Main     Simulation 8Z04 by Richard Pavlicek    

Which Four-Card Major Lead?

Suppose your opponents reach 3 NT without showing any suits, and you are on lead with ace-fourth in one major and queen-fourth in the other. Which lead is better? This is extremely difficult if not impossible to answer because there are many factors involved: tempo, safety, entries, play analysis, etc. The only realistic way to find an answer is empirically from a representative case, as the West hand below.

None Vul
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
Table


West

Pass

North

3 NT

East

All Pass

South
1 NT

3 NT South

Should West lead the S 3 or the H 3?

Step right up, folks! Place your bets, as I am about to spin the wheel. My routine choice would be the H 3 at any form of scoring, but I've always had doubts, especially with recent lead tests showing ace-fourth to be slightly safer. To discover the true answer I created 10,000 random layouts with the West hand fixed, and the North-South hands constrained* to fit the bidding.

*South HCP 15-17; freakness less than 3 (balanced); North HCP 9-11 (more is possible of course but I wanted to have reasonable hopes to set this); freakness less than 5; no four-card major unless 4-3-3-3 shape.

The following table summarizes the results, which were close and dependent on the form of scoring. (Numbers are relative to declarer, so lower values are better for the defense.) At total points or IMPs, the H 3 does better; but at matchpoints the S 3 does better. Evidently the safety advantage of the S 3 prevents enough overtricks to build a matchpoint edge despite not defeating the contract as often. Maybe that's why I've never liked matchpoints.

Results for 10,000 Deals
Opening LeadTrick AvgMake PctTPs WonMPs WonIMPs Won
S 3 from A-5-4-39.70786.3433877097378013
H 3 from Q-5-4-39.72185.92324630102637800

Below are 100 of the 10,000 deals, including the first 10 and last 10, and in-between only deals with big swings (one lead sets, other makes). Analysis is based on double-dummy play. Running totals are shown after each deal.

Seed A1B2C3D4 10000 8
W:A543.Q543.J3.K52
#SP15-17F[3NP9-11F[5=0~s[4F=0~h[4
Leads S3 H3 -- Result Avg Mk% TPs MPs IMPs

1.
S J 9 8 6
H J 7 6
D A K 8
C 10 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 2
H 9 8 2
D 9 7 5 2
C A 9 8 7
S K Q 7
H A K 10
D Q 10 6 4
C Q J 4

S3 = A 10.000 100 0 1 0
H3 = A 10.000 100 0 1 0


2.
S 9 8
H A 7
D A Q 7 6
C 10 8 7 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K J 10 2
H J 10 9 6 2
D 8 4
C 9 6
S Q 7 6
H K 8
D K 10 9 5 2
C A Q J

S3 = 8 9.000 50.00 0 2 0
H3 = 8 9.000 50.00 0 2 0


3.
S Q J
H K 9 8
D K 9 6 5 2
C 9 8 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 10 9 8 7
H 10 7 2
D 10 8 4
C Q 10
S 6 2
H A J 6
D A Q 7
C A J 7 6 4

S3 = 8 8.667 33.33 0 2 0
H3 = 9 9.000 66.67 450 4 10


4.
S 9 8 6
H 10 8
D A 7 6 5
C A Q 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 7 2
H 9 7 2
D Q 4 2
C 10 7 6
S K Q
H A K J 6
D K 10 9 8
C J 9 8

S3 = 9 8.750 50.00 0 2 0
H3 = A 9.250 75.00 480 6 11


5.
S 10 8 7
H J 9 8
D K 8 5 2
C A J 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 2
H K 10 7 2
D 9 7 6
C Q 10 8 6
S K Q 9 6
H A 6
D A Q 10 4
C 9 4 3

S3 = 9 8.800 60.00 0 3 0
H3 = 9 9.200 80.00 480 7 11


6.
S Q 10 7 6
H A 10 7
D K 9 8
C 9 8 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 9
H J 6 2
D 10 6 2
C Q 10 7 4 3
S J 8 2
H K 9 8
D A Q 7 5 4
C A J

S3 = 8 8.667 50.00 0 3 0
H3 = 9 9.167 83.33 930 9 21


7.
S 7 6
H 10 8 7
D A K Q 4
C Q 10 9 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 9
H J 9 6 2
D 8 6 5
C J 4 3
S K Q 8 2
H A K
D 10 9 7 2
C A 8 6

S3 = A 8.857 57.14 30 5 1
H3 = 9 9.143 85.71 930 9 21


8.
S K 9 6
H K 10 9 6
D Q 4 2
C Q 10 8
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 8 7 2
H 8
D A 10 9 7 5
C 7 4 3
S Q J
H A J 7 2
D K 8 6
C A J 9 6

