Study 8C05   Main

by Richard Pavlicek

About five years ago I did a study on Lead Safety Analysis, comparing the safety in leading various four-card suits in common layouts, as well as the merits of leading from a sequence versus fourth-best. This is an expansion on that study, now including all possible four-card holdings, all possible layouts (barring a void or 6+ cards in one hand) and all lead options, using new software specially designed for the purpose.

There are 715 possible four-card holdings, each of which is analyzed in 14,784 layouts for each of the four lead choices, as well as when partner or declarer leads the suit. This required 715 × 14,784 × 6 = 63,423,360 double-dummy solutions. Some holdings of course were trivial, such as A-K-Q-J (duh… fourth-best?) but even those results were welcome as a validity check.

The following table shows which suit distributions were considered. Combinations shows the number of card distributions for each specific suit pattern. Ways shows the number of permutations. Specific (combinations × ways) shows the total number of layouts. Ratio shows the relative probability of one specific lie of the suit pattern. For example, a specific 4=3=3=3 lie is more likely than a specific 4=4=3=2 lie by the ratio 726:660. Each case is then weighted accordingly to obtain the true trick average. (My previous study did not allow for this.)

Suit PatternCombinationsWaysSpecificRatio
4 (3-3-3)9c3 × 6c3 = 168011680726
4 (4-3-2)9c4 × 5c3 = 126067560660
4 (4-4-1)9c4 × 5c4 =  6302*1260550
4 (5-2-2)9c5 × 4c2 =  75632268540
4 (5-3-1)9c5 × 4c3 =  5044*2016495
Totals483016147842971

*Excludes a singleton with declarer to emulate the typical environment of leading against a notrump contract. While hardly impossible due to off-shape notrumps, including these cases on an equal basis would bias the results, and trying to define special cases is arbitrary and fuzzy. Better just to ignore. Similarly, rare patterns with a void or 6+ cards in any hand are excluded despite being possible.

#### Double-Dummy Issues

As noted in my previous study, double-dummy play means nobody misguesses. While this balances out to some degree, it favors declarer because he gets to make the first double-dummy play. Therefore, some leads would fare better in practice than their safe percent indicates. For example, leading from 10-x-x-x when dummy has J-9-x and declarer A-K-x loses a trick here, but in actual play would probably survive when declarer misguesses.

Double-dummy play also affects trick averages when choosing the card to lead. For example, it makes no difference which card is led from A-K-x-x when dummy has Q-x-x and declarer 10-x-x with open cards, but in practice leading low gains a trick. Therefore, if the advantage in leading from a sequence (versus low) is only slight, leading low may be better in practice.

When declarer is required to lead the suit on his own, I impose a restriction on double-dummy manipulation. Declarer is not permitted to lead a jack, 10 or nine (from 3+ cards) on the first round unless his side has a touching card. This prevents the grossly anti-percentage backward finesse; e.g., with K-x-x opposite A-J-9 leading the jack to force a cover then finessing the nine on the way back. While this doesn’t eliminate declarer’s overall advantage, it levels the playing field a bit.

In all cases when the defense leads, it is required only once. For analysis purposes, all subsequent leads are made by declarer, who is free to lead from either hand to his best double-dummy advantage. If declarer happens to be out of the suit at trick three or four, the defense is awarded the remainder; hence four tricks are always decided regardless of which hands have a card to contribute.

#### Explanation of Tables

The lengthy tables that follow show the average number of tricks (0-4) won with each holding according to the card led (highest, second, third or fourth) with the best lead tinted gold. An equal sign (=) denotes an equivalent lead to a higher touching card. Trick average is also shown if partner leads the suit, and if declarer leads the suit. Safety shows the percent of time the gold-tinted lead does not lose a trick versus declarer leading. Percentile ranks each safety as a percent of the 715 holdings it exceeds. Since 27 holdings are 100-percent safe, the top percentile is 100×688/715 = 96.22; 50+ indicates above average.

Note that for all holdings, positional play dictates that the best trick average in leading a suit must be less than or equal to the trick average obtained when declarer is required to lead. In other words, it is either an advantage or break-even for declarer to lead, never a disadvantage. In contrast, partner leading the suit can swing either way. For most holdings it is an advantage on average, but weak safe holdings incur a disadvantage (tinted red) with partner leading.

Existence of outside entries and tempo factors are completely ignored; analysis is strictly about a single suit. For instance, the best lead from A-Q-J-10 is clearly the ace (might catch a stiff king) but this would be dubious in practice without a sure side entry. In fact leading the suit at all is usually wrong, as it’s the second worst of all 715 holdings for safety.

 Study 8C05   Main Top   Leading Authority

## Ace Holdings

A-KHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
A-K-Q-J4.0000===4.00004.0000100.0096.22
A-K-Q-103.9274==3.32303.92743.9274100.0096.22
A-K-Q-93.8247==3.32303.82873.828799.5893.15
A-K-Q-83.7098==3.32303.74243.746796.0685.31
A-K-Q-73.6417==3.32303.67613.684595.3684.62
A-K-Q-63.6076==3.32303.63313.645595.8585.17
A-K-Q-53.5921==3.32303.61543.623496.5586.01
A-K-Q-43.5866==3.32303.60803.614496.9286.71
A-K-Q-33.5854==3.32303.60473.609197.3887.41
A-K-Q-23.5854==3.32303.60323.606197.7187.83
A-K-J-103.7476=3.3230=3.74763.7476100.0096.22
A-K-J-93.6643=3.26063.26463.66833.668399.5693.01
A-K-J-83.5631=3.18103.26463.59773.602095.7385.03
A-K-J-73.5002=3.10033.26463.53893.549594.6381.82
A-K-J-63.4685=3.05113.26463.49913.514595.0083.92
A-K-J-53.4545=3.02543.26463.48243.493995.7284.90
A-K-J-43.4492=3.01313.26463.47533.485496.0985.45
A-K-J-33.4481=3.00823.26463.47203.480196.5686.15
A-K-J-23.4481=3.00703.26463.47053.477096.9186.57
A-K-10-93.4630=3.2313=3.56573.575887.3848.25
A-K-10-83.4007=3.12843.17363.48373.493889.4458.88
A-K-10-73.3382=3.02813.17363.42093.437289.0957.06
A-K-10-63.3065=2.96663.17363.37423.398889.9161.40
A-K-10-53.2946=2.93343.17363.35403.376391.0665.59
A-K-10-43.2902=2.91703.17363.34623.367791.5768.11
A-K-10-33.2892=2.91073.17363.34283.362392.0872.17
A-K-10-23.2892=2.90953.17363.34123.359392.4376.64
A-K-9-83.1668=3.1118=3.38463.413075.127.69
A-K-9-73.1489=3.00583.07223.32383.357078.4513.15
A-K-9-63.1312=2.94393.07223.26953.311781.0618.32
A-K-9-53.1253=2.90853.07223.24353.286483.0028.39
A-K-9-43.1230=2.89053.07223.23403.275683.9033.43
A-K-9-33.1225=2.88273.07223.22993.269584.5236.08
A-K-9-23.1225=2.88043.07223.22823.266284.8938.46
A-K-8-72.9989=3.0002=3.16053.224573.855.45
A-K-8-62.9971=2.93752.99403.13113.203177.9512.03
A-K-8-52.9951=2.90292.99403.11193.184679.6515.24
A-K-8-42.9944=2.88642.99403.10573.178380.2716.64
A-K-8-32.9943=2.87912.99403.10383.174180.7617.34
A-K-8-22.9943=2.87672.99403.10293.171781.0518.18
A-K-7-62.9295=2.9370=3.02063.087581.1719.16
A-K-7-52.9295=2.90092.93123.01803.083780.9617.76
A-K-7-42.9294=2.88442.93123.01653.080281.3220.14
A-K-7-32.9294=2.87652.93123.01573.077781.6021.54
A-K-7-22.9294=2.87352.93123.01533.076581.7522.38
A-K-6-52.9016=2.9009=2.96603.022386.4744.48
A-K-6-42.9016=2.88442.90092.96603.021786.5544.76
A-K-6-32.9016=2.87652.90092.96573.020786.6745.73
A-K-6-22.9016=2.87352.90092.96563.020186.7545.87
A-K-5-42.8920=2.8844=2.94442.991688.8655.38
A-K-5-32.8920=2.87652.88442.94442.991688.8655.38
A-K-5-22.8920=2.87352.88442.94442.991688.8655.38
A-K-4-32.8902=2.8765=2.93642.979390.0061.54
A-K-4-22.8902=2.87352.87652.93642.979390.0061.54
A-K-3-22.8902=2.8735=2.93492.975790.3663.78

