Main   Study 8J25 by Richard Pavlicek

Optimal IMP Strategy

International Match Points (IMPs) is by far the most widely used form of scoring in major bridge events. Its main objective is to balance the significance of deals, particularly to increase the weight of partscores and to decrease the weight of slams. Virtually all experts agree that it makes bridge a more competitive game than traditional scoring by total points.

Most players are familiar with basic IMP strategy, such as to bid close games, especially vulnerable, and the sundry odds for slam bidding. This study goes much deeper by calculating the optimal bid, on average, for all HCP divisions. Partnerships are appraised in four ways:

Category definitions: (1) Balanced Notrump = both hands balanced, 4-4-4-1 or 5-4-2-2.* (2) Semibalanced Notrump = one hand balanced, 4-4-4-1 or 5-4-2-2, and the other 5-4-3-1, 6-3-2-2, 6-3-3-1, 7-2-2-2 or 7-3-2-1. (3) Eight-Card Major Fit = trumps divided 4-4, 5-3 or 6-2 and no longer fit; (4) Nine-Card Major Fit = trumps divided 5-4, 6-3 or 7-2 and no longer fit. Note that a partnership may qualify for both notrump and trump-fit appraisal.

*I experimented by splitting Category 1 according to whether a 5-card suit was held, but results were virtually the same; hence no practical benefit would emerge. Limiting the breakdown to just four categories (two for notrump, two for suit play) also ensures a uniformly large data source for each.

All statistics were derived from my database of 10,485,760 random solved deals by selecting the partnership with 20-36 HCP.* Notrump contracts were evaluated with the more balanced hand declarer; suit contracts with the longer trump hand declarer. Ties were broken by choosing a fixed declarer (effectively random). Suit identity is irrelevant for this purpose, so any fit was deemed to be a major for trump analysis. Where multiple trump fits of the same length exist (e.g., a 4-4 and 5-3 fit) the higher ranking was chosen to emulate the practice of preferring a major.

*In the case of 20-20 HCP only one side (chosen randomly) was evaluated to avoid skewing the statistics.

Results are determined at double-dummy, which casts some doubt on what might occur in actual play. Previous studies, however, show a close relationship (see Actual Play vs. Double-Dummy) although actual play enjoys a slight advantage (except at the slam level). For these statistics, however, any slight advantage is probably erased, because optimal IMP strategy does not consider that failing contracts may be doubled; hence the actual declarer will fare slightly worse on average. Who knows? While too subjective to calculate, this might put the numbers right on the money.

Balanced Notrump

The following tables apply to partnerships with 20-36 HCP and both hands balanced, 4-4-4-1 or 5-4-2-2. For each HCP division, Tricks shows the average number of tricks won; No Bid shows the percent of cases no notrump bid makes; 1 NT thru 7 NT shows the percent of cases making that contract exactly. Optimal bids are tinted gold (any vul), green (nonvul only) or red (vul only). Underbid (Overbid) shows the difference between the optimal bid and its rival underbid (overbid) for each vulnerability in IMPs per board.

Bids of 2 NT, 4 NT and 5 NT can never be optimal or rivals. A light tinting indicates cases where it is better to overbid further. For example, if 1 NT is optimal and 2 NT is tinted light red, it means that vulnerable it is better to bid 3 NT than play in 2 NT.

A controversial issue is the exact HCP threshold at which 3 NT becomes the optimal venture in general, i.e., for this “balanced notrump” category. There’s no question that 23 HCP is a definite no, and 25 is a definite yes; but what about 24? Evidence from actual play shows an advantage for bidding 3 NT on 24 HCP when the other table did not, but statistics here say no. So which is right? I think the true answer is no. Cases from actual play were not “auto 3 NT on 24 points” but chosen opportunities, often because a player upgraded a hand with good spot cards or well-positioned honors.

Another factoid about 24 HCP (except for lopsided divisions of 18-6 or worse) is that vulnerable it is better to bid 3 NT than stop in 2 NT. For example, if partner opens 1 NT (15-17) vulnerable and you have 9 HCP, you should not invite with 2 NT but just bid 3 NT; hence an invitation should show at most 8 HCP. (Nonvulnerable this does not apply.)

One clear message, defying traditional belief, is the HCP requirement for 6 NT. Pedants for years have dictated 33 HCP, but statistics show that only 31, on average, makes 6 NT a winning venture (except for lopsided divisions of 24-7 or worse). Similarly, 35 HCP is the average threshold for 7 NT to be profitable. The obvious implication is to loosen up your quantitative bidding at IMPs, though you need to be more wary of being off two cashable tricks (or an ace in 7 NT).

20 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
10-10369756.0765.0725.238.511.090.100.01000.631.66
11-9715196.0964.2225.858.711.130.080.01000.581.60
12-8636706.0864.5025.728.681.020.070.01000.591.62
13-7534506.0565.9524.968.070.970.050.00000.681.74
14-6399446.0167.3224.417.390.820.060.01000.771.85
15-5283555.9669.5123.086.630.720.060.00000.902.02
16-4187045.9370.8722.146.310.630.050000.972.12
17-3102645.8473.4920.775.210.500.030001.162.38
18-250585.7576.6118.883.970.470.060001.362.65
19-124595.6680.7615.133.500.6100001.613.00
20-09295.6380.1914.964.090.7500001.633.06

21 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
11-101412386.6045.4033.0917.583.560.340.020.0000.57     3.660.08
12-91301136.5945.5933.1417.413.510.330.020.0000.563.660.10
13-81134266.5845.7533.4017.243.300.290.02000.553.690.12
14-7929676.5646.6933.2116.723.100.260.02000.493.690.18
15-6667926.5248.3333.0215.742.670.240.01000.403.710.30
16-5465786.4650.7432.4814.352.250.180.02000.263.720.47
17-4300936.4252.4931.8613.511.970.160.01000.163.710.59
18-3164376.3455.4131.3911.401.670.140000.010.82
19-275786.2260.2128.939.790.950.120000.291.19
20-135836.1564.0525.519.271.060.110000.521.49
21-013606.1764.1225.298.971.400.220000.501.45

22 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
11-11660507.1227.9033.4828.388.981.190.070.0001.621.243.324.42
12-101262427.1128.0533.7528.258.701.150.090.0101.611.223.344.47
13-91137007.1028.5333.7827.908.601.110.080.0001.581.203.354.49
14-8967097.0828.4234.6227.877.971.040.080.0001.581.193.434.61
15-7756227.0629.0335.0627.487.400.940.080.0001.541.143.494.71
16-6533057.0130.4535.4126.466.890.730.050.0101.451.043.554.82
17-5362466.9731.6636.2725.335.940.770.030.0101.380.953.634.97
18-4227876.9133.4436.7424.105.080.590.05001.270.823.705.12
19-3118846.8136.7036.9921.824.010.410.06001.080.583.775.29
20-254856.7439.1137.8519.363.450.220.02000.940.413.815.40
21-125036.6045.9835.9615.422.480.160000.583.790.02
22-09176.5947.6633.5916.142.400.220000.493.760.13

23 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
12-111157737.6215.4327.6335.4617.563.530.360.020.002.432.232.332.69
13-101079087.6015.9827.7235.5316.953.450.360.0202.402.192.402.79
14-9947507.6015.6328.1935.6316.843.330.350.0202.412.202.432.84
15-8776417.5915.5228.6136.1016.403.070.290.0202.412.212.512.97
16-7595987.5615.9629.6035.8615.572.750.250.0202.372.162.643.16
17-6407447.5116.8730.0736.2014.332.280.240.0102.302.082.813.44
18-5268397.4617.4131.8235.3413.062.170.200.0102.262.032.953.67
19-4164047.4118.0433.6034.8611.591.730.160.0202.201.973.154.00
20-384277.3119.8236.1133.299.521.200.060.0102.081.833.424.44
21-236557.2422.3837.3531.227.501.420.14001.941.663.564.70
22-116307.0925.6439.3328.225.770.980.06001.721.383.745.05
23-05767.1326.0438.8927.267.290.520001.741.433.624.88

24 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
12-12496758.127.9918.8835.7527.468.551.290.060.003.052.950.730.13
13-11968568.127.8118.9135.9727.538.491.200.080.003.062.960.740.14
14-10876168.108.1319.0236.1727.178.261.150.1003.032.930.800.24
15-9739688.097.9719.4936.2827.167.871.130.090.003.032.930.850.31
16-8594508.078.0719.6737.2126.387.590.990.080.003.012.910.980.51
17-7445498.038.1620.6937.9625.436.820.870.0702.982.871.190.81
18-6296637.998.2621.4738.8124.276.310.830.050.002.952.851.371.10
19-5185977.948.5722.8039.2123.365.190.790.080.012.902.791.591.43
20-4110907.888.2524.7540.9620.894.430.680.0502.882.771.972.00
21-355547.7710.2127.7639.7218.193.690.400.0402.732.612.342.61
22-223817.6910.1231.7138.6816.302.940.210.0402.702.592.653.10
23-110297.5412.5436.4436.1511.862.720.190.1002.532.373.113.86
24-03557.4714.6536.9036.0610.421.410.280.2802.392.233.344.24