S3 = 9 8.875 62.50 30 5 1
H3 = A 9.250 87.50 960 11 22


9.
S 7 6
H K 7 6
D K Q 6 2
C J 8 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 8 2
H A J 9 8
D 10 8 7 5
C 7
S K Q 9
H 10 2
D A 9 4
C A Q 10 9 4

S3 = 7 8.667 55.56 30 6 1
H3 = 7 9.000 77.78 960 12 22


10.
S 9 8 2
H A 8 2
D K 9 4
C Q 8 7 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 7
H 6
D 10 8 7 5 2
C A J 6 4
S K Q 6
H K J 10 9 7
D A Q 6
C 10 9

S3 = 9 8.700 60.00 30 7 1
H3 = 9 9.000 80.00 960 13 22


TopMain

11.
S K 7
H 8 7 6
D K 9 7 4
C A 8 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 6 2
H J 2
D 10 8 6 5
C Q 10 9
S Q 9 8
H A K 10 9
D A Q 2
C J 7 6

S3 = 8 8.636 54.55 30 7 1
H3 = 9 9.000 81.82 1410 15 32


16.
S Q 9
H J 7 2
D K Q 10 7 6 2
C Q J
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 8 6 2
H A 10 8
D 8
C 9 8 7 6 4 3
S K J 10 7
H K 9 6
D A 9 5 4
C A 10

S3 = B 8.938 62.50 540 12 12
H3 = 8 9.063 75.00 1440 20 33


25.
S 10 8 2
H J 2
D Q 6 4 2
C A Q 7 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 9 7 6
H 10 8 7
D K 10 5
C 10 8 6
S K J
H A K 9 6
D A 9 8 7
C J 9 3

S3 = 8 9.240 72.00 570 21 13
H3 = 9 9.320 84.00 1890 29 43


28.
S 7 6
H A 7 6
D K Q 8 6 2
C 10 6 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 10 9 8 2
H K 10
D 9 7
C J 9 8 7
S K J
H J 9 8 2
D A 10 5 4
C A Q 3

S3 = 8 9.179 67.86 570 23 13
H3 = 9 9.286 82.14 2340 33 53


32.
S Q J 8 2
H J 9 2
D A 7 6
C Q 7 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K
H 10 7 6
D Q 9 8 4 2
C 9 8 6 3
S 10 9 7 6
H A K 8
D K 10 5
C A J 10

S3 = 8 9.219 68.75 570 26 13
H3 = 9 9.344 84.38 2790 38 63


38.
S 9 8
H A 7 2
D Q 7 2
C A 9 8 7 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 7
H J 10 6
D K 9 8 5
C 10 4 3
S K Q 6 2
H K 9 8
D A 10 6 4
C Q J

S3 = 9 9.263 73.68 1050 33 24
H3 = 8 9.342 84.21 2820 43 64


42.
S Q 9 7
H A 9 7
D Q 8 5 4
C J 9 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 2
H J 10 8
D K 10 6 2
C 8 7 4
S K 8 6
H K 6 2
D A 9 7
C A Q 10 6

S3 = 9 9.262 76.19 1500 36 34
H3 = 8 9.405 83.33 2940 48 68


43.
S J 6 2
H K 7
D Q 7 5 4
C Q J 7 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 7
H J 10 9
D A 10 8 6 2
C 8 6 4
S K Q 10 8
H A 8 6 2
D K 9
C A 10 9

S3 = 9 9.256 76.74 1950 38 44
H3 = 8 9.372 81.40 2940 48 68


50.
S Q 9 6
H 9 8
D A Q 10 5 2
C J 10 9
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 2
H A J 7 2
D 9 6 4
C 7 4 3
S K 8 7
H K 10 6
D K 8 7
C A Q 8 6

S3 = A 9.380 80.00 2460 47 55
H3 = 8 9.420 82.00 2940 53 68


58.
S K 7
H J 6
D A 9 8 5 4
C J 9 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 9 8 2
H 9 8
D Q 10 2
C Q 7 6
S Q 6
H A K 10 7 2
D K 7 6
C A 10 8

S3 = 8 9.276 75.86 2490 51 56
H3 = 9 9.379 79.31 3550 65 84


TopMain

82.
S K 10 8
H 9 2
D K Q 6 4
C J 8 7 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 9
H K J 10 8 6
D 9 8 5 2
C 9 6
S Q 7 6 2
H A 7
D A 10 7
C A Q 10 4

