Study 8C05 Main
| 
Leading Authority
|
 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 Pattern | Combinations | Ways | Specific | Ratio
|
|---|
| 4 (3-3-3) | 9c3 × 6c3 = 1680 | 1 | 1680 | 726
|
| 4 (4-3-2) | 9c4 × 5c3 = 1260 | 6 | 7560 | 660
|
| 4 (4-4-1) | 9c4 × 5c4 = 630 | 2* | 1260 | 550
|
| 4 (5-2-2) | 9c5 × 4c2 = 756 | 3 | 2268 | 540
|
| 4 (5-3-1) | 9c5 × 4c3 = 504 | 4* | 2016 | 495
|
| Totals | 4830 | 16 | 14784 | 2971 |
*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-K | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| A-K-Q-J | 4.0000 | = | = | = | 4.0000 | 4.0000 | 100.00 | 96.22
|
| A-K-Q-10 | 3.9274 | = | = | 3.3230 | 3.9274 | 3.9274 | 100.00 | 96.22
|
| A-K-Q-9 | 3.8247 | = | = | 3.3230 | 3.8287 | 3.8287 | 99.58 | 93.15
|
| A-K-Q-8 | 3.7098 | = | = | 3.3230 | 3.7424 | 3.7467 | 96.06 | 85.31
|
| A-K-Q-7 | 3.6417 | = | = | 3.3230 | 3.6761 | 3.6845 | 95.36 | 84.62
|
| A-K-Q-6 | 3.6076 | = | = | 3.3230 | 3.6331 | 3.6455 | 95.85 | 85.17
|
| A-K-Q-5 | 3.5921 | = | = | 3.3230 | 3.6154 | 3.6234 | 96.55 | 86.01
|
| A-K-Q-4 | 3.5866 | = | = | 3.3230 | 3.6080 | 3.6144 | 96.92 | 86.71
|
| A-K-Q-3 | 3.5854 | = | = | 3.3230 | 3.6047 | 3.6091 | 97.38 | 87.41
|
| A-K-Q-2 | 3.5854 | = | = | 3.3230 | 3.6032 | 3.6061 | 97.71 | 87.83
|
| A-K-J-10 | 3.7476 | = | 3.3230 | = | 3.7476 | 3.7476 | 100.00 | 96.22
|
| A-K-J-9 | 3.6643 | = | 3.2606 | 3.2646 | 3.6683 | 3.6683 | 99.56 | 93.01
|
| A-K-J-8 | 3.5631 | = | 3.1810 | 3.2646 | 3.5977 | 3.6020 | 95.73 | 85.03
|
| A-K-J-7 | 3.5002 | = | 3.1003 | 3.2646 | 3.5389 | 3.5495 | 94.63 | 81.82
|
| A-K-J-6 | 3.4685 | = | 3.0511 | 3.2646 | 3.4991 | 3.5145 | 95.00 | 83.92
|
| A-K-J-5 | 3.4545 | = | 3.0254 | 3.2646 | 3.4824 | 3.4939 | 95.72 | 84.90
|
| A-K-J-4 | 3.4492 | = | 3.0131 | 3.2646 | 3.4753 | 3.4854 | 96.09 | 85.45
|
| A-K-J-3 | 3.4481 | = | 3.0082 | 3.2646 | 3.4720 | 3.4801 | 96.56 | 86.15
|
| A-K-J-2 | 3.4481 | = | 3.0070 | 3.2646 | 3.4705 | 3.4770 | 96.91 | 86.57
|
| A-K-10-9 | 3.4630 | = | 3.2313 | = | 3.5657 | 3.5758 | 87.38 | 48.25
|
| A-K-10-8 | 3.4007 | = | 3.1284 | 3.1736 | 3.4837 | 3.4938 | 89.44 | 58.88
|
| A-K-10-7 | 3.3382 | = | 3.0281 | 3.1736 | 3.4209 | 3.4372 | 89.09 | 57.06
|
| A-K-10-6 | 3.3065 | = | 2.9666 | 3.1736 | 3.3742 | 3.3988 | 89.91 | 61.40
|
| A-K-10-5 | 3.2946 | = | 2.9334 | 3.1736 | 3.3540 | 3.3763 | 91.06 | 65.59
|
| A-K-10-4 | 3.2902 | = | 2.9170 | 3.1736 | 3.3462 | 3.3677 | 91.57 | 68.11
|
| A-K-10-3 | 3.2892 | = | 2.9107 | 3.1736 | 3.3428 | 3.3623 | 92.08 | 72.17
|
| A-K-10-2 | 3.2892 | = | 2.9095 | 3.1736 | 3.3412 | 3.3593 | 92.43 | 76.64
|
| A-K-9-8 | 3.1668 | = | 3.1118 | = | 3.3846 | 3.4130 | 75.12 | 7.69
|
| A-K-9-7 | 3.1489 | = | 3.0058 | 3.0722 | 3.3238 | 3.3570 | 78.45 | 13.15
|
| A-K-9-6 | 3.1312 | = | 2.9439 | 3.0722 | 3.2695 | 3.3117 | 81.06 | 18.32
|
| A-K-9-5 | 3.1253 | = | 2.9085 | 3.0722 | 3.2435 | 3.2864 | 83.00 | 28.39
|
| A-K-9-4 | 3.1230 | = | 2.8905 | 3.0722 | 3.2340 | 3.2756 | 83.90 | 33.43
|
| A-K-9-3 | 3.1225 | = | 2.8827 | 3.0722 | 3.2299 | 3.2695 | 84.52 | 36.08
|
| A-K-9-2 | 3.1225 | = | 2.8804 | 3.0722 | 3.2282 | 3.2662 | 84.89 | 38.46
|
| A-K-8-7 | 2.9989 | = | 3.0002 | = | 3.1605 | 3.2245 | 73.85 | 5.45
|
| A-K-8-6 | 2.9971 | = | 2.9375 | 2.9940 | 3.1311 | 3.2031 | 77.95 | 12.03
|
| A-K-8-5 | 2.9951 | = | 2.9029 | 2.9940 | 3.1119 | 3.1846 | 79.65 | 15.24
|
| A-K-8-4 | 2.9944 | = | 2.8864 | 2.9940 | 3.1057 | 3.1783 | 80.27 | 16.64
|
| A-K-8-3 | 2.9943 | = | 2.8791 | 2.9940 | 3.1038 | 3.1741 | 80.76 | 17.34
|
| A-K-8-2 | 2.9943 | = | 2.8767 | 2.9940 | 3.1029 | 3.1717 | 81.05 | 18.18
|
| A-K-7-6 | 2.9295 | = | 2.9370 | = | 3.0206 | 3.0875 | 81.17 | 19.16
|
| A-K-7-5 | 2.9295 | = | 2.9009 | 2.9312 | 3.0180 | 3.0837 | 80.96 | 17.76
|
| A-K-7-4 | 2.9294 | = | 2.8844 | 2.9312 | 3.0165 | 3.0802 | 81.32 | 20.14
|
| A-K-7-3 | 2.9294 | = | 2.8765 | 2.9312 | 3.0157 | 3.0777 | 81.60 | 21.54
|
| A-K-7-2 | 2.9294 | = | 2.8735 | 2.9312 | 3.0153 | 3.0765 | 81.75 | 22.38
|
| A-K-6-5 | 2.9016 | = | 2.9009 | = | 2.9660 | 3.0223 | 86.47 | 44.48
|
| A-K-6-4 | 2.9016 | = | 2.8844 | 2.9009 | 2.9660 | 3.0217 | 86.55 | 44.76
|
| A-K-6-3 | 2.9016 | = | 2.8765 | 2.9009 | 2.9657 | 3.0207 | 86.67 | 45.73
|
| A-K-6-2 | 2.9016 | = | 2.8735 | 2.9009 | 2.9656 | 3.0201 | 86.75 | 45.87
|
| A-K-5-4 | 2.8920 | = | 2.8844 | = | 2.9444 | 2.9916 | 88.86 | 55.38
|
| A-K-5-3 | 2.8920 | = | 2.8765 | 2.8844 | 2.9444 | 2.9916 | 88.86 | 55.38
|
| A-K-5-2 | 2.8920 | = | 2.8735 | 2.8844 | 2.9444 | 2.9916 | 88.86 | 55.38
|
| A-K-4-3 | 2.8902 | = | 2.8765 | = | 2.9364 | 2.9793 | 90.00 | 61.54
|
| A-K-4-2 | 2.8902 | = | 2.8735 | 2.8765 | 2.9364 | 2.9793 | 90.00 | 61.54
|
| A-K-3-2 | 2.8902 | = | 2.8735 | = | 2.9349 | 2.9757 | 90.36 | 63.78 |
| A-Q | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| A-Q-J-10 | 3.3333 | 3.3230 | = | = | 3.6873 | 3.6873 | 61.61 | 0.14
|
| A-Q-J-9 | 3.3002 | 3.2606 | = | 3.1469 | 3.6079 | 3.6079 | 65.88 | 0.70
|
| A-Q-J-8 | 3.2596 | 3.1810 | = | 3.1469 | 3.5236 | 3.5279 | 69.63 | 1.96
|
| A-Q-J-7 | 3.2245 | 3.1003 | = | 3.1469 | 3.4556 | 3.4662 | 72.43 | 3.64
|
| A-Q-J-6 | 3.2032 | 3.0511 | = | 3.1469 | 3.4046 | 3.4208 | 74.96 | 7.27
|
| A-Q-J-5 | 3.1934 | 3.0254 | = | 3.1469 | 3.3804 | 3.3934 | 76.82 | 9.79
|
| A-Q-J-4 | 3.1895 | 3.0131 | = | 3.1469 | 3.3690 | 3.3811 | 77.71 | 11.19
|
| A-Q-J-3 | 3.1884 | 3.0082 | = | 3.1469 | 3.3645 | 3.3745 | 78.31 | 12.59
|
| A-Q-J-2 | 3.1884 | 3.0070 | = | 3.1469 | 3.3630 | 3.3714 | 78.65 | 13.71
|
| A-Q-10-9 | 3.1825 | 3.1316 | 3.1135 | = | 3.4730 | 3.4831 | 66.92 | 1.12
|
| A-Q-10-8 | 3.1470 | 3.0613 | 3.0271 | 3.0663 | 3.3913 | 3.4014 | 71.10 | 2.80
|
| A-Q-10-7 | 3.1150 | 2.9882 | 2.9323 | 3.0663 | 3.3259 | 3.3423 | 73.92 | 5.59
|
| A-Q-10-6 | 3.0940 | 2.9413 | 2.8720 | 3.0663 | 3.2740 | 3.2976 | 76.47 | 9.65
|
| A-Q-10-5 | 3.0846 | 2.9170 | 2.8393 | 3.0663 | 3.2488 | 3.2704 | 78.41 | 12.73
|
| A-Q-10-4 | 3.0814 | 2.9058 | 2.8239 | 3.0663 | 3.2377 | 3.2588 | 79.33 | 14.83
|
| A-Q-10-3 | 3.0806 | 2.9012 | 2.8179 | 3.0663 | 3.2335 | 3.2527 | 79.95 | 16.08
|
| A-Q-10-2 | 3.0806 | 2.9001 | 2.8167 | 3.0663 | 3.2320 | 3.2497 | 80.30 | 16.78
|
| A-Q-9-8 | 2.9841 | 2.9017 | 3.0050 | = | 3.2928 | 3.3213 | 66.89 | 0.98
|
| A-Q-9-7 | 2.9624 | 2.8491 | 2.9027 | 2.9618 | 3.2285 | 3.2603 | 67.07 | 1.26
|
| A-Q-9-6 | 2.9409 | 2.7990 | 2.8420 | 2.9618 | 3.1684 | 3.2067 | 72.67 | 3.92
|
| A-Q-9-5 | 2.9305 | 2.7729 | 2.8069 | 2.9618 | 3.1369 | 3.1756 | 75.64 | 8.25
|
| A-Q-9-4 | 2.9268 | 2.7628 | 2.7895 | 2.9618 | 3.1237 | 3.1614 | 77.05 | 10.21
|
| A-Q-9-3 | 2.9256 | 2.7589 | 2.7819 | 2.9618 | 3.1189 | 3.1545 | 77.79 | 11.75
|
| A-Q-9-2 | 2.9256 | 2.7579 | 2.7797 | 2.9618 | 3.1172 | 3.1512 | 78.17 | 12.45
|