25 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
13-12810888.604.0011.2329.0934.8417.013.430.370.011.202.847.8110.59
14-11765868.603.8911.4429.3434.6416.873.440.370.011.162.787.7910.57
15-10668208.583.9611.5130.0734.4816.383.310.290.011.072.647.7510.54
16-9552628.573.9511.6030.3334.5915.883.310.320.021.032.587.7110.51
17-8432738.544.2511.9130.6234.9715.062.900.290.000.942.447.6610.47
18-7313618.514.0112.3532.1234.0614.482.670.280.020.752.167.5410.35
19-6203448.463.8013.2533.9333.2513.172.390.190.010.471.757.3910.22
20-5126088.403.9314.1735.3032.9811.292.120.200.020.201.357.2110.07
21-470898.354.1314.6136.9031.8110.811.570.160.013.360.990.049.94
22-334508.264.4917.6837.9128.709.361.620.2303.280.250.529.62
23-215168.155.1518.0741.2927.976.271.190.0703.163.090.990.45
24-16408.063.9124.2242.3422.505.780.780.4703.173.131.671.48
25-01877.886.9528.8839.5718.725.350.53002.962.892.162.28

26 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
13-13319619.091.966.7019.5434.6527.588.441.100.042.945.448.7811.36
14-12627609.092.156.4119.8834.5927.098.631.180.062.915.418.7411.32
15-11568759.082.096.4819.9534.8626.888.441.240.072.905.398.7211.30
16-10488809.062.136.6020.6934.6226.768.081.070.052.815.258.6911.29
17-9389159.041.876.7621.1335.3526.277.551.020.062.765.198.6811.29
18-8296919.021.836.6122.0735.8225.317.291.040.042.685.078.6311.25
19-7208419.001.736.8522.3136.5324.886.830.800.082.645.018.6511.29
20-6133698.921.957.1524.5636.7722.965.800.760.032.344.568.4711.14
21-579438.901.907.2026.2735.9422.035.640.960.052.154.298.3010.97
22-443398.831.777.7927.4537.6619.984.241.060.051.964.028.1710.87
23-321268.662.309.4131.7536.5016.373.200.4701.272.987.8510.63
24-28648.561.8511.3435.6534.3814.122.430.2300.662.097.5310.35
25-13488.443.4512.3639.9429.6010.633.450.5703.420.990.069.80

27 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
14-13482279.571.033.5311.9628.0534.8517.003.360.224.207.339.0611.36
15-12454659.571.063.5912.1227.8134.8117.143.260.214.187.299.0611.37
16-11401219.561.103.6612.3627.4934.8017.193.230.184.147.249.0511.36
17-10339259.561.003.5512.4728.3334.4616.673.300.234.157.259.0311.35
18-9262519.541.023.5512.7128.9934.4815.843.200.214.127.219.0411.37
19-8195259.511.063.5512.8129.6134.4915.412.870.204.107.199.1111.45
20-7130759.471.033.6513.3531.0834.1314.102.520.154.047.099.1511.54
21-681769.400.894.0914.7332.6232.2912.922.320.153.856.829.0811.50
22-548019.380.773.5416.1433.8131.1011.812.620.213.776.708.9511.37
23-426099.251.194.3716.7935.7231.089.011.720.113.576.399.0311.54
24-312469.240.563.6119.4237.3228.178.752.090.083.426.198.8711.39
25-24779.050.636.2921.1742.3520.966.291.890.422.925.458.5311.14
26-11618.9604.3531.0637.8919.884.971.8602.114.298.1110.77

28 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
14-141760110.090.681.876.3317.3335.8128.868.520.605.048.578.3710.27
15-133384910.070.562.106.5917.5535.9528.408.160.694.998.508.4110.32
16-123061010.060.582.136.6817.8035.8228.328.040.634.988.488.4410.36
17-112666410.060.592.036.5218.2236.1828.087.780.605.018.528.5210.46
18-102186410.040.532.226.9518.5535.7827.617.730.634.948.438.4810.43
19-91638610.020.652.126.8518.9936.1726.967.700.574.968.458.5110.46
20-8119459.980.712.267.2919.4636.6925.707.250.644.898.348.5510.53
21-776889.960.561.937.5320.9736.9324.846.720.524.918.388.7010.73
22-647329.920.462.268.1421.6036.3723.886.780.514.818.248.6410.67
23-528029.880.321.578.8924.0236.1923.235.070.714.828.268.9711.09
24-414449.800.353.259.9722.7136.8420.845.330.694.517.808.7210.85
25-36709.650.301.6411.0431.0434.6318.512.390.454.587.919.4711.79
26-22519.5002.7919.1228.2929.4815.544.7803.596.478.4110.73

29 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
15-142388810.580.331.183.689.1027.6838.7117.481.845.449.166.397.76
16-132254610.560.291.283.619.5728.0538.3017.231.675.449.166.487.87
17-122029310.570.371.183.589.0928.1538.6217.151.855.449.176.467.84
18-111701810.550.311.333.899.0928.7238.3616.252.055.409.116.598.00
19-101350810.540.331.123.869.2529.0438.4516.241.715.429.146.688.11
20-91011110.530.381.123.409.6730.4837.2116.011.735.479.216.758.19
21-8700910.470.371.143.9810.7330.9736.2114.921.675.409.116.978.46
22-7448610.470.401.183.4610.4532.7035.7814.581.455.459.197.128.64
23-6264010.440.111.523.9811.1033.3334.1313.792.055.399.097.128.66
24-5147410.360.140.954.0013.0935.5533.1812.280.815.449.187.769.42
25-473110.2500.964.6516.2837.2129.4110.121.375.389.098.089.84
26-333310.170.601.204.2021.0234.8325.5311.411.205.359.037.809.57
27-21259.971.601.606.4022.4036.0023.206.402.404.988.468.3910.36

30 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
15-15788311.040.230.861.753.7416.8542.3729.854.355.699.543.283.97
16-141527211.040.260.692.003.9516.8041.6630.184.455.689.523.173.86
17-131397711.050.190.721.963.7216.4842.3830.344.225.699.543.203.88
18-121211911.050.170.681.943.9316.6241.8730.464.335.709.553.153.83
19-11993711.040.220.641.823.8817.4341.6130.394.005.719.573.253.94
20-10779111.020.100.781.873.7417.9742.4829.233.825.709.553.544.28
21-9568211.020.260.652.133.9817.2542.5228.794.425.679.513.484.22
22-8376010.990.130.771.914.3119.0741.1428.913.755.699.543.624.38
23-7235510.910.420.812.004.9719.7542.9325.903.235.659.484.375.28
24-6138010.860.140.722.255.5822.9740.9424.492.905.669.504.765.75
25-570510.880.140.572.275.6722.9841.1322.844.405.689.524.805.80
26-434610.76002.316.6528.6140.7518.792.895.759.636.077.29
27-317410.5901.156.325.1731.6133.9118.972.875.188.795.676.93

31 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
16-15975211.500.070.450.861.446.9135.1745.849.261.221.396.307.94
17-14923511.510.100.340.991.326.8435.0046.009.421.291.486.307.93
18-13832611.500.100.470.701.537.0034.5846.499.141.331.526.398.05
19-12693911.490.130.431.281.217.2834.2146.279.181.331.526.368.01
20-11555111.480.050.470.791.487.5736.0744.379.210.880.996.137.74
21-10418411.460.070.480.961.468.0335.6444.468.910.850.956.187.80
22-9290511.460.140.480.831.148.3036.5943.618.920.660.736.077.68
23-8188011.420.110.480.901.819.6336.3341.499.260.270.265.787.33
24-7118411.350.250.840.842.1110.4736.8240.468.195.799.680.160.26
25-664311.38000.471.8713.6935.6139.508.865.959.930.330.42
26-532811.2000.300.613.3514.0242.6834.454.575.909.852.352.83
27-416511.23001.214.2413.9437.5836.976.065.879.811.451.78
28-36911.26001.451.4514.4940.5836.235.805.849.771.652.00

32 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
16-16281811.880.110.110.530.212.1620.9458.8417.105.766.796.848.50
17-15555711.8800.180.290.472.3020.8958.7517.115.726.756.838.49
18-14507411.860.080.200.490.372.1522.2956.8217.605.436.396.538.14
19-13446611.880.070.200.400.272.4421.0557.5218.055.676.696.568.17
20-12362811.860.030.220.360.442.5422.1357.3616.925.386.356.688.32
21-11282611.870.040.280.320.422.3721.5157.8217.235.566.556.708.34
22-10204911.860.100.200.390.291.9522.4058.6616.015.486.456.968.65
23-9149711.870.070.130.330.271.8024.3855.1817.845.106.016.307.87
24-888611.810.110.340.450.792.3724.3854.5117.044.815.656.337.91
25-751411.85000.580.192.5323.5457.0016.155.136.056.748.40
26-627911.7800003.2329.7553.0513.983.754.436.558.19
27-513211.58002.271.524.5530.3050.7610.612.663.086.718.41
28-46011.73001.6705.0023.3356.6713.334.525.307.078.80