S3 = 9 9.439 81.71 2970 71 67
H3 = 8 9.573 82.93 3760 93 91


96.
S J 10 7
H 10 8 7 6
D A K 9
C J 7 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K Q 8 6
H 9 2
D 8 7 4
C 10 9 8 4
S 9 2
H A K J
D Q 10 6 5 2
C A Q 3

S3 = 8 9.490 83.33 3060 84 70
H3 = 9 9.604 85.42 4270 108 103


97.
S K Q 9
H 10 7 2
D K 7 5 2
C Q 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 8 6 2
H A J 9 8
D 9 8 6 4
C 8 6
S J 10 7
H K 6
D A Q 10
C A J 10 9 7

S3 = A 9.495 83.51 3540 86 80
H3 = 8 9.588 84.54 4270 108 103


104.
S Q 8 2
H 9
D A K 6 4
C J 9 8 6 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 6
H J 10 8 7 6
D Q 7 5
C Q 10 7
S K J 10 7
H A K 2
D 10 9 8 2
C A 3

S3 = 9 9.577 84.62 4110 96 94
H3 = 8 9.615 84.62 4270 112 103


106.
S 10 6
H 8 7
D A K Q 8 4
C 10 7 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q J 8 7 2
H K 9 6
D 9 7 5
C 9 6
S K 9
H A J 10 2
D 10 6 2
C A Q J 8

S3 = 8 9.557 83.96 4110 96 94
H3 = A 9.623 84.91 4780 116 114


112.
S J 9 2
H 10 8
D K Q 8 4 2
C A 9 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 8 6
H K J 7 6 2
D 10 5
C J 8 3
S K Q 7
H A 9
D A 9 7 6
C Q 10 7 4

S3 = A 9.563 84.82 4590 101 104
H3 = 8 9.625 84.82 4840 123 116


118.
S J 9 8
H A 9
D 8 6 5 2
C A 9 8 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 10 2
H 10 8 7 6
D Q 10 9 4
C J 10
S K 7 6
H K J 2
D A K 7
C Q 6 4 3

S3 = 8 9.593 84.75 4650 106 106
H3 = 9 9.653 85.59 5320 130 127


121.
S Q J 7
H A 8
D 10 8 7 5 4
C Q J 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 6 2
H K 10 9 6 2
D Q 2
C 10 8 7
S K 10 8
H J 7
D A K 9 6
C A 9 6 4

S3 = A 9.579 84.30 5130 109 116
H3 = 8 9.628 84.30 5350 133 128


135.
S K J 10
H J 8 7
D 9 7 5
C A 10 9 8
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 7 2
H K 10 6
D 10 8 4
C J 7 6 4
S 9 8 6
H A 9 2
D A K Q 6 2
C Q 3

S3 = 9 9.556 84.44 5610 121 127
H3 = 8 9.622 83.70 5500 149 133


137.
S Q 9 6
H K J
D 10 6 4 2
C A 6 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 8
H A 9 8 7 6
D 9 8 7
C 10 9 8
S K 10 7 2
H 10 2
D A K Q 5
C Q J 7

S3 = A 9.569 84.67 6150 125 139
H3 = 8 9.606 83.21 5500 149 133


TopMain

147.
S 10 9 8
H J 6 2
D K Q 6 4 2
C Q J
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 7 2
H A 9 7
D 10 9 8 5
C 10 9 7 4
S K Q J 6
H K 10 8
D A 7
C A 8 6 3

S3 = 9 9.558 85.03 6630 134 150
H3 = 8 9.599 82.99 5590 160 136


156.
S 8 7 2
H K 9 2
D A 10
C Q J 10 9 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 9
H J 10 7
D K 6 5 4 2
C 8 3
S K Q 6
H A 8 6
D Q 9 8 7
C A 6 4

S3 = 9 9.603 85.90 7110 144 161
H3 = 8 9.635 83.33 5620 168 137


160.
S K 9
H A 9 8
D 10 7 2
C Q 10 8 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 7 6 2
H J 10 7
D A 9 6 5 4
C 9 4
S Q J 10 8
H K 6 2
D K Q 8
C A J 7

S3 = 9 9.619 86.25 7590 150 172
H3 = 8 9.638 83.13 5620 170 137


170.
S K 9 8
H 10 8
D Q 9 5 4
C A J 7 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 7 6
H 9 7
D K 10 7 6 2
C 10 8 4
S J 10 2
H A K J 6 2
D A 8
C Q 9 3