A-QHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
A-Q-J-103.33333.3230==3.68733.687361.610.14
A-Q-J-93.30023.2606=3.14693.60793.607965.880.70
A-Q-J-83.25963.1810=3.14693.52363.527969.631.96
A-Q-J-73.22453.1003=3.14693.45563.466272.433.64
A-Q-J-63.20323.0511=3.14693.40463.420874.967.27
A-Q-J-53.19343.0254=3.14693.38043.393476.829.79
A-Q-J-43.18953.0131=3.14693.36903.381177.7111.19
A-Q-J-33.18843.0082=3.14693.36453.374578.3112.59
A-Q-J-23.18843.0070=3.14693.36303.371478.6513.71
A-Q-10-93.18253.13163.1135=3.47303.483166.921.12
A-Q-10-83.14703.06133.02713.06633.39133.401471.102.80
A-Q-10-73.11502.98822.93233.06633.32593.342373.925.59
A-Q-10-63.09402.94132.87203.06633.27403.297676.479.65
A-Q-10-53.08462.91702.83933.06633.24883.270478.4112.73
A-Q-10-43.08142.90582.82393.06633.23773.258879.3314.83
A-Q-10-33.08062.90122.81793.06633.23353.252779.9516.08
A-Q-10-23.08062.90012.81673.06633.23203.249780.3016.78
A-Q-9-82.98412.90173.0050=3.29283.321366.890.98
A-Q-9-72.96242.84912.90272.96183.22853.260367.071.26
A-Q-9-62.94092.79902.84202.96183.16843.206772.673.92
A-Q-9-52.93052.77292.80692.96183.13693.175675.648.25
A-Q-9-42.92682.76282.78952.96183.12373.161477.0510.21
A-Q-9-32.92562.75892.78192.96183.11893.154577.7911.75
A-Q-9-22.92562.75792.77972.96183.11723.151278.1712.45
A-Q-8-72.83472.65042.8949=3.06993.132973.254.90
A-Q-8-62.82832.63472.83252.88603.03413.103175.077.55
A-Q-8-52.82182.61892.79802.88603.00863.077477.4710.63
A-Q-8-42.81972.61412.78222.88602.99783.066678.4913.29
A-Q-8-32.81902.61222.77512.88602.99483.061679.0614.41
A-Q-8-22.81902.61172.77272.88602.99393.059279.3615.10
A-Q-7-62.76192.50542.8312=2.92222.987781.1118.46
A-Q-7-52.76112.50372.79562.82542.91342.979481.1619.02
A-Q-7-42.76032.50192.78002.82542.90682.972581.7622.66
A-Q-7-32.76002.50122.77262.82542.90482.969382.0923.92
A-Q-7-22.76002.50112.76952.82542.90432.968182.2424.48
A-Q-6-52.73422.44502.7956=2.85852.915084.7837.62
A-Q-6-42.73422.44502.78002.79562.85712.913784.9038.60
A-Q-6-32.73422.44482.77262.79562.85612.912485.0539.30
A-Q-6-22.73422.44482.76952.79562.85602.911885.1339.72
A-Q-5-42.72512.42022.7800=2.83562.883686.5744.90
A-Q-5-32.72512.42022.77262.78002.83562.883686.5744.90
A-Q-5-22.72512.42022.76952.78002.83562.883686.5744.90
A-Q-4-32.72342.41132.7726=2.82802.871787.1047.13
A-Q-4-22.72342.41132.76952.77262.82802.871787.1047.13
A-Q-3-22.72342.40952.7695=2.82652.868187.1547.55

A-JHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
A-J-10-92.78563.0407==3.32103.350068.501.40
A-J-10-82.77222.9677=2.88263.26653.299966.460.84
A-J-10-72.76302.8756=2.88263.21763.250461.550.00
A-J-10-62.75522.8160=2.88263.17073.202665.850.56
A-J-10-52.75212.7840=2.88263.14203.172868.631.54
A-J-10-42.75102.7692=2.88263.12923.158370.022.10
A-J-10-32.75052.7631=2.88263.12483.151770.692.52
A-J-10-22.75052.7620=2.88263.12313.149270.952.66
A-J-9-82.69402.78442.8384=3.15823.198562.890.28
A-J-9-72.68362.72452.75982.81333.10453.146264.930.42
A-J-9-62.67482.66502.70052.81333.05423.097669.131.82
A-J-9-52.67062.63392.66672.81333.02083.065471.983.50
A-J-9-42.66942.62142.65162.81333.00483.049073.475.31
A-J-9-32.66902.61672.64522.81332.99933.042274.156.01
A-J-9-22.66902.61572.64312.81332.99753.039674.436.29
A-J-8-72.58332.52652.7443=2.96603.036268.991.68
A-J-8-62.57902.50632.68412.72762.92692.999970.452.38
A-J-8-52.57522.48632.65262.72762.89232.965173.385.03
A-J-8-42.57452.47932.63992.72762.87382.947874.816.99
A-J-8-32.57422.47642.63452.72762.86792.941075.477.97
A-J-8-22.57422.47572.63282.72762.86652.938775.748.39
A-J-7-62.52512.36182.6806=2.80212.879477.1510.35
A-J-7-52.52492.35962.64752.67542.78592.867477.5610.91
A-J-7-42.52482.35732.63372.67542.77202.856478.4412.87
A-J-7-32.52472.35632.62772.67542.76742.852778.8113.85
A-J-7-22.52472.35612.62522.67542.76652.851978.9114.13
A-J-6-52.50502.28902.6462=2.72082.797981.5020.84
A-J-6-42.50502.28902.63332.64622.71822.795581.7222.10
A-J-6-32.50502.28882.62762.64622.71652.793681.9123.22
A-J-6-22.50502.28882.62522.64622.71632.793181.9823.64
A-J-5-42.49812.25882.6333=2.69292.765883.5531.47
A-J-5-32.49812.25882.62762.63332.69292.765883.5531.47
A-J-5-22.49812.25882.62522.63332.69292.765883.5531.47
A-J-4-32.49682.24732.6276=2.68502.754184.2034.69
A-J-4-22.49682.24732.62522.62762.68502.754184.2034.69
A-J-3-22.49682.24522.6252=2.68292.750384.3235.38