| A-Q-8-7 | 2.8347 | 2.6504 | 2.8949 | = | 3.0699 | 3.1329 | 73.25 | 4.90
|
| A-Q-8-6 | 2.8283 | 2.6347 | 2.8325 | 2.8860 | 3.0341 | 3.1031 | 75.07 | 7.55
|
| A-Q-8-5 | 2.8218 | 2.6189 | 2.7980 | 2.8860 | 3.0086 | 3.0774 | 77.47 | 10.63
|
| A-Q-8-4 | 2.8197 | 2.6141 | 2.7822 | 2.8860 | 2.9978 | 3.0666 | 78.49 | 13.29
|
| A-Q-8-3 | 2.8190 | 2.6122 | 2.7751 | 2.8860 | 2.9948 | 3.0616 | 79.06 | 14.41
|
| A-Q-8-2 | 2.8190 | 2.6117 | 2.7727 | 2.8860 | 2.9939 | 3.0592 | 79.36 | 15.10
|
| A-Q-7-6 | 2.7619 | 2.5054 | 2.8312 | = | 2.9222 | 2.9877 | 81.11 | 18.46
|
| A-Q-7-5 | 2.7611 | 2.5037 | 2.7956 | 2.8254 | 2.9134 | 2.9794 | 81.16 | 19.02
|
| A-Q-7-4 | 2.7603 | 2.5019 | 2.7800 | 2.8254 | 2.9068 | 2.9725 | 81.76 | 22.66
|
| A-Q-7-3 | 2.7600 | 2.5012 | 2.7726 | 2.8254 | 2.9048 | 2.9693 | 82.09 | 23.92
|
| A-Q-7-2 | 2.7600 | 2.5011 | 2.7695 | 2.8254 | 2.9043 | 2.9681 | 82.24 | 24.48
|
| A-Q-6-5 | 2.7342 | 2.4450 | 2.7956 | = | 2.8585 | 2.9150 | 84.78 | 37.62
|
| A-Q-6-4 | 2.7342 | 2.4450 | 2.7800 | 2.7956 | 2.8571 | 2.9137 | 84.90 | 38.60
|
| A-Q-6-3 | 2.7342 | 2.4448 | 2.7726 | 2.7956 | 2.8561 | 2.9124 | 85.05 | 39.30
|
| A-Q-6-2 | 2.7342 | 2.4448 | 2.7695 | 2.7956 | 2.8560 | 2.9118 | 85.13 | 39.72
|
| A-Q-5-4 | 2.7251 | 2.4202 | 2.7800 | = | 2.8356 | 2.8836 | 86.57 | 44.90
|
| A-Q-5-3 | 2.7251 | 2.4202 | 2.7726 | 2.7800 | 2.8356 | 2.8836 | 86.57 | 44.90
|
| A-Q-5-2 | 2.7251 | 2.4202 | 2.7695 | 2.7800 | 2.8356 | 2.8836 | 86.57 | 44.90
|
| A-Q-4-3 | 2.7234 | 2.4113 | 2.7726 | = | 2.8280 | 2.8717 | 87.10 | 47.13
|
| A-Q-4-2 | 2.7234 | 2.4113 | 2.7695 | 2.7726 | 2.8280 | 2.8717 | 87.10 | 47.13
|
| A-Q-3-2 | 2.7234 | 2.4095 | 2.7695 | = | 2.8265 | 2.8681 | 87.15 | 47.55 |
| A-J | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| A-J-10-9 | 2.7856 | 3.0407 | = | = | 3.3210 | 3.3500 | 68.50 | 1.40
|
| A-J-10-8 | 2.7722 | 2.9677 | = | 2.8826 | 3.2665 | 3.2999 | 66.46 | 0.84
|
| A-J-10-7 | 2.7630 | 2.8756 | = | 2.8826 | 3.2176 | 3.2504 | 61.55 | 0.00
|
| A-J-10-6 | 2.7552 | 2.8160 | = | 2.8826 | 3.1707 | 3.2026 | 65.85 | 0.56
|
| A-J-10-5 | 2.7521 | 2.7840 | = | 2.8826 | 3.1420 | 3.1728 | 68.63 | 1.54
|
| A-J-10-4 | 2.7510 | 2.7692 | = | 2.8826 | 3.1292 | 3.1583 | 70.02 | 2.10
|
| A-J-10-3 | 2.7505 | 2.7631 | = | 2.8826 | 3.1248 | 3.1517 | 70.69 | 2.52
|
| A-J-10-2 | 2.7505 | 2.7620 | = | 2.8826 | 3.1231 | 3.1492 | 70.95 | 2.66
|
| A-J-9-8 | 2.6940 | 2.7844 | 2.8384 | = | 3.1582 | 3.1985 | 62.89 | 0.28
|
| A-J-9-7 | 2.6836 | 2.7245 | 2.7598 | 2.8133 | 3.1045 | 3.1462 | 64.93 | 0.42
|
| A-J-9-6 | 2.6748 | 2.6650 | 2.7005 | 2.8133 | 3.0542 | 3.0976 | 69.13 | 1.82
|
| A-J-9-5 | 2.6706 | 2.6339 | 2.6667 | 2.8133 | 3.0208 | 3.0654 | 71.98 | 3.50
|
| A-J-9-4 | 2.6694 | 2.6214 | 2.6516 | 2.8133 | 3.0048 | 3.0490 | 73.47 | 5.31
|
| A-J-9-3 | 2.6690 | 2.6167 | 2.6452 | 2.8133 | 2.9993 | 3.0422 | 74.15 | 6.01
|
| A-J-9-2 | 2.6690 | 2.6157 | 2.6431 | 2.8133 | 2.9975 | 3.0396 | 74.43 | 6.29
|
| A-J-8-7 | 2.5833 | 2.5265 | 2.7443 | = | 2.9660 | 3.0362 | 68.99 | 1.68
|
| A-J-8-6 | 2.5790 | 2.5063 | 2.6841 | 2.7276 | 2.9269 | 2.9999 | 70.45 | 2.38
|
| A-J-8-5 | 2.5752 | 2.4863 | 2.6526 | 2.7276 | 2.8923 | 2.9651 | 73.38 | 5.03
|
| A-J-8-4 | 2.5745 | 2.4793 | 2.6399 | 2.7276 | 2.8738 | 2.9478 | 74.81 | 6.99
|
| A-J-8-3 | 2.5742 | 2.4764 | 2.6345 | 2.7276 | 2.8679 | 2.9410 | 75.47 | 7.97
|
| A-J-8-2 | 2.5742 | 2.4757 | 2.6328 | 2.7276 | 2.8665 | 2.9387 | 75.74 | 8.39
|
| A-J-7-6 | 2.5251 | 2.3618 | 2.6806 | = | 2.8021 | 2.8794 | 77.15 | 10.35
|
| A-J-7-5 | 2.5249 | 2.3596 | 2.6475 | 2.6754 | 2.7859 | 2.8674 | 77.56 | 10.91
|
| A-J-7-4 | 2.5248 | 2.3573 | 2.6337 | 2.6754 | 2.7720 | 2.8564 | 78.44 | 12.87
|
| A-J-7-3 | 2.5247 | 2.3563 | 2.6277 | 2.6754 | 2.7674 | 2.8527 | 78.81 | 13.85
|
| A-J-7-2 | 2.5247 | 2.3561 | 2.6252 | 2.6754 | 2.7665 | 2.8519 | 78.91 | 14.13
|
| A-J-6-5 | 2.5050 | 2.2890 | 2.6462 | = | 2.7208 | 2.7979 | 81.50 | 20.84
|
| A-J-6-4 | 2.5050 | 2.2890 | 2.6333 | 2.6462 | 2.7182 | 2.7955 | 81.72 | 22.10
|
| A-J-6-3 | 2.5050 | 2.2888 | 2.6276 | 2.6462 | 2.7165 | 2.7936 | 81.91 | 23.22
|
| A-J-6-2 | 2.5050 | 2.2888 | 2.6252 | 2.6462 | 2.7163 | 2.7931 | 81.98 | 23.64
|
| A-J-5-4 | 2.4981 | 2.2588 | 2.6333 | = | 2.6929 | 2.7658 | 83.55 | 31.47
|
| A-J-5-3 | 2.4981 | 2.2588 | 2.6276 | 2.6333 | 2.6929 | 2.7658 | 83.55 | 31.47
|
| A-J-5-2 | 2.4981 | 2.2588 | 2.6252 | 2.6333 | 2.6929 | 2.7658 | 83.55 | 31.47
|
| A-J-4-3 | 2.4968 | 2.2473 | 2.6276 | = | 2.6850 | 2.7541 | 84.20 | 34.69
|
| A-J-4-2 | 2.4968 | 2.2473 | 2.6252 | 2.6276 | 2.6850 | 2.7541 | 84.20 | 34.69
|
| A-J-3-2 | 2.4968 | 2.2452 | 2.6252 | = | 2.6829 | 2.7503 | 84.32 | 35.38 |
| A-10 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| A-10-9-8 | 2.3666 | 2.7406 | = | = | 2.8737 | 2.9642 | 74.75 | 6.71
|
| A-10-9-7 | 2.3641 | 2.6753 | = | 2.6253 | 2.8432 | 2.9388 | 71.27 | 3.08
|
| A-10-9-6 | 2.3624 | 2.6136 | = | 2.6253 | 2.8163 | 2.9117 | 70.42 | 2.24
|
| A-10-9-5 | 2.3608 | 2.5792 | = | 2.6253 | 2.7960 | 2.8947 | 71.83 | 3.36
|
| A-10-9-4 | 2.3607 | 2.5649 | = | 2.6253 | 2.7852 | 2.8866 | 72.47 | 3.78
|
| A-10-9-3 | 2.3607 | 2.5588 | = | 2.6253 | 2.7827 | 2.8836 | 72.77 | 4.06
|
| A-10-9-2 | 2.3607 | 2.5567 | = | 2.6253 | 2.7826 | 2.8824 | 72.91 | 4.48
|
| A-10-8-7 | 2.3411 | 2.4843 | 2.6015 | = | 2.7565 | 2.8566 | 72.78 | 4.20
|
| A-10-8-6 | 2.3394 | 2.4632 | 2.5441 | 2.5851 | 2.7302 | 2.8316 | 73.24 | 4.76
|
| A-10-8-5 | 2.3379 | 2.4408 | 2.5126 | 2.5851 | 2.7099 | 2.8112 | 74.96 | 7.27
|
| A-10-8-4 | 2.3377 | 2.4324 | 2.4997 | 2.5851 | 2.6981 | 2.8008 | 75.82 | 8.53
|
| A-10-8-3 | 2.3377 | 2.4285 | 2.4937 | 2.5851 | 2.6951 | 2.7968 | 76.24 | 9.09
|
| A-10-8-2 | 2.3377 | 2.4271 | 2.4918 | 2.5851 | 2.6948 | 2.7955 | 76.40 | 9.37
|
| A-10-7-6 | 2.3112 | 2.3146 | 2.5335 | = | 2.6190 | 2.7277 | 77.57 | 11.05
|
| A-10-7-5 | 2.3112 | 2.3108 | 2.5017 | 2.5276 | 2.6068 | 2.7181 | 77.87 | 11.89
|
| A-10-7-4 | 2.3112 | 2.3069 | 2.4881 | 2.5276 | 2.5969 | 2.7104 | 78.54 | 13.57
|
| A-10-7-3 | 2.3112 | 2.3046 | 2.4817 | 2.5276 | 2.5940 | 2.7071 | 78.90 | 13.99
|
| A-10-7-2 | 2.3112 | 2.3039 | 2.4794 | 2.5276 | 2.5937 | 2.7062 | 79.02 | 14.27
|
| A-10-6-5 | 2.3007 | 2.2362 | 2.4992 | = | 2.5461 | 2.6568 | 80.96 | 17.76
|
| A-10-6-4 | 2.3007 | 2.2356 | 2.4867 | 2.4989 | 2.5435 | 2.6560 | 81.00 | 18.04
|
| A-10-6-3 | 2.3007 | 2.2349 | 2.4811 | 2.4989 | 2.5422 | 2.6548 | 81.13 | 18.74
|
| A-10-6-2 | 2.3007 | 2.2347 | 2.4789 | 2.4989 | 2.5420 | 2.6546 | 81.17 | 19.16
|
| A-10-5-4 | 2.2964 | 2.2007 | 2.4866 | = | 2.5204 | 2.6294 | 82.53 | 25.73
|
| A-10-5-3 | 2.2964 | 2.2007 | 2.4810 | 2.4866 | 2.5204 | 2.6294 | 82.53 | 25.73
|
| A-10-5-2 | 2.2964 | 2.2007 | 2.4789 | 2.4866 | 2.5204 | 2.6294 | 82.53 | 25.73
|