S3 = 8 9.618 85.88 7680 158 175
H3 = 9 9.647 83.53 6190 182 151


174.
S Q J
H K 10 2
D A 9 5
C 10 9 8 7 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 9
H J 9 6
D 10 8 7 6 4 2
C A 6
S K 8 7 6 2
H A 8 7
D K Q
C Q J 3

S3 = 9 9.609 85.63 8130 163 185
H3 = 8 9.632 82.76 6190 185 151


180.
S K 8 6
H 10 7 6
D Q 9 5
C A 10 6 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 7 2
H J 2
D A 8 6 4 2
C J 9 3
S Q J 9
H A K 9 8
D K 10 7
C Q 8 7

S3 = 8 9.622 85.56 8220 168 188
H3 = 9 9.639 83.33 6670 192 162


201.
S K 10 7
H 10 8 7
D A Q 5 4
C 8 7 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 9 8 6
H A 6 2
D 10 9 7 2
C J 4
S Q 2
H K J 9
D K 8 6
C A Q 10 9 3

S3 = 9 9.642 86.57 8790 191 202
H3 = 8 9.647 84.08 6780 211 166


219.
S Q 10 2
H J 7
D K 7 6 4 2
C A 8 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 9 6
H 10 8 6 2
D Q 10 9
C 10 9 3
S J 8 7
H A K 9
D A 8 5
C Q J 7 6

S3 = 8 9.635 86.76 8970 208 208
H3 = 9 9.635 84.93 7350 230 180


222.
S 2
H K 10 7
D 10 9 7 6 2
C A Q 10 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K J 10 8 7
H 6 2
D Q 4
C 9 8 7 3
S Q 9 6
H A J 9 8
D A K 8 5
C J 4

S3 = 8 9.626 86.49 8970 210 208
H3 = C 9.644 85.14 7890 234 191


245.
S K 6
H J 7 2
D K Q 9 7 5
C 10 9 8
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 2
H A 10 9 6
D 10 8 6
C J 7 4
S Q 9 8 7
H K 8
D A 4 2
C A Q 6 3

S3 = 9 9.633 85.71 9550 235 223
H3 = 8 9.641 84.08 7950 255 193


TopMain

260.
S 6 2
H K J 9
D K Q 9 8 6
C 6 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K Q J 10 8
H 8 7 2
D 10 7 4
C 10 9
S 9 7
H A 10 6
D A 5 2
C A Q J 8 7

S3 = 8 9.612 84.62 9640 247 226
H3 = 9 9.631 83.46 8570 273 209


282.
S J 8 2
H A 10 9
D Q 8 6
C Q J 10 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 9 7 6
H J 8 2
D A 10 5 2
C 9 6
S K Q
H K 7 6
D K 9 7 4
C A 8 7 3

S3 = 8 9.603 84.04 9820 269 232
H3 = 9 9.617 83.33 9140 295 223


286.
S K J 6
H A 2
D 9 5 4
C J 10 8 6 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 8 7 2
H 9 7 6
D A 7 6 2
C 9 7
S 10 9
H K J 10 8
D K Q 10 8
C A Q 3

S3 = 8 9.591 83.57 9900 274 235
H3 = 9 9.601 83.22 9590 298 233


290.
S J 8 2
H 10 9
D K 8 7 6
C A J 9 8
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 6
H K J 7
D 10 5 4 2
C Q 10 6 3
S K Q 9 7
H A 8 6 2
D A Q 9
C 7 4

S3 = 9 9.597 83.79 10380 278 246
H3 = 8 9.607 83.10 9650 302 235


296.
S Q J 2
H 9 8 7
D K Q 2
C Q J 10 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 7 6
H 10
D A 10 8 6 4
C 9 7 6 3
S K 10 8
H A K J 6 2
D 9 7 5
C A 8

S3 = 8 9.584 83.45 10410 282 247
H3 = 9 9.601 83.11 10180 310 248


301.
S K J 6
H 9 8 6
D K 10 8 7 2
C Q 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 9
H 10 7
D Q 6 5 4
C A 10 9 8 6
S Q 8 7 2
H A K J 2
D A 9
C J 7 4

S3 = 8 9.591 83.39 10470 288 249
H3 = 9 9.605 83.39 10630 314 258


307.
S 10 6 2
H K J 10 8
D A 8 2
C J 8 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K J 9
H 9 6 2
D Q 10 9 7
C 10 9 4
S Q 8 7
H A 7
D K 6 5 4
C A Q 6 3

S3 = 9 9.593 83.71 10950 294 260
H3 = 8 9.606 83.39 10690 320 260


316.
S Q 7
H 7 6
D A Q 10 9 8 6
C J 7 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K J 9 8 2
H 9 8 2
D 7 5
C Q 6 4
S 10 6
H A K J 10
D K 4 2
C A 10 9 8

