Study 8J13   Main

Trump Fit Comparisons

by Richard Pavlicek

The general definition of a trump fit, or simply a fit, is a partnership holding of at least eight cards in the same suit. Technically this includes any two suit lengths that add to 8-13, however, this study will cover only fits of 8-11 cards with no suit longer than seven cards — a practical view reminiscent of the old cliche, “What do you call an eight-card suit?” Answer: Trumps!

All statistics were derived from my database of 10,485,760 random solved deals, analyzing partnerships with no fit over 11 cards and no suit over seven cards. Trick production is based on double-dummy play, which previous studies have shown to be in close proximity to actual play. If a partnership contained two fits, each was evaluated separately in the Average Tricks section, and together as a dual fit if appropriate.*

*In the rare case of three fits, all were evaluated in the Average Tricks section, but the deal was thrown out for dual fit analysis. This decision was based on my Uncle Cedric, who did his post-graduate thesis on triple fits. Alas, he succumbed to a fourth fit (schizophrenia) and hasn’t been seen since.

Average Tricks

The following table lists the 12 possible trump fits of 8-11 cards (excluding 8+ card suits) in order of overall trick production. Cases shows how many times the fit occurred in the database, which should be close to the theoretical apportionment as well. Columns 3-11 show the average number of tricks won according to the partnership HCP range. The last column shows the overall average regardless of HCP.

The order shows that fit length is the primary factor in determining trick production, and greater length in one hand is a secondary factor. Several exceptions exist (tinted gold) for 7-3 and 7-2 fits with 22+ HCP, which fare better than a more-balanced longer fit.

Many will be surprised that 5-3 fits produce more tricks than 4-4 fits, which seems to contradict the well-known strategy to prefer the 4-4 fit as trumps. No, it does not, because the table below includes all such fits. If you only consider partnerships that contain both fits, the 4-4 does indeed outperform the 5-3. (See the section on Dual Fit Comparisons.)

FitCases0-910-1213-1516-1819-2122-2425-2728-3031-40Overall
7-41053357.257.858.549.209.9310.6911.4212.0812.639.95
6-51897456.927.688.329.039.7610.5111.2411.9112.509.77
7-33363606.377.238.048.879.7110.5411.3412.0312.609.69
6-48420426.147.037.858.679.5010.3311.1311.8512.509.49
5-55696186.106.977.788.599.4110.2411.0311.7512.389.40
7-25256015.576.487.348.269.2210.2011.1111.9012.519.22
6-319326415.136.137.108.099.0810.0410.9511.7512.449.04
5-436332835.016.087.058.028.989.9210.8111.6012.328.94
7-13819034.905.846.727.658.639.6410.6311.5012.268.65
6-223124824.195.226.227.268.349.4510.5111.4412.258.35
5-363814243.504.745.897.058.219.3210.3611.3012.168.15
4-444363933.324.655.867.058.189.2610.2811.2012.058.11

 Study 8J13   Main Top   Trump Fit Comparisons

Dual Fit Comparisons

An occasional decision is which trump suit to choose when a partnership discovers it has two fits. Most often this is a choice between a 4-4 and 5-3 fit, but various other situations exist. Many factors determine the better trump fit — hand strength, high-card location, suit texture, ruffing potential, etc. — so on any given deal there is no automatic winner. Statistics here indicate only the general winner, or which suit is better on average.*

*Ignored here is the issue of rank, i.e., major vs. minor, which will often dictate the choice of trump suits in practice, especially for bidding games. This of course has nothing to do with trick production and is irrelevant to this study.

The following table lists the 16 most common dual fits in order of frequency.* For uniformity the more lopsided fit is shown as spades with West being longer, and the more even fit is shown as hearts. West and East patterns indicate major-suit lengths only. Side distribution is ignored for this comparison but covered in detail under Dual Fits by Pattern.

*Excluded are dual fits of the same kind (two 5-3 fits) or with obvious selection priority (6-3 vs. 5-3).

Cases shows the number of occurrences. Equal % shows the percent of cases where both fits won the same number of tricks; the next two columns show the win percent for each fit. The last two columns show the average number of tricks won by each fit. Tinted rows indicate dual fits in which the more even fit (hearts) performs better.