| A-10-4-3 | 2.2953 | 2.1868 | 2.4810 | = | 2.5125 | 2.6186 | 83.05 | 28.67
|
| A-10-4-2 | 2.2953 | 2.1868 | 2.4789 | 2.4810 | 2.5125 | 2.6186 | 83.05 | 28.67
|
| A-10-3-2 | 2.2953 | 2.1834 | 2.4789 | = | 2.5101 | 2.6144 | 83.23 | 30.49 |
| A-9 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| A-9-8-7 | 2.1591 | 2.4742 | = | = | 2.4839 | 2.5803 | 86.02 | 42.80
|
| A-9-8-6 | 2.1591 | 2.4506 | = | 2.4382 | 2.4749 | 2.5742 | 84.44 | 35.66
|
| A-9-8-5 | 2.1591 | 2.4255 | = | 2.4382 | 2.4700 | 2.5703 | 82.79 | 27.13
|
| A-9-8-4 | 2.1591 | 2.4169 | = | 2.4382 | 2.4666 | 2.5671 | 83.08 | 29.09
|
| A-9-8-3 | 2.1591 | 2.4131 | = | 2.4382 | 2.4656 | 2.5659 | 83.22 | 30.35
|
| A-9-8-2 | 2.1591 | 2.4116 | = | 2.4382 | 2.4655 | 2.5654 | 83.27 | 30.77
|
| A-9-7-6 | 2.1564 | 2.2973 | 2.4204 | = | 2.4261 | 2.5413 | 83.82 | 33.15
|
| A-9-7-5 | 2.1564 | 2.2926 | 2.3892 | 2.4086 | 2.4213 | 2.5370 | 83.20 | 30.21
|
| A-9-7-4 | 2.1564 | 2.2884 | 2.3764 | 2.4086 | 2.4179 | 2.5336 | 83.52 | 31.33
|
| A-9-7-3 | 2.1564 | 2.2858 | 2.3706 | 2.4086 | 2.4169 | 2.5323 | 83.67 | 32.17
|
| A-9-7-2 | 2.1564 | 2.2848 | 2.3684 | 2.4086 | 2.4167 | 2.5318 | 83.73 | 32.59
|
| A-9-6-5 | 2.1529 | 2.2166 | 2.3827 | = | 2.3734 | 2.4991 | 84.57 | 36.36
|
| A-9-6-4 | 2.1529 | 2.2162 | 2.3727 | 2.3818 | 2.3724 | 2.4983 | 84.58 | 36.50
|
| A-9-6-3 | 2.1529 | 2.2154 | 2.3686 | 2.3818 | 2.3719 | 2.4975 | 84.67 | 36.92
|
| A-9-6-2 | 2.1529 | 2.2151 | 2.3669 | 2.3818 | 2.3718 | 2.4969 | 84.73 | 37.20
|
| A-9-5-4 | 2.1514 | 2.1804 | 2.3722 | = | 2.3545 | 2.4818 | 85.43 | 40.14
|
| A-9-5-3 | 2.1514 | 2.1804 | 2.3684 | 2.3722 | 2.3545 | 2.4816 | 85.45 | 40.28
|
| A-9-5-2 | 2.1514 | 2.1804 | 2.3669 | 2.3722 | 2.3545 | 2.4814 | 85.46 | 40.42
|
| A-9-4-3 | 2.1511 | 2.1659 | 2.3684 | = | 2.3489 | 2.4738 | 85.88 | 42.10
|
| A-9-4-2 | 2.1511 | 2.1659 | 2.3669 | 2.3684 | 2.3489 | 2.4738 | 85.88 | 42.10
|
| A-9-3-2 | 2.1511 | 2.1621 | 2.3669 | = | 2.3474 | 2.4708 | 86.05 | 43.08 |
| A-x | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| A-8-7-6 | 2.0788 | 2.2886 | = | = | 2.2487 | 2.3527 | 90.08 | 62.24
|
| A-8-7-5 | 2.0788 | 2.2843 | = | 2.2775 | 2.2487 | 2.3520 | 89.77 | 60.70
|
| A-8-7-4 | 2.0788 | 2.2801 | = | 2.2775 | 2.2487 | 2.3516 | 89.35 | 58.32
|
| A-8-7-3 | 2.0788 | 2.2772 | = | 2.2775 | 2.2487 | 2.3513 | 89.20 | 57.76
|
| A-8-7-2 | 2.0788 | 2.2757 | = | 2.2775 | 2.2487 | 2.3510 | 89.24 | 58.04
|
| A-8-6-5 | 2.0788 | 2.2078 | 2.2753 | = | 2.2405 | 2.3449 | 89.66 | 60.28
|
| A-8-6-4 | 2.0788 | 2.2073 | 2.2707 | 2.2733 | 2.2405 | 2.3444 | 89.46 | 59.02
|
| A-8-6-3 | 2.0788 | 2.2063 | 2.2680 | 2.2733 | 2.2405 | 2.3441 | 89.49 | 59.16
|
| A-8-6-2 | 2.0788 | 2.2057 | 2.2664 | 2.2733 | 2.2405 | 2.3439 | 89.53 | 59.44
|
| A-8-5-4 | 2.0784 | 2.1714 | 2.2697 | = | 2.2345 | 2.3359 | 90.07 | 61.96
|
| A-8-5-3 | 2.0784 | 2.1714 | 2.2675 | 2.2697 | 2.2345 | 2.3359 | 90.07 | 61.96
|
| A-8-5-2 | 2.0784 | 2.1714 | 2.2664 | 2.2697 | 2.2345 | 2.3358 | 90.08 | 62.24
|
| A-8-4-3 | 2.0784 | 2.1568 | 2.2675 | = | 2.2318 | 2.3322 | 90.19 | 62.80
|
| A-8-4-2 | 2.0784 | 2.1568 | 2.2664 | 2.2675 | 2.2318 | 2.3322 | 90.19 | 62.80
|
| A-8-3-2 | 2.0784 | 2.1522 | 2.2664 | = | 2.2309 | 2.3308 | 90.23 | 63.08
|
| A-7-6-5 | 2.0467 | 2.2060 | = | = | 2.1609 | 2.2540 | 92.11 | 73.15
|
| A-7-6-4 | 2.0467 | 2.2054 | = | 2.2032 | 2.1609 | 2.2540 | 92.03 | 72.03
|
| A-7-6-3 | 2.0467 | 2.2044 | = | 2.2032 | 2.1609 | 2.2540 | 91.90 | 71.75
|
| A-7-6-2 | 2.0467 | 2.2038 | = | 2.2032 | 2.1609 | 2.2540 | 91.82 | 70.07
|
| A-7-5-4 | 2.0467 | 2.1704 | 2.2032 | = | 2.1609 | 2.2533 | 91.83 | 70.21
|
| A-7-5-3 | 2.0467 | 2.1704 | 2.2026 | 2.2032 | 2.1609 | 2.2533 | 91.83 | 70.21
|
| A-7-5-2 | 2.0467 | 2.1704 | 2.2022 | 2.2032 | 2.1609 | 2.2533 | 91.83 | 70.21
|
| A-7-4-3 | 2.0467 | 2.1563 | 2.2026 | = | 2.1607 | 2.2522 | 91.87 | 71.47
|
| A-7-4-2 | 2.0467 | 2.1563 | 2.2022 | 2.2026 | 2.1607 | 2.2522 | 91.87 | 71.47
|
| A-7-3-2 | 2.0467 | 2.1517 | 2.2022 | = | 2.1605 | 2.2514 | 91.92 | 71.89
|
| A-6-5-4 | 2.0367 | 2.1704 | = | = | 2.1328 | 2.2163 | 92.30 | 74.41
|
| A-6-5-3 | 2.0367 | 2.1704 | = | 2.1704 | 2.1328 | 2.2163 | 92.30 | 74.41
|
| A-6-5-2 | 2.0367 | 2.1704 | = | 2.1704 | 2.1328 | 2.2163 | 92.30 | 74.41
|
| A-6-4-3 | 2.0367 | 2.1563 | 2.1704 | = | 2.1328 | 2.2163 | 92.30 | 74.41
|
| A-6-4-2 | 2.0367 | 2.1563 | 2.1704 | 2.1704 | 2.1328 | 2.2163 | 92.30 | 74.41
|
| A-6-3-2 | 2.0367 | 2.1517 | 2.1704 | = | 2.1328 | 2.2163 | 92.30 | 74.41
|
| A-5-4-3 | 2.0348 | 2.1563 | = | = | 2.1221 | 2.2012 | 92.42 | 76.22
|
| A-5-4-2 | 2.0348 | 2.1563 | = | 2.1563 | 2.1221 | 2.2012 | 92.42 | 76.22
|
| A-5-3-2 | 2.0348 | 2.1517 | 2.1563 | = | 2.1221 | 2.2012 | 92.42 | 76.22
|
| A-4-3-2 | 2.0348 | 2.1517 | = | = | 2.1200 | 2.1966 | 92.40 | 76.08 |
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-Q | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| K-Q-J-10 | 3.3230 | = | = | = | 3.3230 | 3.3230 | 100.00 | 96.22
|
| K-Q-J-9 | 3.2606 | = | = | 2.8814 | 3.2939 | 3.2939 | 96.84 | 86.29
|
| K-Q-J-8 | 3.1810 | = | = | 2.8814 | 3.2589 | 3.2589 | 92.59 | 76.78
|
| K-Q-J-7 | 3.1003 | = | = | 2.8814 | 3.2303 | 3.2324 | 87.42 | 48.81
|
| K-Q-J-6 | 3.0511 | = | = | 2.8814 | 3.2071 | 3.2108 | 84.75 | 37.34
|
| K-Q-J-5 | 3.0254 | = | = | 2.8814 | 3.1910 | 3.1956 | 83.70 | 32.31
|
| K-Q-J-4 | 3.0131 | = | = | 2.8814 | 3.1839 | 3.1888 | 83.14 | 29.65
|
| K-Q-J-3 | 3.0082 | = | = | 2.8814 | 3.1811 | 3.1863 | 82.90 | 27.97
|
| K-Q-J-2 | 3.0070 | = | = | 2.8814 | 3.1803 | 3.1858 | 82.84 | 27.55
|
| K-Q-10-9 | 3.1316 | = | 2.8774 | = | 3.1734 | 3.1835 | 94.75 | 82.38
|
| K-Q-10-8 | 3.0613 | = | 2.8339 | 2.8459 | 3.1446 | 3.1504 | 91.63 | 69.23
|
| K-Q-10-7 | 2.9882 | = | 2.7690 | 2.8459 | 3.1208 | 3.1266 | 87.06 | 46.85
|
| K-Q-10-6 | 2.9413 | = | 2.7201 | 2.8459 | 3.1000 | 3.1073 | 84.53 | 36.22
|
| K-Q-10-5 | 2.9170 | = | 2.6917 | 2.8459 | 3.0848 | 3.0931 | 83.57 | 31.89
|
| K-Q-10-4 | 2.9058 | = | 2.6786 | 2.8459 | 3.0781 | 3.0868 | 83.08 | 29.09
|
| K-Q-10-3 | 2.9012 | = | 2.6737 | 2.8459 | 3.0757 | 3.0848 | 82.82 | 27.41
|
| K-Q-10-2 | 2.9001 | = | 2.6726 | 2.8459 | 3.0748 | 3.0843 | 82.75 | 26.99
|
| K-Q-9-8 | 2.9017 | = | 2.8119 | = | 3.0470 | 3.0694 | 83.00 | 28.39
|
| K-Q-9-7 | 2.8491 | = | 2.7305 | 2.7831 | 3.0174 | 3.0358 | 81.87 | 23.08
|
| K-Q-9-6 | 2.7990 | = | 2.6715 | 2.7831 | 2.9933 | 3.0117 | 79.92 | 15.94
|
| K-Q-9-5 | 2.7729 | = | 2.6358 | 2.7831 | 2.9738 | 2.9932 | 79.22 | 14.69
|
| K-Q-9-4 | 2.7628 | = | 2.6182 | 2.7831 | 2.9639 | 2.9838 | 80.03 | 16.36
|
| K-Q-9-3 | 2.7589 | = | 2.6110 | 2.7831 | 2.9604 | 2.9811 | 80.26 | 16.50
|
| K-Q-9-2 | 2.7579 | = | 2.6085 | 2.7831 | 2.9594 | 2.9805 | 80.31 | 16.92
|
| K-Q-8-7 | 2.6504 | = | 2.7167 | = | 2.9083 | 2.9498 | 77.03 | 10.07