S3 = 8 9.611 83.86 10980 302 261
H3 = A 9.630 83.86 11200 330 271


317.
S J 6 2
H A 9 8 2
D 8 5 2
C A J 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 10 9
H J 10 6
D 10 9 7 4
C 10 9 4
S Q 8 7
H K 7
D A K Q 6
C Q 8 6 3

S3 = 9 9.609 83.91 11430 304 271
H3 = 8 9.625 83.60 11200 330 271


318.
S Q 2
H K 7 2
D Q 10 9 7 2
C Q J 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 9 8 7 6
H 10 6
D A 6 5
C 10 8 4
S K J
H A J 9 8
D K 8 4
C A 9 7 3

S3 = 8 9.604 83.65 11430 304 271
H3 = A 9.626 83.65 11680 332 281


TopMain

319.
S K 10 7
H A 9
D 8 2
C Q 10 9 8 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 8 6
H K 10 6 2
D Q 10 9 6 5 4
C 6
S Q J 9 2
H J 8 7
D A K 7
C A J 7

S3 = 9 9.602 83.70 11880 306 281
H3 = 8 9.621 83.39 11680 332 281


320.
S Q 9 2
H J 6
D Q 8 5 4
C A 6 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K J 7
H 10 7 2
D 9 7 6 2
C 10 9 7
S 10 8 6
H A K 9 8
D A K 10
C Q J 8

S3 = 8 9.597 83.44 11880 306 281
H3 = 9 9.619 83.44 12130 334 291


325.
S J 7 6 2
H J 6 2
D A Q 4
C Q 8 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q
H K 10 7
D 10 9 7 6 5 2
C 10 6 3
S K 10 9 8
H A 9 8
D K 8
C A J 9 4

S3 = 9 9.600 83.38 12420 313 294
H3 = 8 9.609 83.08 12130 337 291


333.
S Q J 7
H 2
D A 8 5 4 2
C Q J 9 8
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 9 6
H K J 8 7 6
D 9 7
C 10 7 6
S K 8 2
H A 10 9
D K Q 10 6
C A 4 3

S3 = A 9.595 82.88 13010 324 308
H3 = 8 9.592 82.28 12180 342 293


339.
S J 9 2
H K
D A Q 9 5 2
C 10 9 8 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 10
H J 9 7 6 2
D 7 4
C J 7 6 4
S Q 8 7 6
H A 10 8
D K 10 8 6
C A Q

S3 = 9 9.608 83.19 13460 331 318
H3 = 8 9.602 82.30 12180 347 293


354.
S Q 2
H 8 2
D K Q 10 8 2
C Q 10 9 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 9 7
H J 9
D 9 7 6 5
C A 8 6
S K 8 6
H A K 10 7 6
D A 4
C J 7 3

S3 = 8 9.607 83.33 13550 346 321
H3 = 9 9.602 82.77 12690 362 305


362.
S K 2
H K 10
D A 7 6 5 4
C 10 9 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 10 9 8 6
H J 9 8 7
D Q 9 2
C 7
S J 7
H A 6 2
D K 10 8
C A Q J 8 4

S3 = 8 9.605 83.15 13580 352 322
H3 = 9 9.605 82.87 13200 372 317


364.
S K 6
H 9 2
D A Q 9 5
C 10 9 8 7 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q J 10 9 2
H J 10 6
D 8 4 2
C J 4
S 8 7
H A K 8 7
D K 10 7 6
C A Q 3

S3 = 8 9.602 82.97 13580 353 322
H3 = A 9.607 82.97 13680 375 327


374.
S J 7 6
H A 6
D K 10 8 2
C J 8 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 9 8
H 10 7
D Q 9 7 6 5
C Q 10 7
S K 10 2
H K J 9 8 2
D A 4
C A 9 6

S3 = 9 9.610 83.16 14120 363 335
H3 = 8 9.612 82.89 13790 385 331


377.
S K 8 6
H J 9 2
D A 10 9 4
C J 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 9 7
H K 10 7 6
D 7 6 5
C 10 9 7
S Q 10 2
H A 8
D K Q 8 2
C A Q 8 6

S3 = 9 9.610 83.29 14600 368 346
H3 = 8 9.607 82.76 13790 386 331


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379.
S J 9
H 9 6
D A K 8
C Q 10 9 7 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 8 7 2
H K J 10 7
D 10 7 6 4 2
C 6
S K Q 10 6
H A 8 2
D Q 9 5
C A J 8