A-10HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
A-10-9-82.36662.7406==2.87372.964274.756.71
A-10-9-72.36412.6753=2.62532.84322.938871.273.08
A-10-9-62.36242.6136=2.62532.81632.911770.422.24
A-10-9-52.36082.5792=2.62532.79602.894771.833.36
A-10-9-42.36072.5649=2.62532.78522.886672.473.78
A-10-9-32.36072.5588=2.62532.78272.883672.774.06
A-10-9-22.36072.5567=2.62532.78262.882472.914.48
A-10-8-72.34112.48432.6015=2.75652.856672.784.20
A-10-8-62.33942.46322.54412.58512.73022.831673.244.76
A-10-8-52.33792.44082.51262.58512.70992.811274.967.27
A-10-8-42.33772.43242.49972.58512.69812.800875.828.53
A-10-8-32.33772.42852.49372.58512.69512.796876.249.09
A-10-8-22.33772.42712.49182.58512.69482.795576.409.37
A-10-7-62.31122.31462.5335=2.61902.727777.5711.05
A-10-7-52.31122.31082.50172.52762.60682.718177.8711.89
A-10-7-42.31122.30692.48812.52762.59692.710478.5413.57
A-10-7-32.31122.30462.48172.52762.59402.707178.9013.99
A-10-7-22.31122.30392.47942.52762.59372.706279.0214.27
A-10-6-52.30072.23622.4992=2.54612.656880.9617.76
A-10-6-42.30072.23562.48672.49892.54352.656081.0018.04
A-10-6-32.30072.23492.48112.49892.54222.654881.1318.74
A-10-6-22.30072.23472.47892.49892.54202.654681.1719.16
A-10-5-42.29642.20072.4866=2.52042.629482.5325.73
A-10-5-32.29642.20072.48102.48662.52042.629482.5325.73
A-10-5-22.29642.20072.47892.48662.52042.629482.5325.73
A-10-4-32.29532.18682.4810=2.51252.618683.0528.67
A-10-4-22.29532.18682.47892.48102.51252.618683.0528.67
A-10-3-22.29532.18342.4789=2.51012.614483.2330.49

A-9HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
A-9-8-72.15912.4742==2.48392.580386.0242.80
A-9-8-62.15912.4506=2.43822.47492.574284.4435.66
A-9-8-52.15912.4255=2.43822.47002.570382.7927.13
A-9-8-42.15912.4169=2.43822.46662.567183.0829.09
A-9-8-32.15912.4131=2.43822.46562.565983.2230.35
A-9-8-22.15912.4116=2.43822.46552.565483.2730.77
A-9-7-62.15642.29732.4204=2.42612.541383.8233.15
A-9-7-52.15642.29262.38922.40862.42132.537083.2030.21
A-9-7-42.15642.28842.37642.40862.41792.533683.5231.33
A-9-7-32.15642.28582.37062.40862.41692.532383.6732.17
A-9-7-22.15642.28482.36842.40862.41672.531883.7332.59
A-9-6-52.15292.21662.3827=2.37342.499184.5736.36
A-9-6-42.15292.21622.37272.38182.37242.498384.5836.50
A-9-6-32.15292.21542.36862.38182.37192.497584.6736.92
A-9-6-22.15292.21512.36692.38182.37182.496984.7337.20
A-9-5-42.15142.18042.3722=2.35452.481885.4340.14
A-9-5-32.15142.18042.36842.37222.35452.481685.4540.28
A-9-5-22.15142.18042.36692.37222.35452.481485.4640.42
A-9-4-32.15112.16592.3684=2.34892.473885.8842.10
A-9-4-22.15112.16592.36692.36842.34892.473885.8842.10
A-9-3-22.15112.16212.3669=2.34742.470886.0543.08

A-xHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
A-8-7-62.07882.2886==2.24872.352790.0862.24
A-8-7-52.07882.2843=2.27752.24872.352089.7760.70
A-8-7-42.07882.2801=2.27752.24872.351689.3558.32
A-8-7-32.07882.2772=2.27752.24872.351389.2057.76
A-8-7-22.07882.2757=2.27752.24872.351089.2458.04
A-8-6-52.07882.20782.2753=2.24052.344989.6660.28
A-8-6-42.07882.20732.27072.27332.24052.344489.4659.02
A-8-6-32.07882.20632.26802.27332.24052.344189.4959.16
A-8-6-22.07882.20572.26642.27332.24052.343989.5359.44
A-8-5-42.07842.17142.2697=2.23452.335990.0761.96
A-8-5-32.07842.17142.26752.26972.23452.335990.0761.96
A-8-5-22.07842.17142.26642.26972.23452.335890.0862.24
A-8-4-32.07842.15682.2675=2.23182.332290.1962.80
A-8-4-22.07842.15682.26642.26752.23182.332290.1962.80
A-8-3-22.07842.15222.2664=2.23092.330890.2363.08
A-7-6-52.04672.2060==2.16092.254092.1173.15
A-7-6-42.04672.2054=2.20322.16092.254092.0372.03
A-7-6-32.04672.2044=2.20322.16092.254091.9071.75
A-7-6-22.04672.2038=2.20322.16092.254091.8270.07
A-7-5-42.04672.17042.2032=2.16092.253391.8370.21
A-7-5-32.04672.17042.20262.20322.16092.253391.8370.21
A-7-5-22.04672.17042.20222.20322.16092.253391.8370.21
A-7-4-32.04672.15632.2026=2.16072.252291.8771.47
A-7-4-22.04672.15632.20222.20262.16072.252291.8771.47
A-7-3-22.04672.15172.2022=2.16052.251491.9271.89
A-6-5-42.03672.1704==2.13282.216392.3074.41
A-6-5-32.03672.1704=2.17042.13282.216392.3074.41
A-6-5-22.03672.1704=2.17042.13282.216392.3074.41
A-6-4-32.03672.15632.1704=2.13282.216392.3074.41
A-6-4-22.03672.15632.17042.17042.13282.216392.3074.41
A-6-3-22.03672.15172.1704=2.13282.216392.3074.41
A-5-4-32.03482.1563==2.12212.201292.4276.22
A-5-4-22.03482.1563=2.15632.12212.201292.4276.22
A-5-3-22.03482.15172.1563=2.12212.201292.4276.22
A-4-3-22.03482.1517==2.12002.196692.4076.08

Interesting trivia: With regard to safety, what is the worst lead in bridge? According to this study, A-J-10-7 (see above table) is the goat at 61.55 percent safety, which means it loses a trick 38.45 percent of the time. Who would have guessed that?