|
| K-Q-8-6 | 2.6347 | = | 2.6576 | 2.7064 | 2.8868 | 2.9264 | 78.07 | 12.31
|
| K-Q-8-5 | 2.6189 | = | 2.6232 | 2.7064 | 2.8662 | 2.9050 | 79.90 | 15.80
|
| K-Q-8-4 | 2.6141 | = | 2.6070 | 2.7064 | 2.8544 | 2.8940 | 80.81 | 17.62
|
| K-Q-8-3 | 2.6122 | = | 2.6006 | 2.7064 | 2.8500 | 2.8897 | 81.20 | 19.58
|
| K-Q-8-2 | 2.6117 | = | 2.5991 | 2.7064 | 2.8487 | 2.8887 | 81.31 | 20.00
|
| K-Q-7-6 | 2.5054 | = | 2.6545 | = | 2.7851 | 2.8336 | 81.56 | 20.98
|
| K-Q-7-5 | 2.5037 | = | 2.6205 | 2.6520 | 2.7730 | 2.8256 | 81.94 | 23.50
|
| K-Q-7-4 | 2.5019 | = | 2.6057 | 2.6520 | 2.7626 | 2.8185 | 82.45 | 25.59
|
| K-Q-7-3 | 2.5012 | = | 2.6004 | 2.6520 | 2.7587 | 2.8165 | 82.60 | 26.43
|
| K-Q-7-2 | 2.5011 | = | 2.5991 | 2.6520 | 2.7579 | 2.8161 | 82.64 | 26.57
|
| K-Q-6-5 | 2.4450 | = | 2.6203 | = | 2.7162 | 2.7645 | 84.63 | 36.78
|
| K-Q-6-4 | 2.4450 | = | 2.6056 | 2.6203 | 2.7147 | 2.7627 | 84.77 | 37.48
|
| K-Q-6-3 | 2.4448 | = | 2.6004 | 2.6203 | 2.7136 | 2.7617 | 84.85 | 38.04
|
| K-Q-6-2 | 2.4448 | = | 2.5991 | 2.6203 | 2.7134 | 2.7616 | 84.87 | 38.32
|
| K-Q-5-4 | 2.4202 | = | 2.6056 | = | 2.6872 | 2.7359 | 85.95 | 42.38
|
| K-Q-5-3 | 2.4202 | = | 2.6004 | 2.6056 | 2.6872 | 2.7359 | 85.95 | 42.38
|
| K-Q-5-2 | 2.4202 | = | 2.5991 | 2.6056 | 2.6872 | 2.7359 | 85.95 | 42.38
|
| K-Q-4-3 | 2.4113 | = | 2.6004 | = | 2.6774 | 2.7239 | 86.66 | 45.45
|
| K-Q-4-2 | 2.4113 | = | 2.5991 | 2.6004 | 2.6774 | 2.7239 | 86.66 | 45.45
|
| K-Q-3-2 | 2.4095 | = | 2.5991 | = | 2.6745 | 2.7189 | 87.02 | 46.43 |
| K-J | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| K-J-10-9 | 2.7552 | 2.8661 | = | = | 3.0711 | 3.1001 | 77.36 | 10.49
|
| K-J-10-8 | 2.7265 | 2.8124 | = | 2.7268 | 3.0423 | 3.0713 | 75.21 | 7.83
|
| K-J-10-7 | 2.6949 | 2.7426 | = | 2.7268 | 3.0154 | 3.0397 | 71.12 | 2.94
|
| K-J-10-6 | 2.6683 | 2.6906 | = | 2.7268 | 2.9913 | 3.0122 | 72.88 | 4.34
|
| K-J-10-5 | 2.6525 | 2.6613 | = | 2.7268 | 2.9715 | 2.9897 | 74.84 | 7.13
|
| K-J-10-4 | 2.6450 | 2.6482 | = | 2.7268 | 2.9607 | 2.9773 | 75.89 | 8.67
|
| K-J-10-3 | 2.6418 | 2.6433 | = | 2.7268 | 2.9554 | 2.9720 | 76.32 | 9.23
|
| K-J-10-2 | 2.6407 | 2.6422 | = | 2.7268 | 2.9535 | 2.9704 | 76.43 | 9.51
|
| K-J-9-8 | 2.6253 | 2.6487 | 2.6959 | = | 2.9241 | 2.9582 | 74.77 | 6.85
|
| K-J-9-7 | 2.5948 | 2.6006 | 2.6215 | 2.6737 | 2.8971 | 2.9276 | 75.55 | 8.11
|
| K-J-9-6 | 2.5690 | 2.5551 | 2.5656 | 2.6737 | 2.8727 | 2.9015 | 77.77 | 11.61
|
| K-J-9-5 | 2.5521 | 2.5284 | 2.5309 | 2.6737 | 2.8517 | 2.8789 | 79.69 | 15.38
|
| K-J-9-4 | 2.5444 | 2.5163 | 2.5137 | 2.6737 | 2.8397 | 2.8661 | 80.76 | 17.34
|
| K-J-9-3 | 2.5416 | 2.5122 | 2.5071 | 2.6737 | 2.8343 | 2.8611 | 81.14 | 18.88
|
| K-J-9-2 | 2.5408 | 2.5114 | 2.5050 | 2.6737 | 2.8327 | 2.8600 | 81.22 | 19.86
|
| K-J-8-7 | 2.4584 | 2.4368 | 2.6071 | = | 2.7823 | 2.8348 | 77.75 | 11.47
|
| K-J-8-6 | 2.4397 | 2.4116 | 2.5478 | 2.5939 | 2.7602 | 2.8105 | 78.53 | 13.43
|
| K-J-8-5 | 2.4214 | 2.3868 | 2.5130 | 2.5939 | 2.7378 | 2.7852 | 80.65 | 17.20
|
| K-J-8-4 | 2.4127 | 2.3745 | 2.4965 | 2.5939 | 2.7235 | 2.7709 | 81.77 | 22.80
|
| K-J-8-3 | 2.4096 | 2.3701 | 2.4903 | 2.5939 | 2.7168 | 2.7642 | 82.29 | 24.76
|
| K-J-8-2 | 2.4085 | 2.3688 | 2.4890 | 2.5939 | 2.7149 | 2.7627 | 82.42 | 25.45
|
| K-J-7-6 | 2.3325 | 2.2757 | 2.5430 | = | 2.6568 | 2.7167 | 82.39 | 25.03
|
| K-J-7-5 | 2.3267 | 2.2688 | 2.5085 | 2.5393 | 2.6430 | 2.7046 | 82.96 | 28.11
|
| K-J-7-4 | 2.3208 | 2.2617 | 2.4935 | 2.5393 | 2.6297 | 2.6933 | 83.72 | 32.45
|
| K-J-7-3 | 2.3189 | 2.2593 | 2.4885 | 2.5393 | 2.6229 | 2.6881 | 84.03 | 34.13
|
| K-J-7-2 | 2.3182 | 2.2585 | 2.4875 | 2.5393 | 2.6213 | 2.6870 | 84.09 | 34.27
|
| K-J-6-5 | 2.2709 | 2.1955 | 2.5079 | = | 2.5836 | 2.6414 | 85.81 | 41.54
|
| K-J-6-4 | 2.2701 | 2.1946 | 2.4931 | 2.5079 | 2.5795 | 2.6371 | 86.08 | 43.22
|
| K-J-6-3 | 2.2693 | 2.1938 | 2.4884 | 2.5079 | 2.5753 | 2.6336 | 86.28 | 43.92
|
| K-J-6-2 | 2.2690 | 2.1935 | 2.4875 | 2.5079 | 2.5739 | 2.6329 | 86.32 | 44.06
|
| K-J-5-4 | 2.2470 | 2.1645 | 2.4931 | = | 2.5494 | 2.6081 | 87.40 | 48.67
|
| K-J-5-3 | 2.2470 | 2.1645 | 2.4884 | 2.4931 | 2.5487 | 2.6078 | 87.42 | 48.81
|
| K-J-5-2 | 2.2470 | 2.1645 | 2.4875 | 2.4931 | 2.5479 | 2.6074 | 87.43 | 49.09
|
| K-J-4-3 | 2.2387 | 2.1534 | 2.4884 | = | 2.5388 | 2.5959 | 88.15 | 53.01
|
| K-J-4-2 | 2.2387 | 2.1534 | 2.4875 | 2.4884 | 2.5388 | 2.5959 | 88.15 | 53.01
|
| K-J-3-2 | 2.2370 | 2.1514 | 2.4875 | = | 2.5362 | 2.5913 | 88.52 | 53.71 |
| K-10 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| K-10-9-8 | 2.2678 | 2.5671 | = | = | 2.7334 | 2.8106 | 76.07 | 8.95
|
| K-10-9-7 | 2.2558 | 2.5189 | = | 2.4771 | 2.7160 | 2.7940 | 73.40 | 5.17
|
| K-10-9-6 | 2.2475 | 2.4701 | = | 2.4771 | 2.6997 | 2.7748 | 71.31 | 3.22
|
| K-10-9-5 | 2.2403 | 2.4382 | = | 2.4771 | 2.6827 | 2.7544 | 72.96 | 4.62
|
| K-10-9-4 | 2.2376 | 2.4223 | = | 2.4771 | 2.6713 | 2.7417 | 73.93 | 5.73
|
| K-10-9-3 | 2.2368 | 2.4162 | = | 2.4771 | 2.6653 | 2.7347 | 74.50 | 6.43
|
| K-10-9-2 | 2.2363 | 2.4140 | = | 2.4771 | 2.6638 | 2.7323 | 74.73 | 6.57
|
| K-10-8-7 | 2.1911 | 2.3531 | 2.4440 | = | 2.6296 | 2.7110 | 74.04 | 5.87
|
| K-10-8-6 | 2.1816 | 2.3266 | 2.3913 | 2.4314 | 2.6126 | 2.6925 | 74.26 | 6.15
|
| K-10-8-5 | 2.1734 | 2.2990 | 2.3590 | 2.4314 | 2.5948 | 2.6717 | 75.89 | 8.67
|
| K-10-8-4 | 2.1696 | 2.2855 | 2.3434 | 2.4314 | 2.5821 | 2.6579 | 76.92 | 9.93
|
| K-10-8-3 | 2.1687 | 2.2801 | 2.3377 | 2.4314 | 2.5749 | 2.6499 | 77.53 | 10.77
|
| K-10-8-2 | 2.1682 | 2.2782 | 2.3364 | 2.4314 | 2.5732 | 2.6477 | 77.72 | 11.33
|
| K-10-7-6 | 2.0991 | 2.1960 | 2.3837 | = | 2.5112 | 2.6020 | 77.96 | 12.17
|
| K-10-7-5 | 2.0951 | 2.1865 | 2.3516 | 2.3778 | 2.4981 | 2.5887 | 78.44 | 12.87
|
| K-10-7-4 | 2.0914 | 2.1778 | 2.3375 | 2.3778 | 2.4852 | 2.5755 | 79.33 | 14.83
|
| K-10-7-3 | 2.0907 | 2.1741 | 2.3327 | 2.3778 | 2.4769 | 2.5673 | 79.86 | 15.52
|
| K-10-7-2 | 2.0905 | 2.1726 | 2.3317 | 2.3778 | 2.4746 | 2.5651 | 80.02 | 16.22
|
| K-10-6-5 | 2.0492 | 2.1112 | 2.3502 | = | 2.4372 | 2.5258 | 81.46 | 20.70
|
| K-10-6-4 | 2.0490 | 2.1096 | 2.3364 | 2.3499 | 2.4313 | 2.5209 | 81.66 | 21.96
|
| K-10-6-3 | 2.0488 | 2.1083 | 2.3319 | 2.3499 | 2.4248 | 2.5155 | 81.93 | 23.36
|
| K-10-6-2 | 2.0488 | 2.1078 | 2.3312 | 2.3499 | 2.4224 | 2.5139 | 82.02 | 23.78
|
| K-10-5-4 | 2.0317 | 2.0755 | 2.3362 | = | 2.4000 | 2.4895 | 83.19 | 29.93
|
| K-10-5-3 | 2.0317 | 2.0755 | 2.3318 | 2.3362 | 2.3987 | 2.4886 | 83.23 | 30.49
|
| K-10-5-2 | 2.0317 | 2.0755 | 2.3312 | 2.3362 | 2.3974 | 2.4877 | 83.27 | 30.77
|
| K-10-4-3 | 2.0254 | 2.0625 | 2.3318 | = | 2.3881 | 2.4766 | 83.93 | 33.57
|
| K-10-4-2 | 2.0254 | 2.0625 | 2.3312 | 2.3318 | 2.3881 | 2.4766 | 83.93 | 33.57