Noteworthy is the comparison of 6-2 and 5-3 fits; 6-2 is better with the long suits in different hands, but 5-3 is better with the long suits in the same hand. The same relationship exists for 6-3 vs. 5-4.

5:43:467721559.1016.4024.518.158.23
5:44:430781253.8136.709.498.908.54
6:32:527071648.9827.1623.868.298.24
6:42:419380450.8722.5426.608.638.65
6:43:413710547.7643.828.419.228.74
6:52:35831157.8018.7223.489.119.14
6:44:44620844.0451.234.749.639.00
6:43:54576165.3617.9416.709.649.62
7:31:54411838.0539.6822.278.718.44
7:21:63862636.4141.2422.358.478.19
7:42:42502640.3153.346.369.769.03
6:53:42304064.2617.4218.3210.0410.05
7:41:42082939.9733.7426.299.199.03
7:43:41341134.1163.052.8410.129.15
7:32:61330957.8623.0419.099.559.51
7:42:5998461.3720.0718.5610.0810.07

 Study 8J13   Main Top   Trump Fit Comparisons

Dual Fits by HCP

The following tables break down each of the 16 most common dual fits by partnership HCP. As in the previous section, the more lopsided fit is shown as spades with West longer, and the more even fit is shown as hearts. Side distribution is ignored. Tinted rows indicate cases where the more even fit (hearts) performs better.

Note that many dual fits have a different superior choice depending on HCP. Generally, as partnership HCP increases, relative performance of the more lopsided fit decreases, while the more even fit increases. For instance, a 6-2 fit does better than a 4-4 fit with 0-18 HCP, but the 4-4 fit does better with 19+ HCP. Evidently this is because weak hands with a 4-4 trump fit often lack the resources to establish the 6-2 side suit, but the long tricks can’t be denied if the 6-2 fit is trumps.

W 5:4 E 3:4CasesEqual %5-3 Win %4-4 Win %5-3 Average4-4 Average
0-9863741.4836.2022.313.633.40
10-123036350.2228.6221.164.904.78
13-157965256.1721.1222.725.995.99
16-1813773058.3716.8124.827.097.17
19-2116542659.5614.9425.508.188.30
22-2413784960.3114.1825.519.269.38
25-277904562.0513.1824.7710.2910.41
28-303020664.5812.1823.2411.2311.34
31-40830772.6610.8016.5412.1112.17

W 5:4 E 4:4CasesEqual %5-4 Win %4-4 Win %5-4 Average4-4 Average
0-9327225.8969.105.015.093.95
10-121290337.0156.216.776.085.33
13-153550743.5247.528.967.016.49
16-186333148.6041.2510.157.977.57
19-217687053.8136.599.608.948.60
22-246426859.2531.459.309.879.59
25-273553264.1425.7110.1510.7210.52
28-301293869.9519.6210.4311.5211.40
31-40319177.9714.267.7712.2212.14

W 6:3 E 2:5CasesEqual %6-2 Win %3-5 Win %6-2 Average3-5 Average
0-9343531.0061.757.254.133.37
10-121219435.5752.5411.895.094.55
13-153159141.6741.2617.076.095.77
16-185483046.6530.0223.337.157.07
19-216599449.1823.3227.508.278.33
22-245531352.0820.3327.599.429.51
25-273196355.5119.2525.2410.5210.58
28-301211659.9818.4121.6211.4711.50
31-40328066.7114.9418.3512.2312.26

W 6:4 E 2:4CasesEqual %6-2 Win %4-4 Win %6-2 Average4-4 Average
0-9244421.3674.144.504.433.35
10-12856835.2257.767.015.564.83
13-152263545.3440.1114.566.606.26
16-183962550.7824.9924.237.637.61
19-214713051.9616.2031.858.668.83
22-243965852.9813.7033.329.689.89
25-272269054.8014.4530.7610.6510.82
28-30870458.8714.5026.6311.5011.62
31-40235068.3414.0417.6212.2812.32

W 6:4 E 3:4CasesEqual %6-3 Win %4-4 Win %6-3 Average4-4 Average
0-914408.0691.110.835.473.69
10-12585317.1780.881.956.455.22
13-151578928.8067.473.737.386.51
16-182854341.0951.907.018.327.74
19-213446951.0240.058.939.268.86
22-242801157.1032.1910.7010.199.91
25-271579960.7826.3412.8711.0210.84
28-30576066.2822.5011.2211.7611.61
31-40144175.5719.854.5812.4512.27