 Study 8C05   Main Top   Leading Authority

## King Holdings

K-QHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
K-Q-J-103.3230===3.32303.3230100.0096.22
K-Q-J-93.2606==2.88143.29393.293996.8486.29
K-Q-J-83.1810==2.88143.25893.258992.5976.78
K-Q-J-73.1003==2.88143.23033.232487.4248.81
K-Q-J-63.0511==2.88143.20713.210884.7537.34
K-Q-J-53.0254==2.88143.19103.195683.7032.31
K-Q-J-43.0131==2.88143.18393.188883.1429.65
K-Q-J-33.0082==2.88143.18113.186382.9027.97
K-Q-J-23.0070==2.88143.18033.185882.8427.55
K-Q-10-93.1316=2.8774=3.17343.183594.7582.38
K-Q-10-83.0613=2.83392.84593.14463.150491.6369.23
K-Q-10-72.9882=2.76902.84593.12083.126687.0646.85
K-Q-10-62.9413=2.72012.84593.10003.107384.5336.22
K-Q-10-52.9170=2.69172.84593.08483.093183.5731.89
K-Q-10-42.9058=2.67862.84593.07813.086883.0829.09
K-Q-10-32.9012=2.67372.84593.07573.084882.8227.41
K-Q-10-22.9001=2.67262.84593.07483.084382.7526.99
K-Q-9-82.9017=2.8119=3.04703.069483.0028.39
K-Q-9-72.8491=2.73052.78313.01743.035881.8723.08
K-Q-9-62.7990=2.67152.78312.99333.011779.9215.94
K-Q-9-52.7729=2.63582.78312.97382.993279.2214.69
K-Q-9-42.7628=2.61822.78312.96392.983880.0316.36
K-Q-9-32.7589=2.61102.78312.96042.981180.2616.50
K-Q-9-22.7579=2.60852.78312.95942.980580.3116.92
K-Q-8-72.6504=2.7167=2.90832.949877.0310.07
K-Q-8-62.6347=2.65762.70642.88682.926478.0712.31
K-Q-8-52.6189=2.62322.70642.86622.905079.9015.80
K-Q-8-42.6141=2.60702.70642.85442.894080.8117.62
K-Q-8-32.6122=2.60062.70642.85002.889781.2019.58
K-Q-8-22.6117=2.59912.70642.84872.888781.3120.00
K-Q-7-62.5054=2.6545=2.78512.833681.5620.98
K-Q-7-52.5037=2.62052.65202.77302.825681.9423.50
K-Q-7-42.5019=2.60572.65202.76262.818582.4525.59
K-Q-7-32.5012=2.60042.65202.75872.816582.6026.43
K-Q-7-22.5011=2.59912.65202.75792.816182.6426.57
K-Q-6-52.4450=2.6203=2.71622.764584.6336.78
K-Q-6-42.4450=2.60562.62032.71472.762784.7737.48
K-Q-6-32.4448=2.60042.62032.71362.761784.8538.04
K-Q-6-22.4448=2.59912.62032.71342.761684.8738.32
K-Q-5-42.4202=2.6056=2.68722.735985.9542.38
K-Q-5-32.4202=2.60042.60562.68722.735985.9542.38
K-Q-5-22.4202=2.59912.60562.68722.735985.9542.38
K-Q-4-32.4113=2.6004=2.67742.723986.6645.45
K-Q-4-22.4113=2.59912.60042.67742.723986.6645.45
K-Q-3-22.4095=2.5991=2.67452.718987.0246.43

K-JHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
K-J-10-92.75522.8661==3.07113.100177.3610.49
K-J-10-82.72652.8124=2.72683.04233.071375.217.83
K-J-10-72.69492.7426=2.72683.01543.039771.122.94
K-J-10-62.66832.6906=2.72682.99133.012272.884.34
K-J-10-52.65252.6613=2.72682.97152.989774.847.13
K-J-10-42.64502.6482=2.72682.96072.977375.898.67
K-J-10-32.64182.6433=2.72682.95542.972076.329.23
K-J-10-22.64072.6422=2.72682.95352.970476.439.51
K-J-9-82.62532.64872.6959=2.92412.958274.776.85
K-J-9-72.59482.60062.62152.67372.89712.927675.558.11
K-J-9-62.56902.55512.56562.67372.87272.901577.7711.61
K-J-9-52.55212.52842.53092.67372.85172.878979.6915.38
K-J-9-42.54442.51632.51372.67372.83972.866180.7617.34
K-J-9-32.54162.51222.50712.67372.83432.861181.1418.88
K-J-9-22.54082.51142.50502.67372.83272.860081.2219.86
K-J-8-72.45842.43682.6071=2.78232.834877.7511.47
K-J-8-62.43972.41162.54782.59392.76022.810578.5313.43
K-J-8-52.42142.38682.51302.59392.73782.785280.6517.20
K-J-8-42.41272.37452.49652.59392.72352.770981.7722.80
K-J-8-32.40962.37012.49032.59392.71682.764282.2924.76
K-J-8-22.40852.36882.48902.59392.71492.762782.4225.45
K-J-7-62.33252.27572.5430=2.65682.716782.3925.03
K-J-7-52.32672.26882.50852.53932.64302.704682.9628.11
K-J-7-42.32082.26172.49352.53932.62972.693383.7232.45
K-J-7-32.31892.25932.48852.53932.62292.688184.0334.13
K-J-7-22.31822.25852.48752.53932.62132.687084.0934.27
K-J-6-52.27092.19552.5079=2.58362.641485.8141.54
K-J-6-42.27012.19462.49312.50792.57952.637186.0843.22
K-J-6-32.26932.19382.48842.50792.57532.633686.2843.92
K-J-6-22.26902.19352.48752.50792.57392.632986.3244.06
K-J-5-42.24702.16452.4931=2.54942.608187.4048.67
K-J-5-32.24702.16452.48842.49312.54872.607887.4248.81
K-J-5-22.24702.16452.48752.49312.54792.607487.4349.09
K-J-4-32.23872.15342.4884=2.53882.595988.1553.01
K-J-4-22.23872.15342.48752.48842.53882.595988.1553.01
K-J-3-22.23702.15142.4875=2.53622.591388.5253.71

K-10HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
K-10-9-82.26782.5671==2.73342.810676.078.95
K-10-9-72.25582.5189=2.47712.71602.794073.405.17
K-10-9-62.24752.4701=2.47712.69972.774871.313.22
K-10-9-52.24032.4382=2.47712.68272.754472.964.62
K-10-9-42.23762.4223=2.47712.67132.741773.935.73
K-10-9-32.23682.4162=2.47712.66532.734774.506.43
K-10-9-22.23632.4140=2.47712.66382.732374.736.57
K-10-8-72.19112.35312.4440=2.62962.711074.045.87
K-10-8-62.18162.32662.39132.43142.61262.692574.266.15
K-10-8-52.17342.29902.35902.43142.59482.671775.898.67
K-10-8-42.16962.28552.34342.43142.58212.657976.929.93
K-10-8-32.16872.28012.33772.43142.57492.649977.5310.77
K-10-8-22.16822.27822.33642.43142.57322.647777.7211.33
K-10-7-62.09912.19602.3837=2.51122.602077.9612.17
K-10-7-52.09512.18652.35162.37782.49812.588778.4412.87
K-10-7-42.09142.17782.33752.37782.48522.575579.3314.83
K-10-7-32.09072.17412.33272.37782.47692.567379.8615.52
K-10-7-22.09052.17262.33172.37782.47462.565180.0216.22
K-10-6-52.04922.11122.3502=2.43722.525881.4620.70
K-10-6-42.04902.10962.33642.34992.43132.520981.6621.96
K-10-6-32.04882.10832.33192.34992.42482.515581.9323.36
K-10-6-22.04882.10782.33122.34992.42242.513982.0223.78
K-10-5-42.03172.07552.3362=2.40002.489583.1929.93
K-10-5-32.03172.07552.33182.33622.39872.488683.2330.49
K-10-5-22.03172.07552.33122.33622.39742.487783.2730.77
K-10-4-32.02542.06252.3318=2.38812.476683.9333.57
K-10-4-22.02542.06252.33122.33182.38812.476683.9333.57
K-10-3-22.02412.05942.3312=2.38542.471984.3035.24