|
| K-10-3-2 | 2.0241 | 2.0594 | 2.3312 | = | 2.3854 | 2.4719 | 84.30 | 35.24 |
| K-9 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| K-9-8-7 | 1.9073 | 2.3278 | = | = | 2.3805 | 2.4819 | 83.44 | 31.19
|
| K-9-8-6 | 1.9048 | 2.2974 | = | 2.2897 | 2.3718 | 2.4739 | 81.58 | 21.26
|
| K-9-8-5 | 1.9031 | 2.2688 | = | 2.2897 | 2.3631 | 2.4650 | 81.19 | 19.44
|
| K-9-8-4 | 1.9015 | 2.2552 | = | 2.2897 | 2.3555 | 2.4591 | 81.56 | 20.98
|
| K-9-8-3 | 1.9013 | 2.2507 | = | 2.2897 | 2.3505 | 2.4557 | 81.74 | 22.24
|
| K-9-8-2 | 1.9013 | 2.2498 | = | 2.2897 | 2.3493 | 2.4548 | 81.78 | 22.94
|
| K-9-7-6 | 1.8845 | 2.1708 | 2.2717 | = | 2.3218 | 2.4336 | 82.32 | 24.90
|
| K-9-7-5 | 1.8828 | 2.1606 | 2.2427 | 2.2634 | 2.3136 | 2.4257 | 82.14 | 24.20
|
| K-9-7-4 | 1.8813 | 2.1517 | 2.2291 | 2.2634 | 2.3061 | 2.4189 | 82.58 | 26.29
|
| K-9-7-3 | 1.8811 | 2.1485 | 2.2242 | 2.2634 | 2.3004 | 2.4149 | 82.81 | 27.27
|
| K-9-7-2 | 1.8811 | 2.1476 | 2.2229 | 2.2634 | 2.2988 | 2.4139 | 82.87 | 27.83
|
| K-9-6-5 | 1.8579 | 2.0868 | 2.2387 | = | 2.2674 | 2.3795 | 84.01 | 33.99
|
| K-9-6-4 | 1.8579 | 2.0850 | 2.2260 | 2.2378 | 2.2629 | 2.3759 | 84.12 | 34.55
|
| K-9-6-3 | 1.8579 | 2.0837 | 2.2220 | 2.2378 | 2.2579 | 2.3727 | 84.29 | 35.10
|
| K-9-6-2 | 1.8579 | 2.0831 | 2.2214 | 2.2378 | 2.2560 | 2.3718 | 84.36 | 35.52
|
| K-9-5-4 | 1.8490 | 2.0520 | 2.2256 | = | 2.2365 | 2.3521 | 85.12 | 39.58
|
| K-9-5-3 | 1.8490 | 2.0518 | 2.2218 | 2.2256 | 2.2354 | 2.3518 | 85.13 | 39.72
|
| K-9-5-2 | 1.8490 | 2.0516 | 2.2214 | 2.2256 | 2.2343 | 2.3515 | 85.14 | 40.00
|
| K-9-4-3 | 1.8452 | 2.0383 | 2.2218 | = | 2.2267 | 2.3426 | 85.70 | 40.70
|
| K-9-4-2 | 1.8452 | 2.0383 | 2.2214 | 2.2218 | 2.2267 | 2.3426 | 85.70 | 40.70
|
| K-9-3-2 | 1.8441 | 2.0348 | 2.2214 | = | 2.2247 | 2.3391 | 86.03 | 42.94 |
| K-x | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| K-8-7-6 | 1.7248 | 2.1638 | = | = | 2.1491 | 2.2493 | 89.38 | 58.46
|
| K-8-7-5 | 1.7248 | 2.1529 | = | 2.1527 | 2.1465 | 2.2476 | 88.81 | 55.24
|
| K-8-7-4 | 1.7248 | 2.1438 | = | 2.1527 | 2.1446 | 2.2463 | 88.52 | 53.71
|
| K-8-7-3 | 1.7248 | 2.1407 | = | 2.1527 | 2.1427 | 2.2451 | 88.59 | 53.99
|
| K-8-7-2 | 1.7248 | 2.1400 | = | 2.1527 | 2.1418 | 2.2449 | 88.61 | 54.13
|
| K-8-6-5 | 1.7222 | 2.0791 | 2.1436 | = | 2.1313 | 2.2348 | 88.80 | 55.10
|
| K-8-6-4 | 1.7222 | 2.0769 | 2.1340 | 2.1416 | 2.1294 | 2.2335 | 88.62 | 54.27
|
| K-8-6-3 | 1.7222 | 2.0756 | 2.1309 | 2.1416 | 2.1275 | 2.2323 | 88.69 | 54.83
|
| K-8-6-2 | 1.7222 | 2.0751 | 2.1301 | 2.1416 | 2.1267 | 2.2322 | 88.71 | 54.97
|
| K-8-5-4 | 1.7190 | 2.0451 | 2.1330 | = | 2.1136 | 2.2196 | 89.14 | 57.20
|
| K-8-5-3 | 1.7190 | 2.0450 | 2.1304 | 2.1330 | 2.1131 | 2.2196 | 89.14 | 57.20
|
| K-8-5-2 | 1.7190 | 2.0450 | 2.1301 | 2.1330 | 2.1127 | 2.2196 | 89.14 | 57.20
|
| K-8-4-3 | 1.7175 | 2.0319 | 2.1304 | = | 2.1072 | 2.2140 | 89.41 | 58.60
|
| K-8-4-2 | 1.7175 | 2.0319 | 2.1301 | 2.1304 | 2.1072 | 2.2140 | 89.41 | 58.60
|
| K-8-3-2 | 1.7172 | 2.0276 | 2.1301 | = | 2.1052 | 2.2116 | 89.61 | 59.86
|
| K-7-6-5 | 1.6530 | 2.0770 | = | = | 2.0455 | 2.1412 | 91.44 | 67.55
|
| K-7-6-4 | 1.6530 | 2.0749 | = | 2.0758 | 2.0455 | 2.1412 | 91.28 | 66.29
|
| K-7-6-3 | 1.6530 | 2.0738 | = | 2.0758 | 2.0455 | 2.1412 | 91.28 | 66.29
|
| K-7-6-2 | 1.6530 | 2.0734 | = | 2.0758 | 2.0455 | 2.1412 | 91.28 | 66.29
|
| K-7-5-4 | 1.6530 | 2.0442 | 2.0744 | = | 2.0431 | 2.1394 | 91.34 | 66.99
|
| K-7-5-3 | 1.6530 | 2.0442 | 2.0735 | 2.0744 | 2.0431 | 2.1394 | 91.34 | 66.99
|
| K-7-5-2 | 1.6530 | 2.0442 | 2.0734 | 2.0744 | 2.0431 | 2.1394 | 91.34 | 66.99
|
| K-7-4-3 | 1.6526 | 2.0317 | 2.0735 | = | 2.0409 | 2.1374 | 91.47 | 67.69
|
| K-7-4-2 | 1.6526 | 2.0317 | 2.0734 | 2.0735 | 2.0409 | 2.1374 | 91.47 | 67.69
|
| K-7-3-2 | 1.6526 | 2.0274 | 2.0734 | = | 2.0398 | 2.1363 | 91.57 | 68.11
|
| K-6-5-4 | 1.6255 | 2.0442 | = | = | 2.0125 | 2.1022 | 92.08 | 72.17
|
| K-6-5-3 | 1.6255 | 2.0442 | = | 2.0442 | 2.0125 | 2.1022 | 92.08 | 72.17
|
| K-6-5-2 | 1.6255 | 2.0442 | = | 2.0442 | 2.0125 | 2.1022 | 92.08 | 72.17
|
| K-6-4-3 | 1.6255 | 2.0317 | 2.0442 | = | 2.0125 | 2.1022 | 92.08 | 72.17
|
| K-6-4-2 | 1.6255 | 2.0317 | 2.0442 | 2.0442 | 2.0125 | 2.1022 | 92.08 | 72.17
|
| K-6-3-2 | 1.6255 | 2.0274 | 2.0442 | = | 2.0125 | 2.1022 | 92.08 | 72.17
|
| K-5-4-3 | 1.6162 | 2.0317 | = | = | 2.0024 | 2.0880 | 92.23 | 73.71
|
| K-5-4-2 | 1.6162 | 2.0317 | = | 2.0317 | 2.0024 | 2.0880 | 92.23 | 73.71
|
| K-5-3-2 | 1.6162 | 2.0274 | 2.0317 | = | 2.0024 | 2.0880 | 92.23 | 73.71
|
| K-4-3-2 | 1.6143 | 2.0274 | = | = | 2.0005 | 2.0837 | 92.23 | 73.71 |
| Study 8C05 Main | | Top Leading Authority |
Queen Holdings
| Q-J | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| Q-J-10-9 | 2.7095 | = | = | = | 2.6512 | 2.7095 | 100.00 | 96.22
|
| Q-J-10-8 | 2.6674 | = | = | 2.4001 | 2.6418 | 2.7001 | 97.35 | 87.27
|
| Q-J-10-7 | 2.6198 | = | = | 2.4001 | 2.6323 | 2.6906 | 94.31 | 79.30
|
| Q-J-10-6 | 2.5779 | = | = | 2.4001 | 2.6245 | 2.6817 | 91.53 | 67.97
|
| Q-J-10-5 | 2.5532 | = | = | 2.4001 | 2.6170 | 2.6730 | 90.27 | 63.50
|
| Q-J-10-4 | 2.5422 | = | = | 2.4001 | 2.6114 | 2.6673 | 89.82 | 61.26
|
| Q-J-10-3 | 2.5381 | = | = | 2.4001 | 2.6082 | 2.6640 | 89.76 | 60.56
|
| Q-J-10-2 | 2.5370 | = | = | 2.4001 | 2.6071 | 2.6625 | 89.80 | 60.98
|
| Q-J-9-8 | 2.5605 | = | 2.3941 | = | 2.5704 | 2.6326 | 93.59 | 77.62
|
| Q-J-9-7 | 2.5155 | = | 2.3626 | 2.3762 | 2.5622 | 2.6216 | 91.30 | 66.85
|
| Q-J-9-6 | 2.4754 | = | 2.3248 | 2.3762 | 2.5556 | 2.6120 | 88.92 | 55.80
|
| Q-J-9-5 | 2.4497 | = | 2.2974 | 2.3762 | 2.5488 | 2.6034 | 87.76 | 50.91
|
| Q-J-9-4 | 2.4383 | = | 2.2824 | 2.3762 | 2.5436 | 2.5976 | 87.39 | 48.39
|
| Q-J-9-3 | 2.4348 | = | 2.2755 | 2.3762 | 2.5405 | 2.5944 | 87.39 | 48.39
|
| Q-J-9-2 | 2.4340 | = | 2.2726 | 2.3762 | 2.5398 | 2.5935 | 87.43 | 49.09
|
| Q-J-8-7 | 2.3692 | = | 2.3468 | = | 2.4946 | 2.5593 | 82.40 | 25.17
|
| Q-J-8-6 | 2.3399 | = | 2.3026 | 2.3345 | 2.4868 | 2.5488 | 81.35 | 20.28
|
| Q-J-8-5 | 2.3118 | = | 2.2733 | 2.3345 | 2.4792 | 2.5392 | 82.15 | 24.34
|
| Q-J-8-4 | 2.2981 | = | 2.2576 | 2.3345 | 2.4731 | 2.5321 | 82.69 | 26.85
|
| Q-J-8-3 | 2.2937 | = | 2.2503 | 2.3345 | 2.4692 | 2.5274 | 83.07 | 28.95
|
| Q-J-8-2 | 2.2924 | = | 2.2480 | 2.3345 | 2.4680 | 2.5263 | 83.17 | 29.79
|
| Q-J-7-6 | 2.2096 | = | 2.2944 | = | 2.4110 | 2.4854 | 82.98 | 28.25
|
| Q-J-7-5 | 2.2002 | = | 2.2667 | 2.2913 | 2.4054 | 2.4779 | 83.34 | 31.05
|
| Q-J-7-4 | 2.1913 | = | 2.2531 | 2.2913 | 2.4001 | 2.4713 | 83.80 | 33.01
|
| Q-J-7-3 | 2.1888 | = | 2.2477 | 2.2913 | 2.3961 | 2.4669 | 84.11 | 34.41
|
| Q-J-7-2 | 2.1882 | = | 2.2461 | 2.2913 | 2.3951 | 2.4656 | 84.22 | 34.97
|