W 6:5 E 2:3CasesEqual %6-2 Win %5-3 Win %6-2 Average5-3 Average
0-977022.0870.267.664.773.79
10-12261536.7953.0010.216.045.44
13-15681749.7134.0316.257.216.97
16-181182356.5119.8523.648.238.25
19-211412759.4312.7927.789.199.35
22-241202062.5510.4926.9610.1210.29
25-27674163.8011.7524.4510.9311.06
28-30267166.7913.4019.8111.6611.73
31-4072768.9114.1716.9212.3312.35

W 6:4 E 4:4CasesEqual %6-4 Win %4-4 Win %6-4 Average4-4 Average
0-93837.5792.4306.254.25
10-12177220.4979.180.347.175.87
13-15523231.0867.181.747.967.02
16-18962438.2059.092.718.818.06
19-211203844.9650.864.199.689.08
22-24975950.8742.816.3210.4810.01
25-27521554.5235.2410.2411.2210.89
28-30177863.3927.509.1111.8811.65
31-4040775.6821.133.1912.5312.32

W 6:4 E 3:5CasesEqual %6-3 Win %4-5 Win %6-3 Average4-5 Average
0-940549.3837.7812.846.025.71
10-12177656.1429.1114.757.006.83
13-15509957.1323.7919.087.887.83
16-18952859.5920.8019.618.798.78
19-211190863.9718.0517.989.659.65
22-24962369.6914.7015.6110.5410.55
25-27521276.3811.5112.1111.3411.35
28-30181581.718.379.9211.9511.97
31-4039584.057.098.8612.4712.49

W 7:3 E 1:5CasesEqual %7-1 Win %3-5 Win %7-1 Average3-5 Average
0-955912.7086.231.074.983.36
10-12203717.9776.885.155.834.53
13-15514625.9664.509.546.745.84
16-18895136.1648.1615.677.717.24
19-211074340.6634.7424.608.708.58
22-24895642.7527.0030.259.749.80
25-27522243.7422.8833.3810.7310.87
28-30201550.1219.8530.0211.5211.65
31-4048958.6916.9724.3412.2512.33

W 7:2 E 1:6CasesEqual %7-1 Win %2-6 Win %7-1 Average2-6 Average
0-947433.7651.0515.194.664.06
10-12169633.2051.4215.395.625.05
13-15459730.5252.5116.976.535.96
16-18780333.6447.1119.257.416.99
19-21942836.0441.7522.218.428.16
22-24788938.4135.4426.159.469.34
25-27454540.5531.2228.2310.5210.50
28-30172144.7427.7227.5411.4811.48
31-4047357.5120.5121.9912.2712.28

W 7:4 E 2:4CasesEqual %7-2 Win %4-4 Win %7-2 Average4-4 Average
0-92631.1498.8606.213.59
10-1210664.5095.220.287.145.07
13-15288412.8685.891.258.026.53
16-18518126.8568.914.258.937.96
19-21621244.2047.798.009.809.28
22-24515354.5136.219.2810.6510.31
25-27284461.6429.119.2511.4011.16
28-30114866.3826.317.3212.0611.82
31-4027574.1822.183.6412.5612.34

W 6:5 E 3:4CasesEqual %6-3 Win %5-4 Win %6-3 Average5-4 Average
0-921245.7545.758.496.696.25
10-1283352.4631.8115.737.597.40
13-15262858.6022.3419.068.468.42
16-18482458.8320.7720.409.349.33
19-21602762.4517.3420.2110.0910.12
22-24488168.6713.3817.9510.8510.90
25-27258574.3110.6815.0111.5311.58
28-3086281.218.1210.6712.0512.08
31-4018882.989.577.4512.5412.52

W 7:4 E 1:4CasesEqual %7-1 Win %4-4 Win %7-1 Average4-4 Average
0-92296.9992.580.445.413.38
10-1295012.2184.842.956.484.99
13-15242024.8868.186.947.416.48
16-18425738.2943.2518.468.277.93
19-21508643.6725.1931.149.229.29
22-24421744.7017.0538.2510.1110.37
25-27245148.6713.3437.9810.9611.24
28-3096450.9316.0832.9911.6611.86
31-4025567.4514.1218.4312.3712.44