K-9HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
K-9-8-71.90732.3278==2.38052.481983.4431.19
K-9-8-61.90482.2974=2.28972.37182.473981.5821.26
K-9-8-51.90312.2688=2.28972.36312.465081.1919.44
K-9-8-41.90152.2552=2.28972.35552.459181.5620.98
K-9-8-31.90132.2507=2.28972.35052.455781.7422.24
K-9-8-21.90132.2498=2.28972.34932.454881.7822.94
K-9-7-61.88452.17082.2717=2.32182.433682.3224.90
K-9-7-51.88282.16062.24272.26342.31362.425782.1424.20
K-9-7-41.88132.15172.22912.26342.30612.418982.5826.29
K-9-7-31.88112.14852.22422.26342.30042.414982.8127.27
K-9-7-21.88112.14762.22292.26342.29882.413982.8727.83
K-9-6-51.85792.08682.2387=2.26742.379584.0133.99
K-9-6-41.85792.08502.22602.23782.26292.375984.1234.55
K-9-6-31.85792.08372.22202.23782.25792.372784.2935.10
K-9-6-21.85792.08312.22142.23782.25602.371884.3635.52
K-9-5-41.84902.05202.2256=2.23652.352185.1239.58
K-9-5-31.84902.05182.22182.22562.23542.351885.1339.72
K-9-5-21.84902.05162.22142.22562.23432.351585.1440.00
K-9-4-31.84522.03832.2218=2.22672.342685.7040.70
K-9-4-21.84522.03832.22142.22182.22672.342685.7040.70
K-9-3-21.84412.03482.2214=2.22472.339186.0342.94

K-xHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
K-8-7-61.72482.1638==2.14912.249389.3858.46
K-8-7-51.72482.1529=2.15272.14652.247688.8155.24
K-8-7-41.72482.1438=2.15272.14462.246388.5253.71
K-8-7-31.72482.1407=2.15272.14272.245188.5953.99
K-8-7-21.72482.1400=2.15272.14182.244988.6154.13
K-8-6-51.72222.07912.1436=2.13132.234888.8055.10
K-8-6-41.72222.07692.13402.14162.12942.233588.6254.27
K-8-6-31.72222.07562.13092.14162.12752.232388.6954.83
K-8-6-21.72222.07512.13012.14162.12672.232288.7154.97
K-8-5-41.71902.04512.1330=2.11362.219689.1457.20
K-8-5-31.71902.04502.13042.13302.11312.219689.1457.20
K-8-5-21.71902.04502.13012.13302.11272.219689.1457.20
K-8-4-31.71752.03192.1304=2.10722.214089.4158.60
K-8-4-21.71752.03192.13012.13042.10722.214089.4158.60
K-8-3-21.71722.02762.1301=2.10522.211689.6159.86
K-7-6-51.65302.0770==2.04552.141291.4467.55
K-7-6-41.65302.0749=2.07582.04552.141291.2866.29
K-7-6-31.65302.0738=2.07582.04552.141291.2866.29
K-7-6-21.65302.0734=2.07582.04552.141291.2866.29
K-7-5-41.65302.04422.0744=2.04312.139491.3466.99
K-7-5-31.65302.04422.07352.07442.04312.139491.3466.99
K-7-5-21.65302.04422.07342.07442.04312.139491.3466.99
K-7-4-31.65262.03172.0735=2.04092.137491.4767.69
K-7-4-21.65262.03172.07342.07352.04092.137491.4767.69
K-7-3-21.65262.02742.0734=2.03982.136391.5768.11
K-6-5-41.62552.0442==2.01252.102292.0872.17
K-6-5-31.62552.0442=2.04422.01252.102292.0872.17
K-6-5-21.62552.0442=2.04422.01252.102292.0872.17
K-6-4-31.62552.03172.0442=2.01252.102292.0872.17
K-6-4-21.62552.03172.04422.04422.01252.102292.0872.17
K-6-3-21.62552.02742.0442=2.01252.102292.0872.17
K-5-4-31.61622.0317==2.00242.088092.2373.71
K-5-4-21.61622.0317=2.03172.00242.088092.2373.71
K-5-3-21.61622.02742.0317=2.00242.088092.2373.71
K-4-3-21.61432.0274==2.00052.083792.2373.71

 Study 8C05   Main Top   Leading Authority

## Queen Holdings

Q-JHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
Q-J-10-92.7095===2.65122.7095100.0096.22
Q-J-10-82.6674==2.40012.64182.700197.3587.27
Q-J-10-72.6198==2.40012.63232.690694.3179.30
Q-J-10-62.5779==2.40012.62452.681791.5367.97
Q-J-10-52.5532==2.40012.61702.673090.2763.50
Q-J-10-42.5422==2.40012.61142.667389.8261.26
Q-J-10-32.5381==2.40012.60822.664089.7660.56
Q-J-10-22.5370==2.40012.60712.662589.8060.98
Q-J-9-82.5605=2.3941=2.57042.632693.5977.62
Q-J-9-72.5155=2.36262.37622.56222.621691.3066.85
Q-J-9-62.4754=2.32482.37622.55562.612088.9255.80
Q-J-9-52.4497=2.29742.37622.54882.603487.7650.91
Q-J-9-42.4383=2.28242.37622.54362.597687.3948.39
Q-J-9-32.4348=2.27552.37622.54052.594487.3948.39
Q-J-9-22.4340=2.27262.37622.53982.593587.4349.09
Q-J-8-72.3692=2.3468=2.49462.559382.4025.17
Q-J-8-62.3399=2.30262.33452.48682.548881.3520.28
Q-J-8-52.3118=2.27332.33452.47922.539282.1524.34
Q-J-8-42.2981=2.25762.33452.47312.532182.6926.85
Q-J-8-32.2937=2.25032.33452.46922.527483.0728.95
Q-J-8-22.2924=2.24802.33452.46802.526383.1729.79
Q-J-7-62.2096=2.2944=2.41102.485482.9828.25
Q-J-7-52.2002=2.26672.29132.40542.477983.3431.05
Q-J-7-42.1913=2.25312.29132.40012.471383.8033.01
Q-J-7-32.1888=2.24772.29132.39612.466984.1134.41
Q-J-7-22.1882=2.24612.29132.39512.465684.2234.97
Q-J-6-52.1286=2.2655=2.35712.431784.8237.90
Q-J-6-42.1271=2.25242.26552.35432.429584.9138.74
Q-J-6-32.1261=2.24742.26552.35112.427085.0339.16
Q-J-6-22.1258=2.24612.26552.34992.426385.0639.44
Q-J-5-42.0980=2.2524=2.33012.405285.7941.26
Q-J-5-32.0980=2.24742.25242.32932.404885.8041.40
Q-J-5-22.0980=2.24612.25242.32862.404585.8141.54
Q-J-4-32.0873=2.2474=2.32082.394986.2343.64
Q-J-4-22.0873=2.24612.24742.32082.394986.2343.64
Q-J-3-22.0854=2.2461=2.31822.390686.5044.62