| Q-J-6-5 | 2.1286 | = | 2.2655 | = | 2.3571 | 2.4317 | 84.82 | 37.90
|
| Q-J-6-4 | 2.1271 | = | 2.2524 | 2.2655 | 2.3543 | 2.4295 | 84.91 | 38.74
|
| Q-J-6-3 | 2.1261 | = | 2.2474 | 2.2655 | 2.3511 | 2.4270 | 85.03 | 39.16
|
| Q-J-6-2 | 2.1258 | = | 2.2461 | 2.2655 | 2.3499 | 2.4263 | 85.06 | 39.44
|
| Q-J-5-4 | 2.0980 | = | 2.2524 | = | 2.3301 | 2.4052 | 85.79 | 41.26
|
| Q-J-5-3 | 2.0980 | = | 2.2474 | 2.2524 | 2.3293 | 2.4048 | 85.80 | 41.40
|
| Q-J-5-2 | 2.0980 | = | 2.2461 | 2.2524 | 2.3286 | 2.4045 | 85.81 | 41.54
|
| Q-J-4-3 | 2.0873 | = | 2.2474 | = | 2.3208 | 2.3949 | 86.23 | 43.64
|
| Q-J-4-2 | 2.0873 | = | 2.2461 | 2.2474 | 2.3208 | 2.3949 | 86.23 | 43.64
|
| Q-J-3-2 | 2.0854 | = | 2.2461 | = | 2.3182 | 2.3906 | 86.50 | 44.62 |
| Q-10 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| Q-10-9-8 | 2.2027 | 2.3710 | = | = | 2.4573 | 2.5420 | 84.69 | 37.06
|
| Q-10-9-7 | 2.1846 | 2.3329 | = | 2.2821 | 2.4492 | 2.5338 | 82.26 | 24.62
|
| Q-10-9-6 | 2.1714 | 2.2906 | = | 2.2821 | 2.4425 | 2.5233 | 79.14 | 14.55
|
| Q-10-9-5 | 2.1602 | 2.2596 | = | 2.2821 | 2.4357 | 2.5121 | 79.87 | 15.66
|
| Q-10-9-4 | 2.1551 | 2.2432 | = | 2.2821 | 2.4305 | 2.5036 | 80.63 | 17.06
|
| Q-10-9-3 | 2.1533 | 2.2363 | = | 2.2821 | 2.4274 | 2.4977 | 81.20 | 19.58
|
| Q-10-9-2 | 2.1521 | 2.2334 | = | 2.2821 | 2.4267 | 2.4953 | 81.45 | 20.56
|
| Q-10-8-7 | 2.1049 | 2.1891 | 2.2560 | = | 2.3761 | 2.4596 | 81.64 | 21.68
|
| Q-10-8-6 | 2.0906 | 2.1651 | 2.2144 | 2.2474 | 2.3691 | 2.4508 | 81.58 | 21.26
|
| Q-10-8-5 | 2.0783 | 2.1394 | 2.1863 | 2.2474 | 2.3619 | 2.4408 | 82.41 | 25.31
|
| Q-10-8-4 | 2.0722 | 2.1264 | 2.1718 | 2.2474 | 2.3563 | 2.4326 | 83.09 | 29.37
|
| Q-10-8-3 | 2.0705 | 2.1209 | 2.1654 | 2.2474 | 2.3528 | 2.4267 | 83.61 | 32.03
|
| Q-10-8-2 | 2.0696 | 2.1187 | 2.1635 | 2.2474 | 2.3520 | 2.4248 | 83.79 | 32.87
|
| Q-10-7-6 | 1.9883 | 2.0400 | 2.2075 | = | 2.2915 | 2.3815 | 83.74 | 32.73
|
| Q-10-7-5 | 1.9820 | 2.0301 | 2.1790 | 2.2030 | 2.2859 | 2.3747 | 83.94 | 33.85
|
| Q-10-7-4 | 1.9764 | 2.0208 | 2.1652 | 2.2030 | 2.2806 | 2.3677 | 84.45 | 35.94
|
| Q-10-7-3 | 1.9750 | 2.0167 | 2.1600 | 2.2030 | 2.2766 | 2.3625 | 84.85 | 38.04
|
| Q-10-7-2 | 1.9743 | 2.0149 | 2.1585 | 2.2030 | 2.2756 | 2.3608 | 84.99 | 39.02
|
| Q-10-6-5 | 1.9237 | 1.9574 | 2.1769 | = | 2.2330 | 2.3252 | 85.67 | 40.56
|
| Q-10-6-4 | 1.9231 | 1.9559 | 2.1640 | 2.1769 | 2.2302 | 2.3222 | 85.84 | 41.96
|
| Q-10-6-3 | 1.9227 | 1.9544 | 2.1594 | 2.1769 | 2.2270 | 2.3184 | 86.08 | 43.22
|
| Q-10-6-2 | 1.9224 | 1.9536 | 2.1585 | 2.1769 | 2.2258 | 2.3169 | 86.18 | 43.50
|
| Q-10-5-4 | 1.9012 | 1.9247 | 2.1640 | = | 2.2030 | 2.2953 | 86.93 | 46.15
|
| Q-10-5-3 | 1.9012 | 1.9247 | 2.1594 | 2.1640 | 2.2023 | 2.2944 | 86.99 | 46.29
|
| Q-10-5-2 | 1.9012 | 1.9247 | 2.1585 | 2.1640 | 2.2016 | 2.2934 | 87.05 | 46.71
|
| Q-10-4-3 | 1.8936 | 1.9136 | 2.1594 | = | 2.1932 | 2.2841 | 87.47 | 49.51
|
| Q-10-4-2 | 1.8936 | 1.9136 | 2.1585 | 2.1594 | 2.1932 | 2.2841 | 87.47 | 49.51
|
| Q-10-3-2 | 1.8922 | 1.9109 | 2.1585 | = | 2.1909 | 2.2805 | 87.72 | 50.63 |
| Q-9 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| Q-9-8-7 | 1.7950 | 2.1361 | = | = | 2.2000 | 2.3109 | 83.83 | 33.29
|
| Q-9-8-6 | 1.7910 | 2.1113 | = | 2.0980 | 2.1959 | 2.3066 | 82.09 | 23.92
|
| Q-9-8-5 | 1.7884 | 2.0867 | = | 2.0980 | 2.1919 | 2.3018 | 81.12 | 18.60
|
| Q-9-8-4 | 1.7862 | 2.0742 | = | 2.0980 | 2.1884 | 2.2979 | 81.40 | 20.42
|
| Q-9-8-3 | 1.7858 | 2.0691 | = | 2.0980 | 2.1859 | 2.2947 | 81.64 | 21.68
|
| Q-9-8-2 | 1.7856 | 2.0676 | = | 2.0980 | 2.1851 | 2.2934 | 81.75 | 22.38
|
| Q-9-7-6 | 1.7635 | 1.9909 | 2.0777 | = | 2.1420 | 2.2579 | 82.68 | 26.71
|
| Q-9-7-5 | 1.7608 | 1.9811 | 2.0510 | 2.0719 | 2.1382 | 2.2534 | 82.56 | 26.15
|
| Q-9-7-4 | 1.7586 | 1.9721 | 2.0379 | 2.0719 | 2.1347 | 2.2493 | 82.85 | 27.69
|
| Q-9-7-3 | 1.7582 | 1.9687 | 2.0332 | 2.0719 | 2.1320 | 2.2460 | 83.10 | 29.51
|
| Q-9-7-2 | 1.7580 | 1.9674 | 2.0319 | 2.0719 | 2.1311 | 2.2448 | 83.19 | 29.93
|
| Q-9-6-5 | 1.7265 | 1.9120 | 2.0473 | = | 2.0855 | 2.2023 | 84.44 | 35.66
|
| Q-9-6-4 | 1.7265 | 1.9101 | 2.0356 | 2.0470 | 2.0834 | 2.1997 | 84.59 | 36.64
|
| Q-9-6-3 | 1.7264 | 1.9085 | 2.0319 | 2.0470 | 2.0812 | 2.1969 | 84.80 | 37.76
|
| Q-9-6-2 | 1.7263 | 1.9076 | 2.0314 | 2.0470 | 2.0803 | 2.1956 | 84.91 | 38.74
|
| Q-9-5-4 | 1.7138 | 1.8814 | 2.0354 | = | 2.0540 | 2.1729 | 85.71 | 40.98
|
| Q-9-5-3 | 1.7138 | 1.8810 | 2.0318 | 2.0354 | 2.0535 | 2.1722 | 85.76 | 41.12
|
| Q-9-5-2 | 1.7138 | 1.8805 | 2.0314 | 2.0354 | 2.0530 | 2.1714 | 85.82 | 41.82
|
| Q-9-4-3 | 1.7086 | 1.8700 | 2.0318 | = | 2.0439 | 2.1620 | 86.34 | 44.20
|
| Q-9-4-2 | 1.7086 | 1.8700 | 2.0314 | 2.0318 | 2.0439 | 2.1620 | 86.34 | 44.20
|
| Q-9-3-2 | 1.7072 | 1.8673 | 2.0314 | = | 2.0418 | 2.1587 | 86.62 | 45.31 |
| Q-x | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| Q-8-7-6 | 1.5782 | 1.9781 | = | = | 1.9723 | 2.0879 | 88.13 | 52.87
|
| Q-8-7-5 | 1.5782 | 1.9670 | = | 1.9685 | 1.9710 | 2.0864 | 87.44 | 49.37
|
| Q-8-7-4 | 1.5782 | 1.9577 | = | 1.9685 | 1.9701 | 2.0853 | 87.53 | 49.79
|
| Q-8-7-3 | 1.5782 | 1.9545 | = | 1.9685 | 1.9691 | 2.0843 | 87.60 | 50.07
|
| Q-8-7-2 | 1.5782 | 1.9539 | = | 1.9685 | 1.9687 | 2.0837 | 87.66 | 50.35
|
| Q-8-6-5 | 1.5744 | 1.9000 | 1.9590 | = | 1.9507 | 2.0706 | 87.96 | 51.75
|
| Q-8-6-4 | 1.5744 | 1.8979 | 1.9501 | 1.9579 | 1.9498 | 2.0695 | 87.88 | 51.61
|
| Q-8-6-3 | 1.5744 | 1.8965 | 1.9472 | 1.9579 | 1.9488 | 2.0685 | 87.96 | 51.75
|
| Q-8-6-2 | 1.5744 | 1.8959 | 1.9467 | 1.9579 | 1.9484 | 2.0680 | 88.01 | 52.17
|
| Q-8-5-4 | 1.5700 | 1.8700 | 1.9495 | = | 1.9302 | 2.0524 | 88.63 | 54.41
|
| Q-8-5-3 | 1.5700 | 1.8699 | 1.9469 | 1.9495 | 1.9300 | 2.0522 | 88.65 | 54.55
|
| Q-8-5-2 | 1.5700 | 1.8697 | 1.9467 | 1.9495 | 1.9298 | 2.0520 | 88.67 | 54.69
|
| Q-8-4-3 | 1.5679 | 1.8596 | 1.9469 | = | 1.9228 | 2.0467 | 88.92 | 55.80
|
| Q-8-4-2 | 1.5679 | 1.8596 | 1.9467 | 1.9469 | 1.9228 | 2.0467 | 88.92 | 55.80
|
| Q-8-3-2 | 1.5673 | 1.8562 | 1.9467 | = | 1.9209 | 2.0449 | 89.06 | 56.64
|
| Q-7-6-5 | 1.4914 | 1.8966 | = | = | 1.8602 | 1.9769 | 90.89 | 65.03
|
| Q-7-6-4 | 1.4914 | 1.8947 | = | 1.8954 | 1.8602 | 1.9769 | 90.71 | 64.48
|
| Q-7-6-3 | 1.4914 | 1.8937 | = | 1.8954 | 1.8602 | 1.9769 | 90.71 | 64.48
|
| Q-7-6-2 | 1.4914 | 1.8934 | = | 1.8954 | 1.8602 | 1.9769 | 90.71 | 64.48
|
| Q-7-5-4 | 1.4914 | 1.8682 | 1.8940 | = | 1.8570 | 1.9738 | 90.89 | 65.03
|
| Q-7-5-3 | 1.4914 | 1.8682 | 1.8931 | 1.8940 | 1.8570 | 1.9738 | 90.89 | 65.03
|
| Q-7-5-2 | 1.4914 | 1.8682 | 1.8931 | 1.8940 | 1.8570 | 1.9738 | 90.89 | 65.03
|
| Q-7-4-3 | 1.4910 | 1.8587 | 1.8931 | = | 1.8545 | 1.9713 | 91.07 | 65.73
|