33 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
17-16323412.1800.120.150.090.719.3459.0930.498.7310.315.136.39
18-15287912.200.030.100.140.070.498.5859.9930.608.9510.575.226.50
19-14268112.2000.040.070.070.459.8158.5631.008.7110.295.006.24
20-13228312.200.090.040.1300.2210.2957.5131.718.6510.214.785.98
21-12179912.170.060.060.170.060.399.5660.6429.078.7610.345.506.84
22-11125612.21000.320.080.569.1656.7733.128.8010.394.515.65
23-1092212.19000.220.110.5411.8254.1233.198.229.714.185.27
24-963912.140.1600.3100.4711.2759.1528.648.359.855.386.70
25-839812.150000.250.5011.5659.5528.148.299.805.496.83
26-722912.1900000.4411.3557.2131.008.419.934.836.05
27-610612.19000.94005.6665.0928.309.6111.346.137.58
28-56412.1300001.5612.5057.8128.137.919.345.286.59

34 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
17-1777212.46000003.2447.5449.2210.2912.161.311.78
18-16152712.4500000.132.9549.0547.8710.3212.201.662.21
19-15137112.4600000.072.3349.3148.2910.4712.371.642.18
20-14123612.48000002.9945.7151.2910.3412.220.821.19
21-1399212.4400000.103.3348.9947.5810.2512.111.692.25
22-1273012.4500000.142.4749.7347.6710.4312.321.772.33
23-1159212.43000003.3849.8346.7910.2612.121.902.49
24-1037012.3900000.272.4354.8642.4310.4112.303.073.89
25-927312.46000004.4045.0550.5510.0311.860.841.22
26-815712.4900000.642.5543.9552.8710.3012.170.400.69
27-78712.41000004.6049.4345.989.9911.801.952.56

35 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
18-1774312.70000000.4029.6169.993.554.05
19-1672212.67000001.1131.0267.873.103.52
20-1560312.67000000.3332.6767.002.793.15
21-1449912.69000001.0029.0669.943.614.12
22-1343812.68000000.6830.3768.953.323.78
23-1234412.71000000.2928.7870.933.774.32
24-1122912.65000000.8733.6265.502.482.77
25-1016412.62000000.6137.2062.201.621.74
26-912312.63000000.8134.9664.232.152.38

36 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
18-1816212.8100000019.1480.866.227.26
19-1732712.8700000013.4686.547.648.96
20-1630112.8500000015.2884.727.188.42
21-1522312.8500000014.8085.207.308.56
22-1419812.9000000010.1089.908.479.97
23-1316312.82000000.6116.5682.826.787.93
24-129612.8500000014.5885.427.358.63
25-118112.8600000013.5886.427.608.93
26-105012.8600000014.0086.007.508.80

Semibalanced Notrump

The following tables apply to partnerships with 20-36 HCP, one hand balanced, 4-4-4-1 or 5-4-2-2, and the other 5-4-3-1, 6-3-2-2, 6-3-3-1, 7-2-2-2 or 7-3-2-1. For each HCP division, Tricks shows the average number of tricks won; No Bid shows the percent of cases no notrump bid makes; 1 NT thru 7 NT shows the percent of cases making that contract exactly. Optimal bids are tinted gold (any vul), green (nonvul only) or red (vul only). Underbid (Overbid) shows the difference between the optimal bid and its rival underbid (overbid) for each vulnerability in IMPs per board.

Bids of 2 NT, 4 NT and 5 NT can never be optimal or rivals. A light tinting indicates cases where it is better to overbid further. For example, if 1 NT is optimal and 2 NT is tinted light red, it means that vulnerable it is better to bid 3 NT than play in 2 NT.

From 20-23 HCP there is little difference between this and the balanced notrump category. At 24 HCP, however, the optimal bid shifts to 3 NT when vulnerable (for most HCP divisions); nonvulnerable, 1 NT remains optimal by a slight margin, but it’s better to bid 3 NT than languish in 2 NT. The slam bidding thresholds drop a point to 30 HCP for 6 NT, and 34 HCP for 7 NT.

20 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
10-10280426.1159.8725.4011.482.820.400.02000.441.51
11-9533746.1160.0924.7411.772.980.380.030.0100.441.51
12-8476986.0860.9724.5711.252.830.350.020.0000.501.60
13-7401296.0761.4624.4311.032.670.380.03000.531.63
14-6299506.0063.3823.7110.222.310.360.020.0000.661.81
15-5208925.9765.0822.789.652.200.270.02000.751.92
16-4136785.9067.6421.208.902.030.200.03000.922.15
17-375385.8470.0620.127.801.860.160001.072.34
18-234335.7273.0618.476.931.310.230001.282.66
19-116785.6575.5116.815.961.610.120001.452.89
20-06095.6977.0113.966.402.460.160001.482.90

21 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
11-101070686.6443.6229.7718.996.241.230.130.010.000.63     3.290.08
12-9979566.6244.6829.3818.526.181.140.100.010.000.573.290.16
13-8852956.6144.7629.4718.535.991.140.100.0100.563.310.16
14-7694286.5746.1729.0417.845.731.030.160.0200.483.310.28
15-6497916.5447.0629.4117.235.240.930.120.0100.423.370.35
16-5340926.4849.4528.5916.204.870.820.060.0000.283.380.53
17-4214956.4450.7628.0115.884.610.710.040.0000.193.400.64
18-3115476.3454.0627.1813.894.180.610.0600.010.010.92
19-251126.2557.0825.8613.093.380.550.020.0200.211.17
20-122996.2159.9024.1411.663.610.520.130.0400.351.35
21-08646.3355.5624.0715.973.820.460.12000.101.03

22 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
11-11501447.1728.9129.1226.2511.913.290.450.050.011.591.152.693.49
12-10954967.1529.8729.1825.5211.783.150.440.060.011.541.082.713.52
13-9861227.1529.6529.6525.6111.483.160.420.040.001.551.102.753.59
14-8716127.1429.8529.6425.6611.373.070.370.030.001.541.092.773.62
15-7563417.1030.8230.1425.0610.722.800.410.040.001.471.002.853.76
16-6393687.0232.7730.5824.169.832.290.330.030.011.340.852.973.98
17-5259557.0033.8430.3223.999.022.490.320.030.001.290.783.024.07
18-4160366.9535.0830.8223.108.642.050.270.040.011.200.683.094.20
19-385566.8437.8631.4921.107.661.740.150.0101.010.433.194.41
20-236666.7940.0430.3121.446.761.280.140.0300.890.293.304.59
21-116696.7343.6228.0419.896.771.560.12000.700.053.204.49
22-05336.7644.0925.3320.647.881.690.38000.680.013.024.22

23 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
12-11872407.6818.3424.6529.7418.687.101.310.150.022.362.091.631.70
13-10811477.6718.5824.6329.5518.737.061.300.140.022.342.071.631.70
14-9705057.6518.6825.0729.6318.556.741.150.170.022.332.051.701.80
15-8577437.6419.0725.3729.5418.066.541.230.170.022.302.031.761.90
16-7438977.5919.6826.2629.3917.316.031.150.160.022.251.961.892.12
17-6299437.5320.6927.0529.6416.105.331.040.140.012.171.872.102.45
18-5192917.5020.6628.2729.3815.884.690.940.150.032.151.852.202.61
19-4112407.4321.7230.3527.9514.484.580.840.080.012.071.762.372.89
20-357987.3025.6629.8227.5812.493.590.720.120.021.821.462.623.33
21-224677.2826.6329.4727.7311.673.850.490.120.041.771.392.693.44
22-110617.1629.5030.7325.7310.273.200.3800.191.581.152.873.77
23-03407.1927.0635.2925.009.712.350.59001.721.383.074.06

24 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
12-12376488.2210.7017.9328.4324.9713.973.460.470.063.030.800.069.69
13-11726378.2110.6918.1728.4625.4213.413.240.520.083.030.750.099.66
14-10655728.1811.0218.2428.8824.8313.173.300.510.053.000.620.189.61
15-9549358.1810.7518.7629.0624.5413.163.160.510.073.010.550.239.58
16-8435278.1511.0319.2129.3824.5612.452.890.420.052.970.380.349.55
17-7320128.1011.3119.8930.0924.0111.422.770.450.072.930.110.519.43
18-6213558.0512.0020.7230.1723.2810.892.520.350.072.862.700.680.15
19-5132447.9812.3322.5231.6421.109.592.390.360.052.802.641.070.74
20-477047.9511.6624.1832.5520.378.412.320.440.062.812.651.291.07
21-338557.8414.0125.4531.2819.387.552.020.230.082.652.471.501.43
22-214517.6816.2028.0531.2216.756.271.240.2802.462.241.982.19
23-16787.6716.8129.6530.6814.316.052.060.4402.442.232.152.47
24-02147.7414.0231.3129.9116.826.071.400.4702.622.462.002.21

