing ability as a factor. A suit contract is sometimes right-sided because the opening leader cannot deliver a ruff, which is irrelevant to this issue.

Doubletons and tripletons are the obvious candidates. Singleton honors may have positional value in actual play but not at double-dummy. On this farm, you can run but you can’t hide; bid 3 NT with a stiff king, and the ace will be led every time. Honors in 4+ card suits certainly can have positional value, but it’s less likely, and the ranking would almost surely mirror the 3-card holdings.

The following table lists each doubleton or tripleton honor holding and the number of times it occurred in sided notrump contracts. Declarer shows the percent of time the holding appeared in the hand of the optimal declarer as opposed to dummy.

For the most part the list flows as expected, save a few oddball results. Why would A-K and K-Q doubleton appear significantly more often in the optimal declaring hand? Strange, since the only possible positional advantage would be if the opening leader were void, which seems too remote to account for the percentage. This prompted me to recheck the numbers via different software, but the results were the same. Something to think about, though I’ll pass on examining 40,000+ deals individually.

[Addendum] I think I understand the above anomaly. If one hand has A-K or K-Q doubleton, that suit is eliminated from having positional value in either hand (barring voids). The hand with A-K or K-Q doubleton has 11 available spaces for positional holdings in the other suits. The opposite hand, however, rates to have 3+ cards (3.67 on average) facing the A-K or K-Q doubleton, hence fewer available spaces for positional holdings in the other suits.

HoldingOccurrenceDeclarer
A-Q4182679.05
K-102645873.49
A-J2849572.64
K-x21548571.98
A-Q-101447470.84
A-J-x10662470.20
K-J2552969.55
A-Q-x11442468.89
K-J-x9111368.48
A-102510468.19
A-J-101151866.10
A-K-101347465.40
K-10-x7723363.90
A-K-J1395163.74
A-Q-J1318162.80
K-x-x27414462.20
Q-x-x25185461.75
K-J-10963661.19
Q-x18114560.18
K-Q-x8584560.06
Q-10-x6327559.84
A-10-x7105659.10
K-Q-101059059.10
Q-102036255.43
K-Q1937155.27
A-K-x8994955.08
Q-J-x6577954.66
A-K2296254.48
A-x21059154.16
K-Q-J982350.74
A-K-Q1230049.61
J-x12173149.47
J-x-x17551848.79
A-x-x24112048.68
Q-J-10725647.97
Q-J1868845.37
J-101425543.95
J-10-x5187342.28
10-x-x14122540.54
10-x11668038.31
x-x-x28419537.41
x-x43223733.43

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© 2014 Richard Pavlicek