Q-10HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
Q-10-9-82.20272.3710==2.45732.542084.6937.06
Q-10-9-72.18462.3329=2.28212.44922.533882.2624.62
Q-10-9-62.17142.2906=2.28212.44252.523379.1414.55
Q-10-9-52.16022.2596=2.28212.43572.512179.8715.66
Q-10-9-42.15512.2432=2.28212.43052.503680.6317.06
Q-10-9-32.15332.2363=2.28212.42742.497781.2019.58
Q-10-9-22.15212.2334=2.28212.42672.495381.4520.56
Q-10-8-72.10492.18912.2560=2.37612.459681.6421.68
Q-10-8-62.09062.16512.21442.24742.36912.450881.5821.26
Q-10-8-52.07832.13942.18632.24742.36192.440882.4125.31
Q-10-8-42.07222.12642.17182.24742.35632.432683.0929.37
Q-10-8-32.07052.12092.16542.24742.35282.426783.6132.03
Q-10-8-22.06962.11872.16352.24742.35202.424883.7932.87
Q-10-7-61.98832.04002.2075=2.29152.381583.7432.73
Q-10-7-51.98202.03012.17902.20302.28592.374783.9433.85
Q-10-7-41.97642.02082.16522.20302.28062.367784.4535.94
Q-10-7-31.97502.01672.16002.20302.27662.362584.8538.04
Q-10-7-21.97432.01492.15852.20302.27562.360884.9939.02
Q-10-6-51.92371.95742.1769=2.23302.325285.6740.56
Q-10-6-41.92311.95592.16402.17692.23022.322285.8441.96
Q-10-6-31.92271.95442.15942.17692.22702.318486.0843.22
Q-10-6-21.92241.95362.15852.17692.22582.316986.1843.50
Q-10-5-41.90121.92472.1640=2.20302.295386.9346.15
Q-10-5-31.90121.92472.15942.16402.20232.294486.9946.29
Q-10-5-21.90121.92472.15852.16402.20162.293487.0546.71
Q-10-4-31.89361.91362.1594=2.19322.284187.4749.51
Q-10-4-21.89361.91362.15852.15942.19322.284187.4749.51
Q-10-3-21.89221.91092.1585=2.19092.280587.7250.63

Q-9HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
Q-9-8-71.79502.1361==2.20002.310983.8333.29
Q-9-8-61.79102.1113=2.09802.19592.306682.0923.92
Q-9-8-51.78842.0867=2.09802.19192.301881.1218.60
Q-9-8-41.78622.0742=2.09802.18842.297981.4020.42
Q-9-8-31.78582.0691=2.09802.18592.294781.6421.68
Q-9-8-21.78562.0676=2.09802.18512.293481.7522.38
Q-9-7-61.76351.99092.0777=2.14202.257982.6826.71
Q-9-7-51.76081.98112.05102.07192.13822.253482.5626.15
Q-9-7-41.75861.97212.03792.07192.13472.249382.8527.69
Q-9-7-31.75821.96872.03322.07192.13202.246083.1029.51
Q-9-7-21.75801.96742.03192.07192.13112.244883.1929.93
Q-9-6-51.72651.91202.0473=2.08552.202384.4435.66
Q-9-6-41.72651.91012.03562.04702.08342.199784.5936.64
Q-9-6-31.72641.90852.03192.04702.08122.196984.8037.76
Q-9-6-21.72631.90762.03142.04702.08032.195684.9138.74
Q-9-5-41.71381.88142.0354=2.05402.172985.7140.98
Q-9-5-31.71381.88102.03182.03542.05352.172285.7641.12
Q-9-5-21.71381.88052.03142.03542.05302.171485.8241.82
Q-9-4-31.70861.87002.0318=2.04392.162086.3444.20
Q-9-4-21.70861.87002.03142.03182.04392.162086.3444.20
Q-9-3-21.70721.86732.0314=2.04182.158786.6245.31

Q-xHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
Q-8-7-61.57821.9781==1.97232.087988.1352.87
Q-8-7-51.57821.9670=1.96851.97102.086487.4449.37
Q-8-7-41.57821.9577=1.96851.97012.085387.5349.79
Q-8-7-31.57821.9545=1.96851.96912.084387.6050.07
Q-8-7-21.57821.9539=1.96851.96872.083787.6650.35
Q-8-6-51.57441.90001.9590=1.95072.070687.9651.75
Q-8-6-41.57441.89791.95011.95791.94982.069587.8851.61
Q-8-6-31.57441.89651.94721.95791.94882.068587.9651.75
Q-8-6-21.57441.89591.94671.95791.94842.068088.0152.17
Q-8-5-41.57001.87001.9495=1.93022.052488.6354.41
Q-8-5-31.57001.86991.94691.94951.93002.052288.6554.55
Q-8-5-21.57001.86971.94671.94951.92982.052088.6754.69
Q-8-4-31.56791.85961.9469=1.92282.046788.9255.80
Q-8-4-21.56791.85961.94671.94691.92282.046788.9255.80
Q-8-3-21.56731.85621.9467=1.92092.044989.0656.64
Q-7-6-51.49141.8966==1.86021.976990.8965.03
Q-7-6-41.49141.8947=1.89541.86021.976990.7164.48
Q-7-6-31.49141.8937=1.89541.86021.976990.7164.48
Q-7-6-21.49141.8934=1.89541.86021.976990.7164.48
Q-7-5-41.49141.86821.8940=1.85701.973890.8965.03
Q-7-5-31.49141.86821.89311.89401.85701.973890.8965.03
Q-7-5-21.49141.86821.89311.89401.85701.973890.8965.03
Q-7-4-31.49101.85871.8931=1.85451.971391.0765.73
Q-7-4-21.49101.85871.89311.89311.85451.971391.0765.73
Q-7-3-21.49101.85541.8931=1.85371.970191.1866.01
Q-6-5-41.45701.8682==1.82491.937991.8570.63
Q-6-5-31.45701.8682=1.86821.82491.937991.8570.63
Q-6-5-21.45701.8682=1.86821.82491.937991.8570.63
Q-6-4-31.45701.85871.8682=1.82491.937991.8570.63
Q-6-4-21.45701.85871.86821.86821.82491.937991.8570.63
Q-6-3-21.45701.85541.8682=1.82491.937991.8570.63
Q-5-4-31.44481.8587==1.81521.924792.2073.29
Q-5-4-21.44481.8587=1.85871.81521.924792.2073.29
Q-5-3-21.44481.85541.8587=1.81521.924792.2073.29
Q-4-3-21.44281.8554==1.81281.920492.2874.27

Inquiring minds want to know: Why is a lead from Q-4-3-2 safer than Q-5-3-2? One might think it could hardly matter but consider dummy: K-9-8-4, partner: A-10-7, and declarer: J-6. Left to his own devices, declarer can win only one trick (try it) but a lead from Q-5-3-2 allows him to win two. In contrast, if you have Q-4-3-2 and dummy K-9-8-5, declarer can always win two tricks (start by leading the nine). Hence leading from Q-5-3-2 costs a trick, while Q-4-3-2 costs nothing. (There are other cases, too.)