| Q-7-4-2 | 1.4910 | 1.8587 | 1.8931 | 1.8931 | 1.8545 | 1.9713 | 91.07 | 65.73
|
| Q-7-3-2 | 1.4910 | 1.8554 | 1.8931 | = | 1.8537 | 1.9701 | 91.18 | 66.01
|
| Q-6-5-4 | 1.4570 | 1.8682 | = | = | 1.8249 | 1.9379 | 91.85 | 70.63
|
| Q-6-5-3 | 1.4570 | 1.8682 | = | 1.8682 | 1.8249 | 1.9379 | 91.85 | 70.63
|
| Q-6-5-2 | 1.4570 | 1.8682 | = | 1.8682 | 1.8249 | 1.9379 | 91.85 | 70.63
|
| Q-6-4-3 | 1.4570 | 1.8587 | 1.8682 | = | 1.8249 | 1.9379 | 91.85 | 70.63
|
| Q-6-4-2 | 1.4570 | 1.8587 | 1.8682 | 1.8682 | 1.8249 | 1.9379 | 91.85 | 70.63
|
| Q-6-3-2 | 1.4570 | 1.8554 | 1.8682 | = | 1.8249 | 1.9379 | 91.85 | 70.63
|
| Q-5-4-3 | 1.4448 | 1.8587 | = | = | 1.8152 | 1.9247 | 92.20 | 73.29
|
| Q-5-4-2 | 1.4448 | 1.8587 | = | 1.8587 | 1.8152 | 1.9247 | 92.20 | 73.29
|
| Q-5-3-2 | 1.4448 | 1.8554 | 1.8587 | = | 1.8152 | 1.9247 | 92.20 | 73.29
|
| Q-4-3-2 | 1.4428 | 1.8554 | = | = | 1.8128 | 1.9204 | 92.28 | 74.27 |
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-10 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| J-10-9-8 | 2.1635 | = | = | = | 2.0595 | 2.1635 | 100.00 | 96.22
|
| J-10-9-7 | 2.1404 | = | = | 1.9623 | 2.0574 | 2.1614 | 98.75 | 91.75
|
| J-10-9-6 | 2.1244 | = | = | 1.9623 | 2.0561 | 2.1591 | 97.89 | 87.97
|
| J-10-9-5 | 2.1092 | = | = | 1.9623 | 2.0549 | 2.1572 | 96.86 | 86.43
|
| J-10-9-4 | 2.1019 | = | = | 1.9623 | 2.0539 | 2.1553 | 96.47 | 85.87
|
| J-10-9-3 | 2.0991 | = | = | 1.9623 | 2.0530 | 2.1534 | 96.39 | 85.73
|
| J-10-9-2 | 2.0976 | = | = | 1.9623 | 2.0526 | 2.1525 | 96.33 | 85.59
|
| J-10-8-7 | 2.0528 | = | 1.9563 | = | 2.0186 | 2.1294 | 93.73 | 77.76
|
| J-10-8-6 | 2.0358 | = | 1.9381 | 1.9476 | 2.0173 | 2.1269 | 92.86 | 77.48
|
| J-10-8-5 | 2.0195 | = | 1.9212 | 1.9476 | 2.0161 | 2.1249 | 91.80 | 69.79
|
| J-10-8-4 | 2.0111 | = | 1.9111 | 1.9476 | 2.0150 | 2.1229 | 91.36 | 67.41
|
| J-10-8-3 | 2.0084 | = | 1.9062 | 1.9476 | 2.0142 | 2.1211 | 91.29 | 66.71
|
| J-10-8-2 | 2.0071 | = | 1.9047 | 1.9476 | 2.0138 | 2.1202 | 91.25 | 66.15
|
| J-10-7-6 | 1.9212 | = | 1.9303 | = | 1.9819 | 2.0926 | 87.33 | 47.97
|
| J-10-7-5 | 1.9130 | = | 1.9129 | 1.9254 | 1.9807 | 2.0910 | 87.06 | 46.85
|
| J-10-7-4 | 1.9056 | = | 1.9038 | 1.9254 | 1.9796 | 2.0894 | 87.18 | 47.69
|
| J-10-7-3 | 1.9034 | = | 1.9006 | 1.9254 | 1.9788 | 2.0880 | 87.29 | 47.83
|
| J-10-7-2 | 1.9025 | = | 1.8995 | 1.9254 | 1.9784 | 2.0874 | 87.34 | 48.11
|
| J-10-6-5 | 1.8475 | = | 1.9104 | = | 1.9515 | 2.0682 | 87.56 | 49.93
|
| J-10-6-4 | 1.8467 | = | 1.9024 | 1.9104 | 1.9509 | 2.0672 | 87.62 | 50.21
|
| J-10-6-3 | 1.8461 | = | 1.8999 | 1.9104 | 1.9503 | 2.0661 | 87.71 | 50.49
|
| J-10-6-2 | 1.8457 | = | 1.8995 | 1.9104 | 1.9500 | 2.0655 | 87.75 | 50.77
|
| J-10-5-4 | 1.8203 | = | 1.9024 | = | 1.9344 | 2.0556 | 87.81 | 51.05
|
| J-10-5-3 | 1.8203 | = | 1.8999 | 1.9024 | 1.9343 | 2.0552 | 87.84 | 51.19
|
| J-10-5-2 | 1.8203 | = | 1.8995 | 1.9024 | 1.9342 | 2.0549 | 87.87 | 51.33
|
| J-10-4-3 | 1.8108 | = | 1.8999 | = | 1.9296 | 2.0509 | 88.04 | 52.31
|
| J-10-4-2 | 1.8108 | = | 1.8995 | 1.8999 | 1.9296 | 2.0509 | 88.04 | 52.31
|
| J-10-3-2 | 1.8083 | = | 1.8995 | = | 1.9292 | 2.0493 | 88.18 | 53.29 |
| J-9 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| J-9-8-7 | 1.7300 | 1.9259 | = | = | 1.9189 | 2.0437 | 90.52 | 64.06
|
| J-9-8-6 | 1.7255 | 1.9093 | = | 1.8902 | 1.9175 | 2.0418 | 89.24 | 58.04
|
| J-9-8-5 | 1.7219 | 1.8929 | = | 1.8902 | 1.9164 | 2.0402 | 87.87 | 51.33
|
| J-9-8-4 | 1.7187 | 1.8828 | = | 1.8902 | 1.9153 | 2.0385 | 86.91 | 46.01
|
| J-9-8-3 | 1.7177 | 1.8787 | = | 1.8902 | 1.9144 | 2.0370 | 87.04 | 46.57
|
| J-9-8-2 | 1.7172 | 1.8776 | = | 1.8902 | 1.9141 | 2.0363 | 87.11 | 47.41
|
| J-9-7-6 | 1.6951 | 1.8070 | 1.8740 | = | 1.8838 | 2.0082 | 88.04 | 52.31
|
| J-9-7-5 | 1.6917 | 1.7991 | 1.8568 | 1.8701 | 1.8826 | 2.0066 | 87.96 | 51.75
|
| J-9-7-4 | 1.6887 | 1.7913 | 1.8474 | 1.8701 | 1.8816 | 2.0051 | 88.08 | 52.73
|
| J-9-7-3 | 1.6877 | 1.7885 | 1.8444 | 1.8701 | 1.8807 | 2.0036 | 88.20 | 53.43
|
| J-9-7-2 | 1.6873 | 1.7877 | 1.8435 | 1.8701 | 1.8803 | 2.0030 | 88.24 | 53.57
|
| J-9-6-5 | 1.6522 | 1.7381 | 1.8542 | = | 1.8538 | 1.9785 | 89.02 | 56.36
|
| J-9-6-4 | 1.6519 | 1.7361 | 1.8457 | 1.8542 | 1.8531 | 1.9776 | 89.08 | 56.78
|
| J-9-6-3 | 1.6513 | 1.7343 | 1.8435 | 1.8542 | 1.8525 | 1.9765 | 89.18 | 57.62
|
| J-9-6-2 | 1.6509 | 1.7333 | 1.8435 | 1.8542 | 1.8522 | 1.9759 | 89.23 | 57.90
|
| J-9-5-4 | 1.6357 | 1.7107 | 1.8457 | = | 1.8354 | 1.9620 | 89.74 | 60.42
|
| J-9-5-3 | 1.6355 | 1.7101 | 1.8435 | 1.8457 | 1.8352 | 1.9616 | 89.77 | 60.70
|
| J-9-5-2 | 1.6352 | 1.7094 | 1.8435 | 1.8457 | 1.8351 | 1.9613 | 89.81 | 61.12
|
| J-9-4-3 | 1.6282 | 1.6994 | 1.8435 | = | 1.8298 | 1.9560 | 90.16 | 62.52
|
| J-9-4-2 | 1.6282 | 1.6994 | 1.8435 | 1.8435 | 1.8298 | 1.9560 | 90.16 | 62.52
|
| J-9-3-2 | 1.6261 | 1.6966 | 1.8435 | = | 1.8287 | 1.9542 | 90.37 | 63.92 |
| J-x | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| J-8-7-6 | 1.4984 | 1.7875 | = | = | 1.7501 | 1.8824 | 90.04 | 61.82
|
| J-8-7-5 | 1.4982 | 1.7774 | = | 1.7756 | 1.7496 | 1.8817 | 89.49 | 59.16
|
| J-8-7-4 | 1.4981 | 1.7689 | = | 1.7756 | 1.7493 | 1.8813 | 89.01 | 56.22
|
| J-8-7-3 | 1.4979 | 1.7665 | = | 1.7756 | 1.7490 | 1.8808 | 89.05 | 56.50
|
| J-8-7-2 | 1.4978 | 1.7660 | = | 1.7756 | 1.7488 | 1.8805 | 89.08 | 56.78
|
| J-8-6-5 | 1.4921 | 1.7152 | 1.7662 | = | 1.7343 | 1.8684 | 89.59 | 59.72
|
| J-8-6-4 | 1.4919 | 1.7129 | 1.7578 | 1.7659 | 1.7340 | 1.8679 | 89.58 | 59.58
|
| J-8-6-3 | 1.4918 | 1.7115 | 1.7557 | 1.7659 | 1.7337 | 1.8675 | 89.62 | 60.00
|
| J-8-6-2 | 1.4916 | 1.7110 | 1.7556 | 1.7659 | 1.7335 | 1.8672 | 89.64 | 60.14
|
| J-8-5-4 | 1.4845 | 1.6872 | 1.7577 | = | 1.7196 | 1.8552 | 90.25 | 63.22
|
| J-8-5-3 | 1.4844 | 1.6869 | 1.7556 | 1.7577 | 1.7195 | 1.8551 | 90.26 | 63.36
|
| J-8-5-2 | 1.4844 | 1.6867 | 1.7556 | 1.7577 | 1.7194 | 1.8549 | 90.28 | 63.64
|
| J-8-4-3 | 1.4807 | 1.6771 | 1.7556 | = | 1.7143 | 1.8507 | 90.58 | 64.20
|
| J-8-4-2 | 1.4807 | 1.6771 | 1.7556 | 1.7556 | 1.7143 | 1.8507 | 90.58 | 64.20
|
| J-8-3-2 | 1.4796 | 1.6740 | 1.7556 | = | 1.7126 | 1.8493 | 90.75 | 64.90
|
| J-7-6-5 | 1.4018 | 1.7087 | = | = | 1.6567 | 1.7888 | 91.69 | 69.37
|
| J-7-6-4 | 1.4018 | 1.7068 | = | 1.7081 | 1.6567 | 1.7888 | 91.61 | 68.81
|
| J-7-6-3 | 1.4018 | 1.7059 | = | 1.7081 | 1.6567 | 1.7888 | 91.61 | 68.81
|
| J-7-6-2 | 1.4018 | 1.7058 | = | 1.7081 | 1.6567 | 1.7888 | 91.61 | 68.81
|
| J-7-5-4 | 1.4010 | 1.6841 | 1.7064 | = | 1.6535 | 1.7878 | 91.60 | 68.39
|
| J-7-5-3 | 1.4010 | 1.6841 | 1.7055 | 1.7064 | 1.6535 | 1.7878 | 91.60 | 68.39
|
| J-7-5-2 | 1.4010 | 1.6841 | 1.7055 | 1.7064 | 1.6535 | 1.7878 | 91.60 | 68.39
|
| J-7-4-3 | 1.4000 | 1.6754 | 1.7055 | = | 1.6514 | 1.7864 | 91.72 | 69.51