W 7:4 E 3:4CasesEqual %7-3 Win %4-4 Win %7-3 Average4-4 Average
0-91220.8299.1806.933.94
10-124992.2097.8007.715.39
13-1514837.6291.910.478.586.83
16-18277923.3575.061.589.338.17
19-21349837.1960.212.6010.169.34
22-24283246.0849.264.6610.9310.32
25-27157452.3541.745.9111.5811.11
28-3052758.4439.282.2812.1911.75
31-409763.9234.022.0612.5812.18

W 7:3 E 2:6CasesEqual %7-2 Win %3-6 Win %7-2 Average3-6 Average
0-913228.7964.396.825.895.17
10-1247837.6653.978.376.876.33
13-15147344.7437.6817.587.727.50
16-18283552.1726.8121.028.648.59
19-21347657.5919.4822.939.579.62
22-24281963.7516.8919.3710.5010.54
25-27144471.8112.5315.6511.3211.37
28-3053277.6311.6510.7112.0412.03
31-4012080.0010.839.1712.4712.48

W 7:4 E 2:5CasesEqual %7-2 Win %4-5 Win %7-2 Average4-5 Average
0-98411.9086.901.196.905.65
10-1238833.7658.517.737.737.04
13-15109547.6736.2616.078.488.26
16-18207755.4222.9221.679.329.32
19-21261663.8814.9121.2210.1510.24
22-24211667.0612.9519.9910.8610.95
25-27115373.2012.2314.5711.5611.60
28-3037983.645.2811.0812.1512.21
31-407681.587.8910.5312.5712.61

 Study 8J13   Main Top   Trump Fit Comparisons

Dual Fits by Pattern

The following tables break down each of the 16 most common dual fits by specific hand patterns, i.e., each non-fit distribution is considered as a separate case. As in the previous sections, the more lopsided fit is shown as spades with West longer, and the more even fit is shown as hearts. Further, West’s longer non-fit suit is shown as diamonds to avoid redundancy. For example, it makes no difference if West is 5=4=3=1 or 5=4=1=3 as long as East’s minors are synchronized, so they are combined as one listing.

Tinted rows indicate cases where the more even fit (hearts) performs better. As in the previous section, the superior trump suit of many dual fits varies, though the consequence of differing patterns is a mixed bag. Some of the reasons can be logically inferred, while others remain a mystery. Perhaps if I broke down each specific pattern by HCP, a hidden truth might emerge… No, enough already!

West 5:4East 3:4CasesEqual %5-3 Win %4-4 Win %5-3 Average4-4 Average
2:23:310467262.3916.7620.847.867.90
2:24:213990563.3417.6718.997.877.88
2:25:13935255.5316.3028.168.518.62
3:10:6433048.3815.2936.339.229.47
3:11:53714253.1413.7433.128.648.84
3:12:410479057.7215.4126.878.258.36
3:13:312464558.9115.7525.338.008.10
3:14:26555957.6817.1625.168.198.27
4:00:6148451.1516.0432.829.309.49
4:01:51037353.3714.2632.378.919.11
4:02:42317955.3117.4927.208.738.83
4:03:32178453.9817.3728.658.748.86

West 5:4East 4:4CasesEqual %5-4 Win %4-4 Win %5-4 Average4-4 Average
2:23:28710059.2229.3211.458.278.02
2:24:13513254.7638.296.959.118.71
2:25:0441945.7349.065.2010.129.56
3:10:5473937.1059.743.1710.259.53
3:11:42890444.8551.333.829.609.01
3:12:35835654.8137.547.659.018.63
3:13:24648354.9828.7316.298.538.35
3:14:11476254.7134.2411.068.748.42
4:00:5147031.8467.011.1610.569.74
4:01:4738039.7657.902.3410.089.38
4:02:31167244.3550.754.919.859.26
4:03:2739552.2135.9311.869.679.35