 Study 8C05   Main Top   Leading Authority

## Jack Holdings

J-10HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
J-10-9-82.1635===2.05952.1635100.0096.22
J-10-9-72.1404==1.96232.05742.161498.7591.75
J-10-9-62.1244==1.96232.05612.159197.8987.97
J-10-9-52.1092==1.96232.05492.157296.8686.43
J-10-9-42.1019==1.96232.05392.155396.4785.87
J-10-9-32.0991==1.96232.05302.153496.3985.73
J-10-9-22.0976==1.96232.05262.152596.3385.59
J-10-8-72.0528=1.9563=2.01862.129493.7377.76
J-10-8-62.0358=1.93811.94762.01732.126992.8677.48
J-10-8-52.0195=1.92121.94762.01612.124991.8069.79
J-10-8-42.0111=1.91111.94762.01502.122991.3667.41
J-10-8-32.0084=1.90621.94762.01422.121191.2966.71
J-10-8-22.0071=1.90471.94762.01382.120291.2566.15
J-10-7-61.9212=1.9303=1.98192.092687.3347.97
J-10-7-51.9130=1.91291.92541.98072.091087.0646.85
J-10-7-41.9056=1.90381.92541.97962.089487.1847.69
J-10-7-31.9034=1.90061.92541.97882.088087.2947.83
J-10-7-21.9025=1.89951.92541.97842.087487.3448.11
J-10-6-51.8475=1.9104=1.95152.068287.5649.93
J-10-6-41.8467=1.90241.91041.95092.067287.6250.21
J-10-6-31.8461=1.89991.91041.95032.066187.7150.49
J-10-6-21.8457=1.89951.91041.95002.065587.7550.77
J-10-5-41.8203=1.9024=1.93442.055687.8151.05
J-10-5-31.8203=1.89991.90241.93432.055287.8451.19
J-10-5-21.8203=1.89951.90241.93422.054987.8751.33
J-10-4-31.8108=1.8999=1.92962.050988.0452.31
J-10-4-21.8108=1.89951.89991.92962.050988.0452.31
J-10-3-21.8083=1.8995=1.92922.049388.1853.29

J-9HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
J-9-8-71.73001.9259==1.91892.043790.5264.06
J-9-8-61.72551.9093=1.89021.91752.041889.2458.04
J-9-8-51.72191.8929=1.89021.91642.040287.8751.33
J-9-8-41.71871.8828=1.89021.91532.038586.9146.01
J-9-8-31.71771.8787=1.89021.91442.037087.0446.57
J-9-8-21.71721.8776=1.89021.91412.036387.1147.41
J-9-7-61.69511.80701.8740=1.88382.008288.0452.31
J-9-7-51.69171.79911.85681.87011.88262.006687.9651.75
J-9-7-41.68871.79131.84741.87011.88162.005188.0852.73
J-9-7-31.68771.78851.84441.87011.88072.003688.2053.43
J-9-7-21.68731.78771.84351.87011.88032.003088.2453.57
J-9-6-51.65221.73811.8542=1.85381.978589.0256.36
J-9-6-41.65191.73611.84571.85421.85311.977689.0856.78
J-9-6-31.65131.73431.84351.85421.85251.976589.1857.62
J-9-6-21.65091.73331.84351.85421.85221.975989.2357.90
J-9-5-41.63571.71071.8457=1.83541.962089.7460.42
J-9-5-31.63551.71011.84351.84571.83521.961689.7760.70
J-9-5-21.63521.70941.84351.84571.83511.961389.8161.12
J-9-4-31.62821.69941.8435=1.82981.956090.1662.52
J-9-4-21.62821.69941.84351.84351.82981.956090.1662.52
J-9-3-21.62611.69661.8435=1.82871.954290.3763.92

J-xHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
J-8-7-61.49841.7875==1.75011.882490.0461.82
J-8-7-51.49821.7774=1.77561.74961.881789.4959.16
J-8-7-41.49811.7689=1.77561.74931.881389.0156.22
J-8-7-31.49791.7665=1.77561.74901.880889.0556.50
J-8-7-21.49781.7660=1.77561.74881.880589.0856.78
J-8-6-51.49211.71521.7662=1.73431.868489.5959.72
J-8-6-41.49191.71291.75781.76591.73401.867989.5859.58
J-8-6-31.49181.71151.75571.76591.73371.867589.6260.00
J-8-6-21.49161.71101.75561.76591.73351.867289.6460.14
J-8-5-41.48451.68721.7577=1.71961.855290.2563.22
J-8-5-31.48441.68691.75561.75771.71951.855190.2663.36
J-8-5-21.48441.68671.75561.75771.71941.854990.2863.64
J-8-4-31.48071.67711.7556=1.71431.850790.5864.20
J-8-4-21.48071.67711.75561.75561.71431.850790.5864.20
J-8-3-21.47961.67401.7556=1.71261.849390.7564.90
J-7-6-51.40181.7087==1.65671.788891.6969.37
J-7-6-41.40181.7068=1.70811.65671.788891.6168.81
J-7-6-31.40181.7059=1.70811.65671.788891.6168.81
J-7-6-21.40181.7058=1.70811.65671.788891.6168.81
J-7-5-41.40101.68411.7064=1.65351.787891.6068.39
J-7-5-31.40101.68411.70551.70641.65351.787891.6068.39
J-7-5-21.40101.68411.70551.70641.65351.787891.6068.39
J-7-4-31.40001.67541.7055=1.65141.786491.7269.51
J-7-4-21.40001.67541.70551.70551.65141.786491.7269.51
J-7-3-21.39971.67251.7055=1.65061.785891.8069.79
J-6-5-41.36121.6840==1.62491.757492.3775.24
J-6-5-31.36121.6840=1.68401.62491.757492.3775.24
J-6-5-21.36121.6840=1.68401.62491.757492.3775.24
J-6-4-31.36121.67531.6840=1.62491.757492.3775.24
J-6-4-21.36121.67531.68401.68401.62491.757492.3775.24
J-6-3-21.36121.67251.6840=1.62491.757492.3775.24
J-5-4-31.34631.6753==1.61531.745492.6376.92
J-5-4-21.34631.6753=1.67531.61531.745492.6376.92
J-5-3-21.34631.67251.6753=1.61531.745492.6376.92
J-4-3-21.34301.6725==1.61261.740892.7877.34

“Never lead from a jack” is a well-known bridge maxim, yet totally debunked by the above table. In fact, leading from a jack is safer than from any higher honor in general.

 Study 8C05   Main Top   Leading Authority

## Weak Holdings

10-9HighestSecondThirdFourthPartnerDeclarerSafetyPercentile
10-9-8-71.7004===1.57831.7004100.0096.22
10-9-8-61.6958==1.65331.57831.700199.7594.97
10-9-8-51.6922==1.65331.57831.699999.5192.87
10-9-8-41.6891==1.65331.57831.699799.2992.73
10-9-8-31.6881==1.65331.57831.699699.2092.17
10-9-8-21.6876==1.65331.57831.699499.1691.89
10-9-7-61.6613=1.6490=1.56761.691697.6287.69
10-9-7-51.6579=1.64241.64511.56761.691497.4287.55
10-9-7-41.6549=1.63751.64511.56761.691297.2387.13
10-9-7-31.6540=1.63561.64511.56761.691197.1586.99
10-9-7-21.6535=1.63481.64511.56761.690997.1286.85
10-9-6-51.6142=1.6398=1.56141.685994.6081.54
10-9-6-41.6139=1.63581.63981.56141.685794.6181.68
10-9-6-31.6133=1.63481.63981.56141.685694.6381.82
10-9-6-21.6129=1.63481.63981.56141.685494.6582.10
10-9-5-41.5970=1.6358=1.55651.680794.9182.94
10-9-5-31.5967=1.63481.63581.55651.680794.9283.08
10-9-5-21.5965=1.63481.63581.55651.680694.9383.50
10-9-4-31.5894=1.6348=1.55471.679195.0384.06
10-9-4-21.5894=1.63481.63481.55471.679195.0384.06
10-9-3-21.5872=1.6348=1.55391.678695.0984.34