S3 = A 9.612 83.38 15110 372 357
H3 = 8 9.602 82.59 13790 386 331


381.
S Q J 10
H A 2
D K 6 4
C J 10 7 6 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 8 7
H K J 10 9 7
D 10 9 8 2
C 9
S K 6 2
H 8 6
D A Q 7 5
C A Q 8 3

S3 = 9 9.614 83.46 15610 375 368
H3 = 7 9.598 82.41 13790 387 331


391.
S K 9
H J 8 6
D K 9 5
C A 10 9 8 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 10 7 6 2
H 10 7
D 10 8 7 6 2
C Q
S J 8
H A K 9 2
D A Q 4
C J 7 6 3

S3 = 8 9.621 83.63 15700 384 371
H3 = B 9.609 82.86 14330 398 343


394.
S K J 10 7
H K 10 2
D 10 8 5
C Q 8 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 8 2
H J 9 8 6
D A 9 7 6 2
C J 4
S Q 9 6
H A 7
D K Q 4
C A 10 9 7 3

S3 = 9 9.619 83.76 16150 387 381
H3 = 8 9.607 82.74 14360 401 344


405.
S 10 7 6
H 6 2
D A K Q 7 5
C 9 8 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 9 2
H K J 8 7
D 8 6 4 2
C 10 4
S K Q 8
H A 10 9
D 10 9
C A Q J 7 3

S3 = 9 9.612 83.70 16660 401 393
H3 = 8 9.593 82.47 14360 409 344


412.
S 10 2
H J 10
D Q 10 7 4 2
C A Q 8 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q J 9 8 6
H 9 2
D K 8 5
C 10 6 4
S K 7
H A K 8 7 6
D A 9 6
C J 9 3

S3 = 8 9.612 83.74 16690 407 394
H3 = A 9.597 82.77 14870 417 355


414.
S K 10 2
H 10 8
D 10 9 8 5
C A Q 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 9 7
H J 7 2
D Q 6 4 2
C J 10 7
S J 8 6
H A K 9 6
D A K 7
C 9 8 4

S3 = 8 9.606 83.57 16690 408 394
H3 = 9 9.594 82.85 15320 420 365


417.
S 10 2
H J 6
D A Q 9 5 2
C Q 8 6 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 8 7 6
H 10 9 2
D K 10 7 6
C J 10
S K J 9
H A K 8 7
D 8 4
C A 9 7 3

S3 = 8 9.595 83.21 16740 410 396
H3 = 9 9.585 82.73 15800 424 376


418.
S K 10 8 7
H J 10 7
D A 8 2
C J 10 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS
H A 9 6
D 9 7 6 5 4
C Q 9 8 6 4
S Q J 9 6 2
H K 8 2
D K Q 10
C A 7

S3 = 9 9.593 83.25 17240 412 407
H3 = 7 9.579 82.54 15800 424 376


424.
S Q 10 9
H K 9
D 10 9 8 6 5
C A 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 7 6
H J 10 8 7 6
D Q 4 2
C J 4
S K 8 2
H A 2
D A K 7
C Q 10 9 8 7

S3 = A 9.594 83.49 17720 418 417
H3 = 8 9.580 82.55 15860 430 378


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425.
S 8 6
H A 8 7
D K Q 8
C J 10 9 8 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 10 9 7 2
H J 10 2
D 10 7 6 2
C 4
S K J
H K 9 6
D A 9 5 4
C A Q 6 3

S3 = 8 9.591 83.29 17720 418 417
H3 = A 9.581 82.59 16340 432 388


426.
S K 10 9 6
H J 9 2
D A 5 2
C Q 9 8
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 7 2
H A 10 8
D 8 7 6 4
C 7 6 3
S Q 8
H K 7 6
D K Q 10 9
C A J 10 4

S3 = 9 9.589 83.33 18170 420 427
H3 = 8 9.577 82.39 16340 432 388


428.
S Q J 9
H K
D K 8 7 5
C 10 9 7 6 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 8 2
H A 10 7 6 2
D 10 4 2
C J 3
S K 7 6
H J 9 8
D A Q 9 6
C A Q 8

S3 = 9 9.582 83.18 18620 422 437
H3 = 8 9.570 82.01 16390 434 390


434.
S J 2
H J 8 7
D K 10 9 5
C A 7 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 8 6
H K 10 9
D Q 8 2
C 10 9 8 4
S K Q 10 7
H A 6 2
D A 7 6 4
C Q J