25 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
13-12600318.736.5112.2522.7027.4122.017.441.490.191.573.317.7310.35
14-11578038.736.3912.3222.9527.4921.637.481.520.231.553.287.7010.32
15-10497548.726.2512.4823.3327.3421.597.351.470.181.503.217.6910.32
16-9406028.696.5512.5423.9027.6220.757.061.360.221.403.067.6410.29
17-8313438.666.3513.0724.4527.8120.136.591.400.191.302.917.5810.23
18-7225508.626.5513.7625.2527.3719.456.111.340.161.122.647.4810.15
19-6145108.566.4114.3526.8927.8617.405.751.170.160.892.307.3710.07
20-586658.496.8715.1328.1727.0916.235.350.980.180.621.897.239.96
21-448158.427.6815.9729.2226.4814.005.401.040.210.341.467.029.77
22-324438.318.8417.0730.4124.6013.884.420.570.203.170.910.029.66
23-29298.199.0421.6430.7921.7412.493.770.5403.090.040.589.39
24-13498.0510.3225.7928.0822.648.603.720.8602.952.810.850.42
25-0988.097.1419.3938.7827.556.121.02003.062.991.040.57

26 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
13-13242349.253.818.1216.0524.2829.5514.253.400.553.005.488.1710.54
14-12462469.273.767.8216.1724.3929.3814.353.590.543.025.528.1510.50
15-11421399.263.697.9216.6424.3729.0714.023.740.552.975.448.0810.43
16-10363359.233.788.1516.7624.8128.5414.123.260.582.925.378.1510.53
17-9285099.193.898.7317.4424.5428.3413.283.380.402.775.148.0610.46
18-8214749.173.908.3817.9025.8327.8012.423.240.532.765.138.0610.47
19-7146369.133.468.7219.6525.9426.9311.643.150.512.574.867.9710.40
20-691979.044.099.6220.5926.4924.7811.072.980.382.314.467.8610.33
21-554689.034.029.1621.0927.9624.109.973.130.572.314.477.7910.26
22-428658.874.1510.4424.9227.9921.578.102.440.381.743.627.6110.17
23-313798.844.4211.6025.6726.8320.238.192.320.731.503.267.419.97
24-25188.724.0512.3628.1928.7617.765.982.320.581.182.787.249.86
25-12078.505.3115.9433.3322.2214.986.761.4500.101.166.869.57

27 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
14-13356129.812.215.0510.6517.2331.7023.718.081.384.077.117.679.64
15-12328479.802.155.2110.7817.5331.2323.808.031.294.057.077.689.67
16-11298309.782.225.0411.0117.8731.6323.217.751.264.047.057.749.74
17-10245509.802.024.9710.5618.1332.2123.077.861.184.117.167.789.78
18-9187799.762.165.2111.3218.5631.5122.317.641.303.996.987.739.74
19-8133469.682.255.5312.5019.9430.8520.347.491.113.816.727.699.75
20-792339.662.445.4212.9519.8730.7619.847.431.293.766.647.639.68
21-657349.602.485.6214.0621.4229.1419.386.631.293.616.427.719.83
22-532659.482.246.5814.9823.8028.7017.125.640.953.436.157.8910.10
23-416659.452.885.5917.4223.5426.5516.766.071.203.215.837.599.79
24-37709.212.477.0121.5627.5324.2912.733.640.782.644.997.8610.26
25-23169.211.5810.4420.2526.9020.8914.245.380.322.484.757.499.85
26-11078.945.617.4828.0424.3018.6912.152.800.931.593.407.309.80

28 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
14-141294310.341.393.296.3810.0527.6832.5715.613.034.818.216.137.59
15-132470710.351.313.156.4510.4727.6232.0616.002.944.838.246.077.53
16-122242010.321.363.506.5210.4127.7632.2115.422.814.788.166.197.68
17-111921610.311.413.416.4710.8428.2931.4715.242.884.798.176.227.72
18-101565310.321.303.306.6110.7028.1231.5115.433.034.798.196.157.63
19-91171710.251.473.577.5612.0327.2930.1914.922.984.647.966.187.71
20-8827410.241.373.737.3012.2128.2229.5514.872.764.667.996.267.80
21-7542610.201.492.997.2114.0129.4928.7713.342.714.748.126.658.27
22-6314110.151.242.778.9815.7027.7027.4113.912.294.607.916.538.16
23-5180910.031.823.989.6715.5928.7524.9912.882.324.337.506.578.27
24-495410.021.363.257.9720.7529.7722.1211.952.834.647.976.878.61
25-33889.812.064.3813.6618.5626.8021.3912.111.033.836.766.708.56
26-21489.670.683.3816.8922.9729.7317.577.431.353.716.627.609.69

29 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
15-141725210.870.922.213.564.7618.9436.5326.926.165.288.923.254.05
16-131634210.850.882.203.954.8419.1236.5626.406.065.258.863.374.19
17-121432310.830.842.113.705.6219.6735.8926.315.865.288.923.464.29
18-111219710.810.932.074.125.3519.8235.9326.115.675.238.853.514.36
19-10953410.850.872.024.055.1219.4935.3527.016.095.258.883.234.03
20-9692510.790.841.923.996.1420.9235.7424.625.835.278.913.834.74
21-8477510.780.822.014.296.1620.8435.1024.825.975.238.853.734.63
22-7296210.720.711.865.036.9522.6233.6323.535.675.188.774.045.02
23-6179410.700.781.954.018.3623.3034.0021.635.965.278.914.465.51
24-592610.680.652.814.007.6724.9531.1022.895.945.198.794.135.13
25-442710.430.472.589.848.9024.3631.8516.865.154.597.925.266.59
26-319010.250.535.267.8912.1128.4226.3213.685.794.517.765.767.24
27-26310.2406.3512.709.5226.9817.4620.636.353.906.893.734.94

30 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
15-15555111.330.541.352.042.0010.7032.8839.3411.150.380.345.276.72
16-141078911.340.571.362.212.129.8433.3638.3512.180.410.375.026.42
17-131000811.330.551.222.402.339.4933.2339.1711.610.460.435.196.63
18-12855111.340.571.252.202.259.8432.0340.3911.470.690.705.366.82
19-11704911.330.451.191.942.0710.8533.5438.6611.290.240.185.176.61
20-10532311.340.411.152.372.2711.1630.9439.5112.190.650.655.166.58
21-9370911.300.671.192.702.3710.6032.1938.5811.700.380.325.116.53
22-8247511.210.651.782.833.0711.7632.4437.1310.345.449.150.190.37
23-7150411.230.601.663.062.7312.7730.8536.7711.570.019.144.910.14
24-681211.180.491.232.834.5613.6732.1433.2511.825.519.260.761.05
25-543211.040.460.932.316.0215.0538.6628.478.105.609.402.693.33
26-420910.930.962.392.396.2221.0528.7128.719.575.399.072.182.77
27-38610.8803.492.336.9826.7423.2624.4212.795.369.032.413.05

31 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
16-15674411.790.400.580.870.823.8323.1249.5620.834.625.405.246.60
17-14634511.780.270.661.580.873.4822.6549.1321.374.685.475.126.46
18-13563811.750.410.901.210.823.7823.6148.6220.664.425.165.156.50
19-12472611.770.080.661.400.953.9422.8950.0820.004.575.345.416.81
20-11384011.760.310.761.250.834.3023.3948.0221.154.385.115.016.34
21-10278311.730.471.011.290.934.0223.2849.0519.944.375.095.296.68
22-9194811.730.361.081.180.875.1822.0748.8720.384.425.155.226.58
23-8123611.750.320.890.650.894.6925.0846.5220.953.974.654.866.16
24-774911.7700.531.340.675.7423.7745.9322.034.084.774.655.91
25-642711.680.700.470.700.477.7326.4642.8620.613.093.614.465.70
26-520111.6500.501.000.509.9525.3744.2818.412.903.384.926.25
27-47911.54003.805.067.5921.5240.5121.522.913.304.065.23

32 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
16-16198912.130.050.200.700.200.6012.3755.0530.827.969.384.605.78
17-15387012.110.230.540.850.231.0312.3051.5833.237.779.143.874.90
18-14354312.120.250.370.930.231.4110.9552.0733.788.009.413.864.88
19-13304612.120.130.390.620.231.1212.5152.1332.867.789.173.985.04
20-12245012.140.200.450.570.121.0212.3750.8234.457.849.243.624.60
21-11191912.100.210.471.090.100.8912.5152.4232.317.769.144.095.17
22-10133512.120.300.300.600.151.2011.7652.9632.737.949.354.105.18
23-992012.050.220.760.650.431.6314.0250.9831.307.228.494.055.13
24-858112.000.170.521.3803.1013.0853.7028.067.138.384.806.03
25-731011.980.320.650.320.652.2614.1956.1325.487.058.295.426.78
26-618412.0600.540.540.542.7215.2247.2833.156.777.973.364.32
27-57211.93001.3902.7818.0655.5622.226.217.315.787.22