10-xHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
10-8-7-61.46041.6238==1.51661.657395.5184.76
10-8-7-51.46011.6182=1.60601.51661.657195.2084.48
10-8-7-41.46001.6140=1.60601.51661.656994.9783.78
10-8-7-31.45991.6129=1.60601.51661.656894.9283.08
10-8-7-21.45971.6127=1.60601.51661.656694.9283.08
10-8-6-51.45271.56651.6006=1.51041.650994.0577.90
10-8-6-41.45251.56551.59661.60061.51041.650894.0678.04
10-8-6-31.45241.56491.59561.60061.51041.650694.0878.18
10-8-6-21.45221.56471.59561.60061.51041.650594.1078.32
10-8-5-41.44431.54381.5966=1.50561.645494.4380.00
10-8-5-31.44421.54371.59561.59661.50561.645394.4380.00
10-8-5-21.44421.54361.59561.59661.50561.645394.4480.28
10-8-4-31.44031.53511.5956=1.50371.643694.5781.26
10-8-4-21.44031.53511.59561.59561.50371.643694.5781.26
10-8-3-21.43881.53201.5956=1.50291.642994.6582.10
10-7-6-51.35981.5563==1.45481.605594.3279.44
10-7-6-41.35981.5555=1.55521.45481.605594.2779.16
10-7-6-31.35981.5550=1.55521.45481.605594.1878.46
10-7-6-21.35981.5550=1.55521.45481.605594.1878.46
10-7-5-41.35921.53811.5543=1.45351.604694.2678.74
10-7-5-31.35921.53811.55391.55431.45351.604694.2678.74
10-7-5-21.35921.53811.55391.55431.45351.604694.2678.74
10-7-4-31.35831.53131.5539=1.45281.603794.3379.58
10-7-4-21.35831.53131.55391.55391.45281.603794.3379.58
10-7-3-21.35781.52881.5539=1.45251.603094.4179.86
10-6-5-41.31911.5376==1.43281.586094.5180.42
10-6-5-31.31911.5376=1.53761.43281.586094.5180.42
10-6-5-21.31911.5376=1.53761.43281.586094.5180.42
10-6-4-31.31911.53101.5376=1.43281.585894.5380.84
10-6-4-21.31911.53101.53761.53761.43281.585894.5380.84
10-6-3-21.31911.52881.5376=1.43281.585694.5481.12
10-5-4-31.30361.5310==1.42611.576894.7782.52
10-5-4-21.30361.5310=1.53101.42611.576894.7782.52
10-5-3-21.30361.52881.5310=1.42611.576894.7782.52
10-4-3-21.29981.5288==1.42441.573194.9683.64

9-xHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
9-8-7-61.4481===1.31351.4481100.0096.22
9-8-7-51.4479==1.43031.31351.448199.9996.08
9-8-7-41.4477==1.43031.31351.448199.9895.94
9-8-7-31.4476==1.43031.31351.448199.9795.80
9-8-7-21.4474==1.43031.31351.448199.9695.66
9-8-6-51.4399=1.4303=1.31351.447499.2292.59
9-8-6-41.4397=1.43031.43031.31351.447499.2192.45
9-8-6-31.4396=1.43031.43031.31351.447499.2092.17
9-8-6-21.4395=1.43031.43031.31351.447499.1992.03
9-8-5-41.4307=1.4303=1.31351.447098.0688.81
9-8-5-31.4306=1.43031.43031.31351.447098.0588.53
9-8-5-21.4306=1.43031.43031.31351.447098.0588.53
9-8-4-31.4264=1.4303=1.31351.446797.9788.11
9-8-4-21.4264=1.43031.43031.31351.446797.9788.11
9-8-3-21.4244=1.4303=1.31351.446498.0188.39
9-7-6-51.34711.4262==1.30491.439998.3489.79
9-7-6-41.34711.4262=1.42391.30491.439998.3489.79
9-7-6-31.34711.4262=1.42391.30491.439998.3489.79
9-7-6-21.34711.4262=1.42391.30491.439998.3489.79
9-7-5-41.34641.41831.4239=1.30491.439598.0988.95
9-7-5-31.34641.41831.42391.42391.30491.439598.0988.95
9-7-5-21.34641.41831.42391.42391.30491.439598.0988.95
9-7-4-31.34521.41401.4239=1.30491.439298.1389.37
9-7-4-21.34521.41401.42391.42391.30491.439298.1389.37
9-7-3-21.34441.41191.4239=1.30491.438998.1789.65
9-6-5-41.30661.4171==1.29811.430498.4290.35
9-6-5-31.30661.4171=1.41711.29811.430498.4290.35
9-6-5-21.30661.4171=1.41711.29811.430498.4290.35
9-6-4-31.30661.41351.4171=1.29811.430398.4290.35
9-6-4-21.30661.41351.41711.41711.29811.430398.4290.35
9-6-3-21.30661.41191.4171=1.29811.430398.4391.05
9-5-4-31.29091.4135==1.29471.426298.4391.05
9-5-4-21.29091.4135=1.41351.29471.426298.4391.05
9-5-3-21.29091.41191.4135=1.29471.426298.4391.05
9-4-3-21.28621.4119==1.29341.424498.4791.61

x-xHighestSecondThirdFourthPartnerDeclarerSafetyPercentile
8-7-6-51.3446===1.21971.3446100.0096.22
8-7-6-41.3446==1.34191.21971.3446100.0096.22
8-7-6-31.3446==1.34191.21971.3446100.0096.22
8-7-6-21.3446==1.34191.21971.3446100.0096.22
8-7-5-41.3439=1.3419=1.21971.344699.9095.24
8-7-5-31.3439=1.34191.34191.21971.344699.9095.24
8-7-5-21.3439=1.34191.34191.21971.344699.9095.24
8-7-4-31.3428=1.3419=1.21971.344699.7494.69
8-7-4-21.3428=1.34191.34191.21971.344699.7494.69
8-7-3-21.3420=1.3419=1.21971.344699.6493.29
8-6-5-41.30521.3418==1.21971.343999.6893.43
8-6-5-31.30521.3418=1.34181.21971.343999.6893.43
8-6-5-21.30521.3418=1.34181.21971.343999.6893.43
8-6-4-31.30521.34091.3418=1.21971.343999.6893.43
8-6-4-21.30521.34091.34181.34181.21971.343999.6893.43
8-6-3-21.30521.34041.3418=1.21971.343999.6893.43
8-5-4-31.28991.3409==1.21931.342899.7294.27
8-5-4-21.28991.3409=1.34091.21931.342899.7294.27
8-5-3-21.28991.34041.3409=1.21931.342899.7294.27
8-4-3-21.28531.3404==1.21921.342099.7695.10
7-6-5-41.3049===1.18901.3049100.0096.22
7-6-5-31.3049==1.30491.18901.3049100.0096.22
7-6-5-21.3049==1.30491.18901.3049100.0096.22
7-6-4-31.3049=1.3049=1.18901.3049100.0096.22
7-6-4-21.3049=1.30491.30491.18901.3049100.0096.22
7-6-3-21.3049=1.3049=1.18901.3049100.0096.22
7-5-4-31.28951.3049==1.18901.3049100.0096.22
7-5-4-21.28951.3049=1.30491.18901.3049100.0096.22
7-5-3-21.28951.30491.3049=1.18901.3049100.0096.22
7-4-3-21.28491.3049==1.18901.3049100.0096.22
6-5-4-31.2895===1.17781.2895100.0096.22
6-5-4-21.2895==1.28951.17781.2895100.0096.22
6-5-3-21.2895=1.2895=1.17781.2895100.0096.22
6-4-3-21.28491.2895==1.17781.2895100.0096.22
5-4-3-21.2849===1.17571.2849100.0096.22