S3 = 9 9.581 83.41 19100 428 448
H3 = 8 9.571 82.03 16480 440 393


448.
S K 2
H A 9 6
D 7 6 5 2
C Q 10 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 6
H K 10 8 2
D 10 9 8
C 9 7 4
S Q 9 8 7
H J 7
D A K Q 4
C A J 8

S3 = 9 9.565 83.26 19580 441 459
H3 = 8 9.560 81.70 16620 455 398


464.
S K 9
H 10 7 2
D Q 8 6 4
C A 8 7 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q J 10 6
H J 9 8
D 10 9 5
C Q 9 3
S 8 7 2
H A K 6
D A K 7 2
C J 10 6

S3 = 9 9.565 83.41 20060 457 470
H3 = 8 9.560 81.68 16680 471 400


467.
S K 7 2
H A 2
D Q 10 9 5
C 9 7 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 10 6
H K 10 8 6
D 7 6 4 2
C J 6
S J 9 8
H J 9 7
D A K 8
C A Q 10 8

S3 = 9 9.565 83.51 20510 460 480
H3 = 8 9.561 81.58 16710 474 401


469.
S 8 6
H J 6
D A K Q 6 5 2
C 8 7 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 9 2
H K 10 9 8 7
D 10
C J 10 9 6
S K Q J 7
H A 2
D 9 8 7 4
C A Q 4

S3 = B 9.569 83.58 21020 463 491
H3 = 8 9.559 81.45 16710 475 401


498.
S K Q 7
H 9 8
D Q 10 9
C Q J 10 9 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 2
H A J 10 6 2
D 8 7 6 4
C 7 3
S J 10 8 6
H K 7
D A K 5 2
C A 8 4

S3 = A 9.566 83.94 21590 489 504
H3 = 8 9.560 81.73 16960 507 410


523.
S K J 2
H 8 6
D A 9 8 2
C J 9 6 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 7 6
H K J 10 7 2
D 7 6 5 4
C Q
S Q 10 8
H A 9
D K Q 10
C A 10 8 7 3

S3 = A 9.591 84.32 22340 520 523
H3 = 8 9.568 82.03 17020 526 412


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525.
S Q 2
H 7 6
D K 8 4 2
C A Q 9 8 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K J 9 7
H 10 8
D 9 7 6 5
C 10 7 6
S 10 8 6
H A K J 9 2
D A Q 10
C J 3

S3 = 8 9.590 84.19 22340 521 523
H3 = 9 9.570 82.10 17470 529 422


533.
S J 9
H K 2
D A K 9 8 2
C 10 7 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 8 7 6 2
H 10 9 8
D 10 6
C J 8 6
S Q 10
H A J 7 6
D Q 7 5 4
C A Q 9

S3 = 8 9.583 83.86 22370 528 524
H3 = 9 9.565 81.99 17950 538 433


534.
S Q J 10
H 9 8 6
D Q 8 6 5
C A 9 8
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 9 2
H 10 7
D 10 9 7 2
C J 10 6 3
S 8 7 6
H A K J 2
D A K 4
C Q 7 4

S3 = 8 9.581 83.71 22370 528 524
H3 = 9 9.564 82.02 18400 540 443


538.
S Q J 2
H J 9 8
D A 10
C J 10 9 7 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 8 7
H 10 7 6
D K 9 7 6 4 2
C 6
S 10 9 6
H A K 2
D Q 8 5
C A Q 8 3

S3 = 8 9.582 83.64 22400 532 525
H3 = 9 9.565 82.16 18850 544 453


539.
S K 10 7
H K J
D Q 9 8 7 4 2
C 9 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 9 2
H A 9 7 6 2
D 6
C J 8 6 3
S Q 8 6
H 10 8
D A K 10 5
C A Q 10 4

S3 = A 9.583 83.67 22880 534 535
H3 = 8 9.562 82.00 18850 544 453


548.
S Q 8 7
H 9 7 6
D A 9 7 5
C A 10 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10 2
H J 10 8
D 8 6 4
C Q J 7 3
S K 9 6
H A K 2
D K Q 10 2
C 9 8 6

S3 = 9 9.589 83.76 23360 542 546
H3 = 8 9.571 81.93 18940 554 456


551.
S Q 8 6
H A 10
D K 9 7 6 4 2
C 10 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 10
H K 9 8 7 2
D Q 5
C 9 7 4 3
S K 9 7 2
H J 6
D A 10 8
C A Q J 8

S3 = B 9.593 83.85 23900 547 558
H3 = 8 9.568 81.85 18940 555 456


566.
S K 8 6
H 9
D Q 9 8 6 2
C A J 9 8
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10
H A 10 7 6 2
D 10 7 5 4
C 10 4 3
S Q J 9 7 2
H K J 8
D A K
C Q 7 6