33 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
17-16213112.400.050.190.3300.094.7447.4947.119.8511.631.572.11
18-15205812.400.150.150.1900.244.8146.6047.869.8211.591.371.87
19-14178312.4000.060.390.060.344.2647.7347.179.9111.701.602.14
20-13148112.430.140.200.2700.073.3146.4649.5610.1712.001.131.57
21-12117112.400.170.170.0900.174.8747.3147.229.8311.601.542.07
22-1191612.410.330.110.110.110.225.2443.4550.449.6911.440.661.01
23-1063612.4200.310.160.310.165.1942.7751.109.6811.430.490.81
24-936212.4300.830005.8040.8852.499.6011.330.080.33
25-824512.3900.41000.417.3542.4549.399.2310.900.671.04
26-714712.42000005.4446.9447.629.8011.591.441.95
27-65312.28001.8903.773.7743.4047.179.0610.661.081.53

34 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
17-1750612.65000000.9932.8166.212.673.00
18-16100512.660.1000.1000.100.7030.7568.263.183.62
19-1595312.6400.100001.2632.5366.112.693.02
20-1486612.63000.12000.5835.1064.202.132.36
21-1369712.65000001.0033.0066.002.622.94
22-1251712.65000000.9732.6966.342.703.04
23-1135612.5900.560001.6933.9963.762.212.44
24-1024412.6800000031.9768.033.013.41
25-915112.5800.660002.6533.1163.582.292.54
26-88812.64000002.2731.8265.912.753.09
27-75412.6100001.853.7025.9368.523.804.33

35 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
18-1749412.810.200000017.6182.196.577.68
19-1647112.82000000.2117.6282.176.577.68
20-1536912.80000000.2718.9780.766.227.27
21-1430312.7900000021.4578.555.646.56
22-1324012.8100000019.1780.836.217.25
23-1221712.8500000015.2184.797.208.44
24-1114912.8100000018.7981.216.307.36
25-109212.7900000020.6579.355.846.80
26-95212.79000001.9217.3180.776.427.50

36 HCPCasesTricksNo Bid1 NT2 NT3 NT4 NT5 NT6 NT7 NTUnderbidOverbid
18-189012.930000006.6793.339.3311.00
19-1716912.920000008.2891.728.9310.51
20-1616612.920000008.4391.578.8910.47
21-1513412.960000003.7396.2710.0711.88
22-1414012.950000005.0095.009.7511.50
23-1311412.960000004.3995.619.9011.68
24-127012.990000001.4398.5710.6412.57
25-115912.93000001.693.3994.929.9311.71

Eight-Card Major Fit

The following tables apply to partnerships with 20-36 HCP, an 8-card major fit (4-4, 5-3 or 6-2) and no longer fit. For each HCP division, Tricks shows the average number of tricks won; No Bid shows the percent of cases not even 1 M makes; 1 M thru 7 M shows the percent of cases making that contract exactly. Optimal bids are tinted gold (any vul), green (nonvul only) or red (vul only). Underbid (Overbid) shows the difference between the optimal bid and its rival underbid (overbid) for each vulnerability in IMPs per board.

Bids of 2 M, 3 M and 5 M can never be optimal or rivals. A light tinting indicates cases where it is better to overbid further. For example, if the optimal bid is 1 M, and 3 M is tinted light red, it means that vulnerable it is better to bid 4 M than play in 3 M.

The underlying factor of suit-play stats vs. notrump is the power of distribution, or ruffing ability. More bang for the buck! Generally, fewer HCP are required for all contract levels. More specifically, “no bid” is never optimal, vulnerable games become optimal at 23 HCP, and slams at 30 HCP. Of course, the amount of ruffing ability is considered on average, so tables based on HCP alone are just a rough guide.*

*I am considering a follow-up study based on total points (HCP plus distributional points) which might also be a comparison of various point-count methods.

20 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
10-10442288.174.8320.6137.8027.278.081.290.110.003.223.164.125.53
11-9850758.184.7620.3237.8827.338.351.260.100.013.233.174.095.48
12-8755898.174.7720.7937.8027.108.131.300.110.003.223.174.115.52
13-7630668.164.7920.7637.9927.058.111.170.120.013.223.164.125.54
14-6464738.135.0121.6638.4425.967.601.200.1203.183.134.185.66
15-5330328.115.1322.2538.6425.467.261.120.1303.163.114.235.74
16-4213918.105.2322.4339.1224.917.061.120.1403.153.094.265.79
17-3115398.055.4323.9539.2123.686.641.000.090.013.123.064.335.93
18-253897.986.1626.0938.7522.085.860.950.1103.052.984.446.12
19-125527.975.7625.9040.7120.926.000.670.0403.052.994.466.17
20-09597.978.0325.9636.1821.906.571.36002.972.894.315.95

21 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
11-101693898.572.0212.2833.3634.8114.472.770.280.013.603.583.173.92
12-91555298.562.0212.3833.5934.9114.122.690.290.013.593.573.223.99
13-81348578.562.0012.3533.7834.6714.242.690.270.013.593.573.213.97
14-71093978.542.1012.7634.0234.5413.732.570.260.013.573.553.284.09
15-6780058.512.2213.2034.5334.1313.092.530.290.013.553.533.364.22
16-5534858.492.3213.6635.2333.4412.592.500.260.013.533.503.424.33
17-4337788.472.2813.9436.0432.7012.402.390.2603.513.493.464.39
18-3180538.422.4615.2136.7331.7711.452.090.270.023.473.453.614.64
19-281038.392.7315.6137.5330.6710.932.300.2303.443.413.654.72
20-137058.352.7817.4136.5230.5310.532.110.1303.423.393.744.87
21-013728.362.7015.9639.0729.3710.711.970.150.073.423.393.714.83

22 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
11-11792728.950.826.5525.2338.6622.575.440.680.043.933.921.901.86
12-101513448.940.856.4025.1639.3022.325.320.620.033.923.911.941.93
13-91357348.930.816.6025.5739.0022.115.260.630.033.923.911.971.98
14-81144328.940.846.5125.5538.9522.155.320.640.043.923.911.961.96
15-7883998.910.826.8126.1239.0821.445.030.660.033.903.892.072.13
16-6617258.890.856.9527.2438.7320.734.810.650.043.883.872.182.29
17-5409958.870.887.0427.7938.7620.374.500.630.033.863.852.252.41
18-4251238.850.837.5128.3838.2819.664.720.620.023.853.842.322.52
19-3131548.800.968.0429.1538.8918.513.910.530.023.813.792.542.87
20-258238.751.038.8330.5337.5818.053.490.450.053.773.762.653.06
21-126048.731.278.4131.4538.2916.363.610.580.043.743.722.813.29
22-08888.680.5610.4732.8836.4916.103.040.4503.733.732.943.51

23 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
12-111391129.320.313.0416.3737.3931.509.901.430.074.230.610.318.04
13-101292639.320.313.0816.5937.6431.059.881.370.074.220.520.378.01
14-91129549.310.333.0916.8037.6130.889.851.340.104.220.480.398.00
15-8909969.300.293.0917.0837.8030.919.411.340.074.210.410.447.97
16-7692639.280.323.1317.5537.8730.519.221.320.084.200.310.507.93
17-6467449.250.353.3118.0338.5129.858.741.130.074.180.080.657.87
18-5300839.230.393.3918.6438.8329.058.461.190.074.164.150.770.09
19-4177309.210.293.5919.5139.1028.128.131.190.064.144.140.910.31
20-389459.160.383.6620.3740.4426.168.000.930.074.104.091.170.69
21-237839.110.454.7321.2339.3326.496.850.870.054.074.061.270.88
22-117139.100.474.8521.7239.5225.746.481.170.064.054.051.361.02
23-05699.0904.0423.7341.1223.376.331.230.184.054.051.621.38

24 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
12-12595119.700.111.329.4830.5338.3417.092.900.221.433.237.008.87
13-111159329.690.151.299.4130.5338.7216.812.900.201.443.257.018.88
14-101044609.690.141.279.5830.7538.4416.692.910.201.403.196.978.85
15-9877539.670.101.329.5631.5138.2616.242.800.211.313.076.948.82
16-8696259.670.121.349.7031.7038.0416.052.850.191.273.006.908.78
17-7513579.650.111.3610.0232.2037.8615.682.580.201.182.876.898.78
18-6335489.620.091.4110.5533.0037.3914.812.530.231.032.646.798.68
19-5206739.600.131.4310.8333.7236.8214.582.310.190.922.476.768.66
20-4119279.570.081.3611.0335.0736.5513.462.260.200.762.246.668.56
21-359839.540.121.4512.1734.6635.8713.402.120.200.662.096.628.52
22-224239.460.212.1013.4535.9934.7911.471.730.250.291.526.428.34
23-110459.410.191.4414.4537.3235.799.001.8200.111.276.338.26
24-03299.4801.5215.8131.3137.3912.461.5200.642.026.788.71