West 6:3East 2:5CasesEqual %6-2 Win %3-5 Win %6-2 Average3-5 Average
2:23:34218151.2030.2118.598.047.90
2:24:25591350.9525.9523.108.037.99
2:25:11561141.5215.4343.058.448.76
3:10:6177731.9110.5857.518.889.58
3:11:51499343.3017.7638.948.438.71
3:12:44169248.9627.9423.118.318.24
3:13:34987750.2830.2719.458.258.11
3:14:22588851.5424.2724.188.458.44
4:00:658438.8715.7545.389.019.47
4:01:5415344.8624.2030.948.768.85
4:02:4935244.1936.9818.838.878.62
4:03:3869545.1639.4415.409.118.80

West 6:4East 2:4CasesEqual %6-2 Win %4-4 Win %6-2 Average4-4 Average
2:11:6648642.2914.1543.568.839.14
2:12:52808051.5020.4428.068.468.52
2:13:45254552.3424.9522.718.518.46
2:14:34699052.0724.9023.038.598.55
2:15:21947149.9319.0631.018.688.79
3:00:733135.9512.6951.369.119.62
3:01:6310441.0412.4746.498.959.36
3:02:51048747.2220.2032.588.808.91
3:03:41545249.7523.6926.578.828.83
3:04:31085852.1021.0926.819.059.09

West 6:4East 3:4CasesEqual %6-3 Win %4-4 Win %6-3 Average4-4 Average
2:10:696148.0743.398.5310.4810.00
2:11:5930951.7341.986.289.619.13
2:12:42921349.5442.557.918.958.49
2:13:33867447.0545.347.619.038.53
2:14:22358348.6542.438.919.148.69
2:15:1592352.7837.929.309.288.88
3:00:653745.4446.937.6410.6210.11
3:01:5382844.1248.906.9710.029.44
3:02:4961143.5049.067.449.659.05
3:03:31044342.9245.2211.869.368.91
3:04:2502346.7339.3813.909.729.36

West 6:5East 2:3CasesEqual %6-2 Win %5-3 Win %6-2 Average5-3 Average
1:14:41068959.2318.5522.229.049.05
1:15:31496657.9419.1422.929.049.05
1:16:2514456.1617.1926.659.069.13
2:01:773850.4115.7233.889.129.31
2:02:6381456.5817.0726.358.949.01
2:03:5848158.1918.3823.439.099.13
2:04:4923258.1719.7422.109.249.24
2:05:3524756.7019.7423.569.459.46

West 6:4East 4:4CasesEqual %6-4 Win %4-4 Win %6-4 Average4-4 Average
2:10:586131.8267.360.8110.9510.00
2:11:4580640.3458.101.5710.009.23
2:12:31301347.6846.905.429.268.71
2:13:21156946.4347.775.809.318.76
2:14:1431947.9748.713.319.418.82
2:15:048542.4754.852.6810.669.93
3:00:542323.4076.360.2411.4310.24
3:01:4214128.4470.620.9310.679.60
3:02:3387338.1657.714.1310.119.36
3:03:2285945.2644.2810.469.789.31
3:04:185946.2244.709.0810.069.56

West 6:4East 3:5CasesEqual %6-3 Win %4-5 Win %6-3 Average4-5 Average
2:10:584464.4514.2221.3310.7910.87
2:11:4589864.4318.3317.249.939.92
2:12:31279167.8717.5214.619.269.23
2:13:21152266.8417.8615.309.369.33
2:14:1417864.3618.6217.029.439.41
2:15:048062.0822.5015.4210.5410.46
3:00:536962.0611.1126.8311.1011.28
3:01:4209662.7918.9418.2710.5210.52
3:02:3397259.7719.5420.6910.0910.09
3:03:2285363.3016.8919.809.9910.02
3:04:175862.0116.7521.2410.2710.33

West 7:3East 1:5CasesEqual %7-1 Win %3-5 Win %7-1 Average3-5 Average
2:11:6154832.6919.3248.008.578.98
2:12:5639938.8035.9425.258.518.32
2:13:41198936.9945.2617.758.608.17
2:14:31049937.8844.0918.038.708.29
2:15:2443740.7928.7430.478.758.75
3:00:76028.336.6765.008.529.73
3:01:673235.7923.5040.718.578.88
3:02:5241737.1937.6525.168.818.61
3:03:4349238.5543.5617.909.048.64
3:04:3254541.3838.1120.519.329.07