S3 = A 9.617 84.28 24470 561 571
H3 = 8 9.592 82.16 19090 571 461


567.
S Q 10 6
H A J 7
D K 10 9 6 2
C 10 9
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 8 7
H 10 6
D 8 7
C A 8 7 6 4 3
S K J 2
H K 9 8 2
D A Q 5 4
C Q J

S3 = 9 9.616 84.30 24920 563 581
H3 = 8 9.589 82.01 19090 571 461


570.
S K 10 9 7
H K 8 6
D Q 6 5
C J 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 8
H J 9 7 2
D A 9 7 4
C 8 7 4
S Q 6 2
H A 10
D K 10 8 2
C A Q 10 9

S3 = 9 9.618 84.39 25370 566 591
H3 = 8 9.591 81.93 19120 574 462


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9991.
S J 8 7
H A K J 6
D Q 10 2
C 9 7 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 6 2
H 9 7 2
D 8 7 6
C J 10 8 3
S Q 10 9
H 10 8
D A K 9 5 4
C A Q 6

S3 = A 9.708 86.35 338710 9730 8011
H3 = A 9.721 85.92 324030 10252 7785


9992.
S K Q 6
H J 8 7
D K 10 9 4 2
C Q 9
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 8
H 10 9
D Q 7 6
C J 10 7 6 4 3
S J 9 7 2
H A K 6 2
D A 8 5
C A 8

S3 = B 9.708 86.35 338710 9731 8011
H3 = B 9.721 85.92 324030 10253 7785


9993.
S Q J
H A K
D 8 6 5 4 2
C J 7 4 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 9 8 2
H J 10 9 2
D Q 10
C 10 9 8
S K 7 6
H 8 7 6
D A K 9 7
C A Q 6

S3 = B 9.708 86.35 338740 9733 8012
H3 = A 9.721 85.92 324030 10253 7785


9994.
S Q J 6
H K 9 7
D 9 8 5 4
C Q J 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K 10
H J 10 8 6
D 10 7 6 2
C 10 8 3
S 9 8 7 2
H A 2
D A K Q
C A 9 6 4

S3 = 8 9.708 86.34 338740 9734 8012
H3 = 8 9.721 85.91 324030 10254 7785


9995.
S K 10 7
H 9 6
D K 10 7 4
C Q J 10 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q 9 6 2
H 8 7 2
D Q 9 8 2
C 6 4
S J 8
H A K J 10
D A 6 5
C A 9 8 7

S3 = 8 9.707 86.33 338740 9734 8012
H3 = 9 9.721 85.91 324480 10256 7795


9996.
S 10 2
H 7 6
D K 9 7 2
C A Q 9 8 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS J 8 7 6
H 10 9 8
D Q 8 5
C J 6 4
S K Q 9
H A K J 2
D A 10 6 4
C 10 7

S3 = A 9.707 86.33 338740 9734 8012
H3 = B 9.721 85.91 324510 10258 7796


9997.
S K 6
H K 8 7
D K 9 8 5 2
C Q 10 6
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS Q J 9 7 2
H J 9
D 6 4
C 9 8 7 3
S 10 8
H A 10 6 2
D A Q 10 7
C A J 4

S3 = 9 9.707 86.34 338740 9734 8012
H3 = B 9.721 85.92 324570 10260 7798


9998.
S 9 8 6
H K J
D 10 9 6 5
C A Q 10 4
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS K Q 10 2
H 8 7 6
D 8 7 4 2
C 8 6
S J 7
H A 10 9 2
D A K Q
C J 9 7 3

S3 = 9 9.707 86.34 338740 9734 8012
H3 = B 9.721 85.92 324630 10262 7800


9999.
S K J 7
H K 10 8 6
D K 7 4
C 10 6 3
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 9 8
H J 9 7
D 9 8 6 2
C A 8 7 4
S Q 10 6 2
H A 2
D A Q 10 5
C Q J 9

S3 = 9 9.707 86.34 338740 9735 8012
H3 = 9 9.721 85.92 324630 10263 7800


10000.
S J 2
H A 8
D K 10 9 4
C Q J 10 9 7
S A 5 4 3
H Q 5 4 3
D J 3
C K 5 2
TableS 10 9 8 7
H J 10 9 2
D Q 7 2
C 6 4
S K Q 6
H K 7 6
D A 8 6 5
C A 8 3

S3 = A 9.707 86.34 338770 9737 8013
H3 = 9 9.721 85.92 324630 10263 7800

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© 2015 Richard Pavlicek