25 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
13-129745410.050.040.534.7121.9841.0325.525.730.463.005.587.469.21
14-119234110.060.050.544.5921.7641.0625.755.750.503.035.637.479.22
15-107950210.040.060.494.7222.1441.2625.365.490.482.985.557.499.25
16-96530010.030.060.584.7222.4341.3624.975.410.462.945.497.489.25
17-84984710.020.050.584.9622.9541.0224.625.380.442.855.367.449.20
18-73598310.010.050.495.0923.2841.2324.375.050.452.825.317.489.26
19-6227229.980.060.595.1823.9241.7023.114.970.482.725.177.429.20
20-5138159.940.070.595.4625.3341.3822.094.630.452.534.897.379.16
21-474989.940.070.615.7324.5542.3321.974.290.442.594.977.489.29
22-336539.890.140.415.6727.2442.6219.274.300.362.324.587.309.11
23-214639.8000.687.2528.2342.7217.633.420.072.024.127.349.20
24-15819.780.170.695.1634.4236.6620.312.240.341.553.457.209.09
25-01639.7701.236.7533.1336.8117.184.290.611.473.326.638.44

26 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
13-133878910.400.030.222.1113.5537.9634.7710.311.054.257.437.238.77
14-127498610.410.020.182.1013.4637.8534.7710.571.044.267.457.188.72
15-116763710.400.010.242.1413.6237.7034.7310.461.104.247.417.188.71
16-105817710.390.020.232.2013.4238.7834.479.930.964.257.437.348.90
17-94601510.380.020.212.1514.0838.3334.339.910.964.197.347.298.86
18-83432510.370.030.232.1014.0539.1833.569.880.964.197.357.308.87
19-72351110.350.040.242.3814.6939.0233.189.540.924.097.197.318.89
20-61469410.330.020.142.4015.0239.9832.978.590.894.077.167.519.13
21-5862110.3300.202.4915.3239.5332.109.450.904.027.097.288.87
22-4457010.2700.182.5616.8140.5730.928.210.773.856.847.469.10
23-3215210.2300.192.5618.7340.7129.327.810.703.646.537.419.07
24-280910.1700.123.0921.1439.5627.698.030.373.326.077.208.87
25-132510.1800.623.3818.4640.6229.546.460.923.526.357.589.28

27 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
14-135800710.750.000.080.917.3029.6542.0517.802.195.098.665.947.14
15-125415810.740.010.110.877.3229.9542.4017.212.135.088.666.087.31
16-114807010.740.010.100.877.3130.1942.1917.272.065.098.666.097.31
17-103998410.740.010.070.867.4830.2541.9017.162.285.078.646.057.27
18-93054610.720.010.080.917.5031.0541.1117.252.105.068.636.067.29
19-82187710.700.010.080.867.7331.6741.6315.992.025.048.606.347.62
20-71483610.6900.071.018.2431.3641.2715.902.144.978.506.287.56
21-6911210.6500.081.038.4332.9940.7914.951.734.958.466.577.90
22-5512610.6300.080.809.5433.1139.9914.961.524.858.326.547.88
23-4266510.6100.041.139.7634.6738.3113.812.294.808.246.587.94
24-3120810.520.0800.9911.1836.7537.1712.751.084.658.036.988.43
25-245010.49001.7810.6737.7837.5611.330.894.637.997.328.83
26-115610.58000.6412.8233.3335.9015.381.924.527.846.127.42

28 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
14-142132011.070.010.040.333.5220.2844.5126.714.605.579.373.804.55
15-134062411.070.010.060.383.4620.6044.0126.974.505.579.373.764.50
16-123684911.070.000.050.343.4920.4744.4926.784.375.579.373.834.59
17-113163211.060.000.040.363.6220.8943.8326.794.465.569.353.804.55
18-102556511.0600.040.343.5820.8044.6226.454.175.569.363.954.72
19-91892411.030.010.070.333.9621.6444.2725.694.035.529.294.114.92
20-81346911.0100.040.363.8222.4644.5124.913.915.549.324.325.17
21-7860111.0300.020.353.5122.1644.6125.244.105.579.374.235.06
22-6509610.9800.060.534.5522.5744.6424.293.365.439.174.515.40
23-5288610.9500.070.354.3024.9544.1422.833.365.489.244.865.81
24-4142610.97000.704.6324.1941.9424.334.215.419.144.295.15
25-366910.87000.305.9825.8645.1419.583.145.318.995.506.59
26-224810.90001.614.0325.0042.7425.401.215.389.084.695.63

29 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
15-142875111.390.000.020.151.4912.2240.2937.298.545.829.730.780.95
16-132726311.380.000.010.141.5812.3140.1037.638.235.819.720.770.94
17-122391111.360.000.030.171.5512.4541.1736.618.035.819.721.041.26
18-111990511.360.010.020.151.5312.7440.8236.698.065.819.731.021.23
19-101561811.370.010.030.141.5112.4341.0136.917.975.819.730.991.20
20-91147711.3500.020.111.6212.8441.8135.927.685.819.721.271.52
21-8793111.33000.151.7013.0542.5534.947.605.809.701.491.79
22-7486011.32000.101.8313.1343.5034.017.435.799.691.732.07
23-6278311.29000.141.9014.6642.8333.357.115.779.671.932.32
24-5149411.27000.132.2115.0642.2434.006.365.749.621.932.32
25-467611.25000.151.4819.2338.9133.147.105.829.742.022.41
26-331111.14000.322.5718.3344.3730.873.545.689.533.203.82
27-212011.070002.5018.3352.5023.333.335.739.604.935.87

30 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
15-15940711.6700.010.040.616.4132.6445.5914.702.322.735.567.03
16-141816711.6700.010.040.696.5732.3145.5414.832.342.765.547.00
17-131652411.6700.020.050.596.5832.7645.0614.942.252.655.466.92
18-121423411.6700.010.060.796.4532.1645.6014.932.382.815.536.99
19-111160511.6600.010.080.756.8732.2445.9314.132.282.685.677.17
20-10894811.65000.040.666.7733.1745.1314.232.112.495.577.04
21-9621211.66000.060.766.6232.1646.3314.072.352.775.737.24
22-8416611.6200.020.120.607.3933.9744.5813.321.802.115.627.11
23-7251111.61000.040.647.5334.4944.8812.431.661.955.777.30
24-6143111.55000.140.359.6435.4342.6311.811.021.195.587.08
25-572811.550000.829.6235.8540.9312.770.881.035.256.69
26-434011.500001.189.1239.7138.5311.470.090.095.136.56
27-316611.450001.209.0443.9834.9410.845.879.810.831.00

31 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
16-151162211.94000.060.263.4822.3449.9523.925.286.234.886.17
17-141077411.9500.010.010.313.0122.3949.8324.455.376.344.806.06
18-13964311.9400.010.050.343.2022.1750.5023.725.366.334.986.28
19-12792711.92000.010.353.1223.5849.8223.125.085.994.976.27
20-11645911.9400.020.080.123.0323.3249.6123.835.176.114.866.13
21-10474211.9200.020.060.253.4423.1850.0023.055.106.025.006.31
22-9318811.93000.060.192.7623.6850.2223.095.156.085.036.34
23-8208811.91000.050.433.7822.2751.3422.135.206.145.286.65
24-7124311.900000.483.8624.5447.4723.654.685.534.625.86
25-667511.90000.300.153.2624.1549.6322.524.915.795.036.35
26-533111.770000.603.6330.5148.6416.623.404.025.687.15
27-413711.8600007.3022.6346.7223.364.425.224.575.80

32 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
16-16344012.17000.060.091.8913.6949.6234.657.558.923.454.40
17-15673312.18000.010.071.4113.2850.3534.877.769.163.514.47
18-14603312.18000.020.031.5914.2548.9635.147.518.873.314.23
19-13520812.180000.101.4613.3650.2534.837.739.133.504.46
20-12418212.16000.100.171.4814.9948.5734.707.348.673.324.25
21-11326312.16000.060.181.6514.4749.3134.327.428.763.464.41
22-10226212.1400.090.040.091.8113.8452.1232.017.538.894.095.18
23-9158712.160000.191.5814.4349.2834.537.458.803.424.37
24-892812.1100002.1616.2750.1131.476.958.213.924.98
25-754112.140000.180.5514.7953.6030.877.608.984.425.57
26-628212.0600001.0620.2150.7128.016.327.474.445.62
27-512112.0700004.1313.2254.5528.107.188.494.896.14
28-45212.210000017.3144.2338.467.198.502.313.04

33 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
17-16369312.40000.0300.577.5543.1648.699.2110.880.851.25
18-15345712.390000.030.497.0345.0147.449.3411.041.231.71
19-14312512.36000.060.030.748.5144.2646.408.9510.581.281.77
20-13259912.370000.081.048.0843.7947.028.9810.621.141.61
21-12209012.370000.140.678.0944.4546.659.0510.701.271.76
22-11151412.4000000.797.7342.3449.149.1310.780.691.06
23-10106812.39000.0901.038.8039.7950.288.8210.430.240.53
24-966612.3700000.609.3142.9447.158.8210.421.021.47
25-843812.3700001.375.0248.6344.989.5911.341.992.61
26-724112.330000.830.839.5441.9146.898.6010.150.931.37
27-610412.2900000.968.6550.9639.428.8810.502.993.83
28-57512.4100001.3310.6733.3354.671.111.08