West 7:2East 1:6CasesEqual %7-1 Win %2-6 Win %7-1 Average2-6 Average
2:23:3613837.7344.9317.338.347.93
2:24:2811238.0540.5621.398.287.99
2:25:1221835.3519.0745.588.458.86
3:10:622824.1212.2863.608.379.45
3:11:5211836.0229.0834.898.378.48
3:12:4594134.5144.2521.248.388.03
3:13:3692936.4846.5017.028.548.11
3:14:2369339.6236.5823.808.728.54
4:00:610225.4919.6154.908.469.25
4:01:561234.1537.2528.598.438.32
4:02:4134632.8450.0717.098.858.31
4:03:3118928.6858.0313.299.388.67

West 7:4East 2:4CasesEqual %7-2 Win %4-4 Win %7-2 Average4-4 Average
1:14:3825339.0457.023.949.698.86
1:15:2402943.7150.485.819.668.99
1:16:189452.0134.1213.879.669.34
2:00:76233.8738.7127.4210.6010.40
2:01:667945.5140.5013.999.849.42
2:02:5244840.8551.597.569.628.94
2:03:4407137.7155.696.619.768.97
2:04:3332237.8455.456.719.989.23
2:05:2126840.7749.849.3810.179.57

West 6:5East 3:4CasesEqual %6-3 Win %5-4 Win %6-3 Average5-4 Average
1:13:3430165.2918.9715.749.919.87
1:14:2584264.1718.6917.139.899.88
1:15:1168861.9119.1918.909.919.91
1:16:017364.1616.1819.6511.1311.17
2:00:612366.674.8828.4611.2311.47
2:01:5115366.9614.0518.9910.5610.62
2:02:4324265.5217.0017.499.979.98
2:03:3392762.6915.7621.5410.1110.16
2:04:2210762.3216.2321.4510.2210.27
2:05:148470.0415.0814.8810.6510.65

West 7:4East 1:4CasesEqual %7-1 Win %4-4 Win %7-1 Average4-4 Average
1:14:4379038.6838.1323.199.098.81
1:15:3537541.2334.0524.739.138.94
1:16:2189339.4625.9434.609.139.19
2:01:723334.7616.3148.938.959.42
2:02:6132536.5331.4732.009.008.98
2:03:5304640.2535.2324.529.198.99
2:04:4331139.8135.6724.529.359.15
2:05:3185642.4629.7427.809.479.40

West 7:4East 3:4CasesEqual %7-3 Win %4-4 Win %7-3 Average4-4 Average
1:13:3259233.6065.430.969.978.91
1:14:2336534.2364.281.499.999.01
1:15:1100940.3457.781.8810.139.35
1:16:08333.7363.862.4111.1310.28
2:00:69534.7464.211.0511.3610.41
2:01:569934.0565.090.8610.669.64
2:02:4183233.8462.283.889.969.00
2:03:3224932.5562.784.6710.179.19
2:04:2119332.3660.946.7110.319.43
2:05:129436.3956.127.4810.639.90

West 7:3East 2:6CasesEqual %7-2 Win %3-6 Win %7-2 Average3-6 Average
2:10:524250.8313.2235.9510.3910.67
2:11:4172056.5119.5323.959.619.65
2:12:3375159.8522.8717.289.289.23
2:13:2335260.3523.8115.849.349.26
2:14:1126556.7620.8722.379.449.47
2:15:013452.2413.4334.3310.3510.60
3:00:510746.7316.8236.4510.6210.90
3:01:462655.1122.3622.5210.1910.19
3:02:3110251.3631.0317.609.979.81
3:03:278459.5726.1514.299.929.80
3:04:122653.9824.7821.2410.1710.15

West 7:4East 2:5CasesEqual %7-2 Win %4-5 Win %7-2 Average4-5 Average
1:13:3186160.4023.3216.289.999.91
1:14:2249761.9120.3817.709.889.86
1:15:173960.2215.2924.499.9210.03
1:16:07759.746.4933.7710.7411.08
2:00:67554.674.0041.3310.6311.13
2:01:549455.6714.1730.1610.3710.55
2:02:4139461.1920.3718.449.929.91
2:03:3171962.2522.2215.5310.2810.20
2:04:292263.4518.4418.1110.4210.42
2:05:120668.9316.5014.5610.6910.64

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