34 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
17-1789812.57000.110.1104.2333.3062.252.102.30
18-16176412.5700000.234.1434.3061.341.862.01
19-15162812.59000.060.060.253.9332.0663.642.432.69
20-14141012.5600000.354.4733.7661.421.932.10
21-13118012.5500000.174.5835.1760.081.591.69
22-1287912.540000.230.234.1036.1859.271.361.42
23-1163012.5400000.324.2936.1959.211.351.41
24-1038812.5800000.264.3832.4762.892.282.52
25-928912.51000006.2336.6857.091.021.00
26-816112.590000.620.622.4831.6864.602.602.90
27-78612.60000004.6530.2365.122.843.19

35 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
18-1781212.72000001.4824.6373.894.655.37
19-1684912.6800000.122.4726.5070.914.044.63
20-1568212.7200000.152.0523.9073.904.745.48
21-1454712.72000002.7422.4974.775.025.82
22-1344412.73000001.5823.6574.774.885.65
23-1235012.70000002.0026.2971.714.174.79
24-1124412.66000002.4629.1068.443.413.88
25-1015012.6800000.672.0026.0071.334.154.77
26-911612.72000004.3119.8375.865.486.36
27-85112.65000003.9227.4568.633.634.14

36 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
18-1818712.81000000.5317.6581.826.527.62
19-1736312.830000.2800.5515.1584.027.108.32
20-1631612.84000000.3215.5184.187.088.30
21-1524012.8600000014.1785.837.468.75
22-1421212.83000000.4716.5183.026.817.97
23-1317912.87000001.1211.1787.718.069.47
24-1210012.8300000017.0083.006.757.90
25-1110112.7200000027.7272.284.074.68

Nine-Card Major Fit

The following tables apply to partnerships with 20-36 HCP, a 9-card major fit (5-4, 6-3 or 7-2) and no longer fit. For each HCP division, Tricks shows the average number of tricks won; No Bid shows the percent of cases not even 1 M makes; 1 M thru 7 M shows the percent of cases making that contract exactly. Optimal bids are tinted gold (any vul), green (nonvul only) or red (vul only). Underbid (Overbid) shows the difference between the optimal bid and its rival underbid (overbid) for each vulnerability in IMPs per board.

Bids of 2 M, 3 M and 5 M can never be optimal or rivals. A light tinting indicates cases where it is better to overbid further. For example, if the optimal bid is 1 M, and 3 M is tinted light red, it means that vulnerable it is better to bid 4 M than play in 3 M.

What a difference a trump makes! The presence of a ninth trump greatly increases trick-taking ability, generally achieving the results of an 8-card fit with 2 HCP fewer. On average, vulnerable games become optimal with only 21 HCP (nonvulnerable with 22), and slams become optimal with only 28 HCP. As with 8-card trump fits, distribution and ruffing ability are key factors, so individual cases cannot be judged accurately by HCP alone.

20 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
10-10280089.010.987.0023.9035.8023.977.211.100.043.973.961.511.29
11-9534389.030.866.8723.9635.8223.577.601.220.103.983.971.491.26
12-8475519.010.916.8924.1636.0223.537.261.140.103.973.961.541.33
13-7396539.010.906.8124.5135.8823.307.201.310.103.973.961.551.35
14-6293318.990.947.1124.7736.0722.787.101.150.093.953.941.641.49
15-5206269.000.967.0625.0635.2722.987.321.250.123.953.941.581.41
16-4133079.010.737.3624.6635.4523.037.321.360.103.973.961.571.39
17-373808.970.777.1325.7736.6821.227.151.140.143.933.921.801.74
18-235248.930.628.6025.7936.1521.655.681.330.173.923.921.911.91
19-117548.951.087.1826.6834.2123.436.500.800.113.913.901.671.56
20-05929.010.176.4226.8634.8023.657.260.510.343.983.981.571.38

21 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
11-101060349.350.363.6017.2834.6729.9011.612.400.184.240.770.187.86
12-9975479.340.393.6317.2235.2429.7711.512.070.164.230.680.257.90
13-8851029.350.353.5717.3334.9929.5711.782.240.184.230.720.227.87
14-7686309.350.383.5317.3834.9429.9411.272.370.184.230.720.227.84
15-6487029.330.343.7417.8334.8529.5111.362.180.194.220.630.287.84
16-5336299.320.393.7218.1234.9729.1811.232.190.204.210.550.337.80
17-4209899.320.333.9418.0035.1328.8211.402.210.174.210.510.357.79
18-3114159.290.323.8618.8335.3728.6610.782.010.154.190.350.467.77
19-250249.290.323.8018.9535.8727.7311.251.930.164.180.260.527.74
20-123199.310.224.3117.9436.3527.3811.002.410.394.200.280.517.57
21-08029.3204.4919.2034.0428.4310.602.870.374.220.440.407.54

22 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
11-11496389.680.171.6411.0530.6134.9017.144.080.421.202.896.538.35
12-10948989.670.151.6811.2130.6935.0617.003.840.381.182.846.578.40
13-9853109.670.161.6511.1830.8335.0617.023.710.371.162.826.598.43
14-8712859.670.141.7011.2730.6634.9416.983.940.371.172.836.558.38
15-7556479.670.131.7711.3830.6135.0016.793.920.401.162.816.548.37
16-6387269.640.141.8311.7331.2634.5716.413.670.401.042.636.518.35
17-5257269.650.161.7211.7931.1634.2316.683.930.331.052.666.488.31
18-4156529.650.121.6911.3331.6834.4716.643.570.511.062.676.528.35
19-382009.610.111.5512.6132.4833.7715.343.780.370.842.356.358.18
20-236499.610.161.4812.8332.3133.4115.953.340.520.842.346.418.25
21-115669.560.191.7912.7733.6533.5915.072.620.320.662.076.488.36
22-05239.6501.9112.0534.0328.4918.744.400.380.702.146.117.92

23 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
12-11862879.990.050.796.4124.0037.8923.766.400.692.554.916.948.66
13-10809979.990.070.756.3524.2237.6023.996.340.682.544.896.948.66
14-97037710.000.060.746.2324.3937.5323.776.580.702.544.896.888.59
15-85713310.000.040.646.3424.4737.4623.776.580.702.534.886.888.59
16-7432809.990.060.716.2624.6337.7923.506.350.712.514.856.918.63
17-6293139.970.060.716.6425.0237.5523.296.000.742.434.726.928.65
18-5186359.960.070.776.7725.3037.2122.846.260.782.374.646.828.54
19-4109719.960.060.706.5425.6137.5822.655.990.862.374.656.868.59
20-356579.950.050.646.6826.1637.3022.296.100.782.314.556.808.53
21-223659.930.080.637.5725.7137.2122.415.580.802.254.476.888.62
22-110539.9800.856.1727.7334.2822.607.410.952.174.356.388.05
23-03309.940.300.305.7628.4836.0623.334.850.912.174.356.958.72

24 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
12-123684410.310.010.283.2916.8336.7231.3810.261.233.756.696.848.38
13-117155410.320.020.283.1316.6737.0131.0110.531.343.796.746.788.30
14-106544410.310.030.303.1816.7337.1830.9210.401.263.776.726.828.35
15-95397810.320.020.303.1616.9136.7931.2210.341.273.766.706.828.35
16-84299310.310.030.312.9917.2237.0031.0810.121.263.746.676.858.40
17-73161210.310.020.283.2317.1636.9030.8610.201.363.726.656.808.34
18-62091910.280.010.333.0017.5038.4829.809.631.253.706.636.948.50
19-51281610.290.010.403.2517.5537.2330.1410.141.283.666.566.798.33
20-4758110.290.030.383.1117.4438.0629.599.931.463.696.606.828.36
21-3364210.2700.113.6218.7836.5730.319.231.373.526.366.878.44
22-2147410.2500.273.7318.3239.1526.8010.381.363.546.386.638.16
23-163610.28002.6719.8137.2628.939.911.423.536.386.718.26
24-019210.34003.6517.7133.8533.857.813.133.656.556.898.45

25 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
13-125934310.620.010.121.4910.4732.5937.2815.822.204.678.056.077.35
14-115686810.620.010.131.3410.2432.8937.3515.742.304.718.116.097.37
15-104904210.620.010.131.3810.1632.9837.4315.642.284.718.116.137.41
16-93991510.620.020.101.3410.4633.0137.2115.532.344.698.086.127.40
17-83073210.610.010.121.3910.7033.2136.9615.272.354.668.036.157.44
18-72202710.620.010.121.3810.3332.6837.4915.592.394.708.096.107.38
19-61399310.590.010.091.5210.6333.7637.0914.722.184.658.026.307.63
20-5845510.600.010.131.0510.7934.1636.4414.942.484.688.076.217.51
21-4469610.6000.061.1710.9934.2836.0914.742.664.658.036.197.50
22-3227110.57001.8111.8033.3336.2814.132.644.507.806.227.55
23-292310.4900.111.7312.4634.7837.9211.481.524.437.697.008.48
24-135410.50000.8512.7139.2731.3614.411.414.517.826.447.80
25-010010.7900010.0026.0045.0013.006.004.908.406.027.26

26 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
13-132322210.9100.040.565.5825.7441.8322.413.835.329.004.735.68
14-124554010.930.010.050.565.3825.6141.5522.714.135.349.034.625.54
15-114118410.930.000.050.645.2325.5541.3022.974.265.359.044.545.45
16-103545610.9100.060.605.5325.6741.8222.423.915.329.004.715.66
17-92767610.910.000.080.515.4626.2341.6222.343.765.339.034.775.73
18-82058910.9200.050.535.5726.1241.1222.594.025.329.014.655.59
19-71448810.920.010.030.525.3426.7940.8322.254.235.359.054.705.64
20-6896910.8900.030.595.5527.2841.1821.373.995.329.004.935.91
21-5523810.9100.080.405.5027.0541.0321.634.315.349.044.815.78
22-4276610.89000.724.9526.9343.6019.993.805.389.085.316.36
23-3128510.89000.475.8427.8639.9221.874.055.318.994.795.76
24-251610.93000.195.6224.0345.3521.123.685.369.075.086.09
25-120210.91000.996.4423.7642.5722.283.965.188.804.635.58

27 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
14-133497111.220.000.040.272.4117.4141.6631.326.895.709.562.382.85
15-123221711.2100.010.232.6617.5741.9430.886.725.689.532.502.99
16-112850111.2100.020.212.6517.4341.7930.926.985.689.542.432.92
17-102375711.2100.030.182.7017.4442.1530.826.695.689.532.523.02
18-91788311.2000.070.202.5317.8142.4530.056.905.699.552.653.17
19-81312011.2000.020.192.6617.9042.3930.306.545.689.542.663.19
20-7893611.2100.030.172.4117.7642.7530.046.855.719.582.683.20
21-6543511.20000.222.6317.8542.2630.436.615.699.542.623.14
22-5307911.19000.162.6018.3542.5529.786.565.709.562.783.33
23-4156911.15000.193.3819.0642.3828.366.635.619.433.023.62
24-374911.120002.9418.9645.9327.105.075.689.533.694.40
25-228911.070003.8122.1542.5626.305.195.589.393.774.51
26-19611.02001.046.2521.8837.5027.086.255.208.823.083.75

28 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
14-141250711.480.0100.141.1310.3838.2738.9311.150.120.125.226.67
15-132388011.4800.010.101.2110.3838.0539.1811.070.160.175.266.71
16-122150811.480.000.020.091.1410.5438.3638.5911.250.070.065.176.60
17-111872111.4800.030.101.0510.3738.5739.3110.580.070.075.346.81
18-101506311.49000.111.0010.2337.9139.6211.120.250.285.316.77
19-91110411.4600.020.141.0810.8238.9838.7110.275.869.800.130.17
20-8798411.4800.030.131.1311.1837.0639.3011.170.210.235.266.71
21-7509811.47000.161.0210.9738.0938.7810.980.040.035.236.67
22-6302711.480000.9911.2037.7939.1110.900.080.085.286.73
23-5170411.43000.230.8211.6840.2036.6810.395.889.830.560.68
24-490011.44000.111.4410.8939.4437.7810.335.839.750.290.37
25-339111.550000.267.9339.9040.6611.250.440.525.426.89
26-211011.45000014.5539.0933.6412.736.0010.000.800.95

29 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
15-141643811.740.010.010.050.505.2630.7046.4617.023.013.555.366.78
16-131549811.74000.050.465.4331.0146.0616.992.913.435.326.73
17-121366511.730.0100.040.405.4531.7945.3416.962.743.245.246.63
18-111155011.7300.010.050.455.3131.5045.5817.112.833.345.256.64
19-10902211.7400.010.070.395.3431.0045.5617.632.943.475.176.56
20-9655311.73000.050.585.0530.9647.1416.222.993.525.557.00
21-8446211.7300.020.040.475.1531.7346.1516.432.813.315.406.83
22-7274311.71000.070.555.4331.9746.3415.642.683.165.536.98
23-6168411.74000.060.425.4630.6446.1417.282.993.535.296.69
24-589811.760000.334.2330.9648.1116.373.213.795.647.12
25-444611.7200006.5032.2943.7217.492.472.914.976.32
26-317911.680000.566.7030.7348.0413.972.693.175.957.49
27-26211.790001.616.4525.8143.5522.583.684.324.295.48

30 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
15-15518411.97000.020.152.5822.9448.2826.025.366.334.415.60
16-141052511.98000.020.172.6221.8249.4225.955.606.614.565.77
17-13960011.980000.222.4022.1849.9525.265.566.574.715.95
18-12819711.98000.010.122.3921.7050.8624.915.686.714.866.13
19-11654211.9800.0200.282.3722.1649.7425.445.566.574.665.89
20-10499411.990000.282.3021.9349.5825.915.636.654.585.80
21-9343411.980000.232.0423.1548.7525.835.436.414.495.69
22-8230711.960000.222.4323.0249.5024.845.376.354.715.96
23-7148112.000000.072.4321.2049.9026.405.796.844.565.76
24-677211.960000.262.7224.0946.8926.045.065.984.245.40
25-537112.020000.272.4320.2249.6027.495.987.064.385.54
26-418811.9500002.6624.4747.8725.005.035.954.495.70
27-38612.1200002.3316.2848.8432.566.918.163.634.63

31 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
16-15636312.19000.030.081.0513.8049.3535.697.729.123.284.20
17-14600212.21000.020.200.9513.2848.5836.977.849.263.023.89
18-13535012.21000.020.090.9512.8649.6436.437.959.393.224.12
19-12449312.190000.130.9614.3149.0135.597.629.013.254.17
20-11351612.19000.030.111.3714.0848.2936.127.588.963.103.98
21-10262712.1900.0400.111.2213.7449.4535.447.699.083.334.25
22-9179012.18000.0601.0113.5851.2334.137.789.203.714.71
23-8110012.22000.0900.6414.3646.6438.277.699.082.623.41
24-769512.210000.140.5813.8148.9236.557.819.233.124.00
25-634212.2300001.1711.1151.1736.558.309.813.394.32
26-516712.260000014.3745.5140.127.849.262.252.95
27-49012.160001.111.1112.2252.2233.337.919.333.934.98

32 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
16-16178912.3700000.677.7745.8445.729.1410.811.562.10
17-15356612.40000.0300.367.0144.4548.159.3711.081.071.52
18-14322512.390000.030.227.0445.9546.769.4011.111.441.95
19-13280012.380000.040.507.5745.1446.759.2210.901.341.84
20-12223612.4000000.406.8945.0847.639.4011.101.221.69
21-11168412.390000.060.306.9545.9046.799.4011.111.431.94
22-10124612.390000.240.246.5845.9147.039.4711.181.391.90
23-984412.390000.240.596.7545.0247.399.3511.051.241.72
24-852412.36000008.2147.1444.669.1910.871.852.45
25-728512.4100000.355.6147.0247.029.6911.451.532.06
26-615812.40000006.3347.4746.209.6111.351.692.25
27-57512.36000009.3345.3345.338.9510.571.552.09

33 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
17-16190112.5600000.163.8936.1459.811.441.51
18-15181512.5900000.172.7035.2161.931.831.98
19-14159512.580000.060.132.8235.5561.441.721.85
20-13134112.590000.150.152.7634.5362.421.972.15
21-12102612.570000.100.192.9236.1660.621.541.64
22-1178312.59000.130.1303.4533.2163.092.222.45
23-1052312.6200000.382.2932.5064.822.532.82
24-936512.5900000.271.3737.5360.821.401.48
25-821112.5500000.473.7935.5560.191.561.65
26-712512.5400000.804.0035.2060.001.581.67
27-65612.61000001.7935.7162.501.842.00

34 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
17-1746312.71000001.3026.3572.354.244.89
18-1688412.73000000.9025.3473.764.555.25
19-1580712.6900000.121.4927.8870.513.824.38
20-1478712.7000000.251.6526.3071.794.184.80
21-1356912.71000.18001.2325.8372.764.365.02
22-1243812.74000000.4625.1174.434.665.39
23-1132312.75000001.5522.2976.165.236.07
24-1022312.75000000.9023.3275.785.055.86
25-913512.73000000.7425.9373.334.425.10
26-88212.74000002.4420.7376.835.506.39

35 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
18-1744412.86000000.2313.5186.267.598.91
19-1637612.8200000.270.2716.4982.986.817.97
20-1534012.81000000.2917.9481.766.487.57
21-1425312.79000000.7918.9780.246.157.18
22-1322812.84000000.8814.0485.097.388.65
23-1218312.83000000.5515.8583.616.978.16
24-1112012.7800000021.6778.335.586.50
25-109712.82000001.0315.4683.517.008.20
26-95012.82000004.0010.0086.007.989.36

36 HCPCasesTricksNo Bid1 M2 M3 M4 M5 M6 M7 MUnderbidOverbid
18-188012.950000005.0095.009.7511.50
19-1714612.92000000.686.1693.159.3711.04
20-1613012.8900000010.7789.238.319.77
21-1512712.9000000010.2489.768.449.93
22-1410412.930000006.7393.279.3210.98
23-139312.910000008.6091.408.8510.42
24-125712.980000001.7598.2510.5612.47

Stats with little data (say, fewer than 200 cases) are unreliable,
and those with fewer than 50 cases are omitted entirely.