|
| J-7-4-2 | 1.4000 | 1.6754 | 1.7055 | 1.7055 | 1.6514 | 1.7864 | 91.72 | 69.51
|
| J-7-3-2 | 1.3997 | 1.6725 | 1.7055 | = | 1.6506 | 1.7858 | 91.80 | 69.79
|
| J-6-5-4 | 1.3612 | 1.6840 | = | = | 1.6249 | 1.7574 | 92.37 | 75.24
|
| J-6-5-3 | 1.3612 | 1.6840 | = | 1.6840 | 1.6249 | 1.7574 | 92.37 | 75.24
|
| J-6-5-2 | 1.3612 | 1.6840 | = | 1.6840 | 1.6249 | 1.7574 | 92.37 | 75.24
|
| J-6-4-3 | 1.3612 | 1.6753 | 1.6840 | = | 1.6249 | 1.7574 | 92.37 | 75.24
|
| J-6-4-2 | 1.3612 | 1.6753 | 1.6840 | 1.6840 | 1.6249 | 1.7574 | 92.37 | 75.24
|
| J-6-3-2 | 1.3612 | 1.6725 | 1.6840 | = | 1.6249 | 1.7574 | 92.37 | 75.24
|
| J-5-4-3 | 1.3463 | 1.6753 | = | = | 1.6153 | 1.7454 | 92.63 | 76.92
|
| J-5-4-2 | 1.3463 | 1.6753 | = | 1.6753 | 1.6153 | 1.7454 | 92.63 | 76.92
|
| J-5-3-2 | 1.3463 | 1.6725 | 1.6753 | = | 1.6153 | 1.7454 | 92.63 | 76.92
|
| J-4-3-2 | 1.3430 | 1.6725 | = | = | 1.6126 | 1.7408 | 92.78 | 77.34 |
“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
| 10-9 | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| 10-9-8-7 | 1.7004 | = | = | = | 1.5783 | 1.7004 | 100.00 | 96.22
|
| 10-9-8-6 | 1.6958 | = | = | 1.6533 | 1.5783 | 1.7001 | 99.75 | 94.97
|
| 10-9-8-5 | 1.6922 | = | = | 1.6533 | 1.5783 | 1.6999 | 99.51 | 92.87
|
| 10-9-8-4 | 1.6891 | = | = | 1.6533 | 1.5783 | 1.6997 | 99.29 | 92.73
|
| 10-9-8-3 | 1.6881 | = | = | 1.6533 | 1.5783 | 1.6996 | 99.20 | 92.17
|
| 10-9-8-2 | 1.6876 | = | = | 1.6533 | 1.5783 | 1.6994 | 99.16 | 91.89
|
| 10-9-7-6 | 1.6613 | = | 1.6490 | = | 1.5676 | 1.6916 | 97.62 | 87.69
|
| 10-9-7-5 | 1.6579 | = | 1.6424 | 1.6451 | 1.5676 | 1.6914 | 97.42 | 87.55
|
| 10-9-7-4 | 1.6549 | = | 1.6375 | 1.6451 | 1.5676 | 1.6912 | 97.23 | 87.13
|
| 10-9-7-3 | 1.6540 | = | 1.6356 | 1.6451 | 1.5676 | 1.6911 | 97.15 | 86.99
|
| 10-9-7-2 | 1.6535 | = | 1.6348 | 1.6451 | 1.5676 | 1.6909 | 97.12 | 86.85
|
| 10-9-6-5 | 1.6142 | = | 1.6398 | = | 1.5614 | 1.6859 | 94.60 | 81.54
|
| 10-9-6-4 | 1.6139 | = | 1.6358 | 1.6398 | 1.5614 | 1.6857 | 94.61 | 81.68
|
| 10-9-6-3 | 1.6133 | = | 1.6348 | 1.6398 | 1.5614 | 1.6856 | 94.63 | 81.82
|
| 10-9-6-2 | 1.6129 | = | 1.6348 | 1.6398 | 1.5614 | 1.6854 | 94.65 | 82.10
|
| 10-9-5-4 | 1.5970 | = | 1.6358 | = | 1.5565 | 1.6807 | 94.91 | 82.94
|
| 10-9-5-3 | 1.5967 | = | 1.6348 | 1.6358 | 1.5565 | 1.6807 | 94.92 | 83.08
|
| 10-9-5-2 | 1.5965 | = | 1.6348 | 1.6358 | 1.5565 | 1.6806 | 94.93 | 83.50
|
| 10-9-4-3 | 1.5894 | = | 1.6348 | = | 1.5547 | 1.6791 | 95.03 | 84.06
|
| 10-9-4-2 | 1.5894 | = | 1.6348 | 1.6348 | 1.5547 | 1.6791 | 95.03 | 84.06
|
| 10-9-3-2 | 1.5872 | = | 1.6348 | = | 1.5539 | 1.6786 | 95.09 | 84.34 |
| 10-x | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| 10-8-7-6 | 1.4604 | 1.6238 | = | = | 1.5166 | 1.6573 | 95.51 | 84.76
|
| 10-8-7-5 | 1.4601 | 1.6182 | = | 1.6060 | 1.5166 | 1.6571 | 95.20 | 84.48
|
| 10-8-7-4 | 1.4600 | 1.6140 | = | 1.6060 | 1.5166 | 1.6569 | 94.97 | 83.78
|
| 10-8-7-3 | 1.4599 | 1.6129 | = | 1.6060 | 1.5166 | 1.6568 | 94.92 | 83.08
|
| 10-8-7-2 | 1.4597 | 1.6127 | = | 1.6060 | 1.5166 | 1.6566 | 94.92 | 83.08
|
| 10-8-6-5 | 1.4527 | 1.5665 | 1.6006 | = | 1.5104 | 1.6509 | 94.05 | 77.90
|
| 10-8-6-4 | 1.4525 | 1.5655 | 1.5966 | 1.6006 | 1.5104 | 1.6508 | 94.06 | 78.04
|
| 10-8-6-3 | 1.4524 | 1.5649 | 1.5956 | 1.6006 | 1.5104 | 1.6506 | 94.08 | 78.18
|
| 10-8-6-2 | 1.4522 | 1.5647 | 1.5956 | 1.6006 | 1.5104 | 1.6505 | 94.10 | 78.32
|
| 10-8-5-4 | 1.4443 | 1.5438 | 1.5966 | = | 1.5056 | 1.6454 | 94.43 | 80.00
|
| 10-8-5-3 | 1.4442 | 1.5437 | 1.5956 | 1.5966 | 1.5056 | 1.6453 | 94.43 | 80.00
|
| 10-8-5-2 | 1.4442 | 1.5436 | 1.5956 | 1.5966 | 1.5056 | 1.6453 | 94.44 | 80.28
|
| 10-8-4-3 | 1.4403 | 1.5351 | 1.5956 | = | 1.5037 | 1.6436 | 94.57 | 81.26
|
| 10-8-4-2 | 1.4403 | 1.5351 | 1.5956 | 1.5956 | 1.5037 | 1.6436 | 94.57 | 81.26
|
| 10-8-3-2 | 1.4388 | 1.5320 | 1.5956 | = | 1.5029 | 1.6429 | 94.65 | 82.10
|
| 10-7-6-5 | 1.3598 | 1.5563 | = | = | 1.4548 | 1.6055 | 94.32 | 79.44
|
| 10-7-6-4 | 1.3598 | 1.5555 | = | 1.5552 | 1.4548 | 1.6055 | 94.27 | 79.16
|
| 10-7-6-3 | 1.3598 | 1.5550 | = | 1.5552 | 1.4548 | 1.6055 | 94.18 | 78.46
|
| 10-7-6-2 | 1.3598 | 1.5550 | = | 1.5552 | 1.4548 | 1.6055 | 94.18 | 78.46
|
| 10-7-5-4 | 1.3592 | 1.5381 | 1.5543 | = | 1.4535 | 1.6046 | 94.26 | 78.74
|
| 10-7-5-3 | 1.3592 | 1.5381 | 1.5539 | 1.5543 | 1.4535 | 1.6046 | 94.26 | 78.74
|
| 10-7-5-2 | 1.3592 | 1.5381 | 1.5539 | 1.5543 | 1.4535 | 1.6046 | 94.26 | 78.74
|
| 10-7-4-3 | 1.3583 | 1.5313 | 1.5539 | = | 1.4528 | 1.6037 | 94.33 | 79.58
|
| 10-7-4-2 | 1.3583 | 1.5313 | 1.5539 | 1.5539 | 1.4528 | 1.6037 | 94.33 | 79.58
|
| 10-7-3-2 | 1.3578 | 1.5288 | 1.5539 | = | 1.4525 | 1.6030 | 94.41 | 79.86
|
| 10-6-5-4 | 1.3191 | 1.5376 | = | = | 1.4328 | 1.5860 | 94.51 | 80.42
|
| 10-6-5-3 | 1.3191 | 1.5376 | = | 1.5376 | 1.4328 | 1.5860 | 94.51 | 80.42
|
| 10-6-5-2 | 1.3191 | 1.5376 | = | 1.5376 | 1.4328 | 1.5860 | 94.51 | 80.42
|
| 10-6-4-3 | 1.3191 | 1.5310 | 1.5376 | = | 1.4328 | 1.5858 | 94.53 | 80.84
|
| 10-6-4-2 | 1.3191 | 1.5310 | 1.5376 | 1.5376 | 1.4328 | 1.5858 | 94.53 | 80.84
|
| 10-6-3-2 | 1.3191 | 1.5288 | 1.5376 | = | 1.4328 | 1.5856 | 94.54 | 81.12
|
| 10-5-4-3 | 1.3036 | 1.5310 | = | = | 1.4261 | 1.5768 | 94.77 | 82.52
|
| 10-5-4-2 | 1.3036 | 1.5310 | = | 1.5310 | 1.4261 | 1.5768 | 94.77 | 82.52
|
| 10-5-3-2 | 1.3036 | 1.5288 | 1.5310 | = | 1.4261 | 1.5768 | 94.77 | 82.52
|
| 10-4-3-2 | 1.2998 | 1.5288 | = | = | 1.4244 | 1.5731 | 94.96 | 83.64 |
| 9-x | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| 9-8-7-6 | 1.4481 | = | = | = | 1.3135 | 1.4481 | 100.00 | 96.22
|
| 9-8-7-5 | 1.4479 | = | = | 1.4303 | 1.3135 | 1.4481 | 99.99 | 96.08
|
| 9-8-7-4 | 1.4477 | = | = | 1.4303 | 1.3135 | 1.4481 | 99.98 | 95.94
|
| 9-8-7-3 | 1.4476 | = | = | 1.4303 | 1.3135 | 1.4481 | 99.97 | 95.80
|
| 9-8-7-2 | 1.4474 | = | = | 1.4303 | 1.3135 | 1.4481 | 99.96 | 95.66
|
| 9-8-6-5 | 1.4399 | = | 1.4303 | = | 1.3135 | 1.4474 | 99.22 | 92.59
|
| 9-8-6-4 | 1.4397 | = | 1.4303 | 1.4303 | 1.3135 | 1.4474 | 99.21 | 92.45
|
| 9-8-6-3 | 1.4396 | = | 1.4303 | 1.4303 | 1.3135 | 1.4474 | 99.20 | 92.17
|
| 9-8-6-2 | 1.4395 | = | 1.4303 | 1.4303 | 1.3135 | 1.4474 | 99.19 | 92.03
|
| 9-8-5-4 | 1.4307 | = | 1.4303 | = | 1.3135 | 1.4470 | 98.06 | 88.81
|
| 9-8-5-3 | 1.4306 | = | 1.4303 | 1.4303 | 1.3135 | 1.4470 | 98.05 | 88.53
|
| 9-8-5-2 | 1.4306 | = | 1.4303 | 1.4303 | 1.3135 | 1.4470 | 98.05 | 88.53
|
| 9-8-4-3 | 1.4264 | = | 1.4303 | = | 1.3135 | 1.4467 | 97.97 | 88.11
|
| 9-8-4-2 | 1.4264 | = | 1.4303 | 1.4303 | 1.3135 | 1.4467 | 97.97 | 88.11
|
| 9-8-3-2 | 1.4244 | = | 1.4303 | = | 1.3135 | 1.4464 | 98.01 | 88.39
|
| 9-7-6-5 | 1.3471 | 1.4262 | = | = | 1.3049 | 1.4399 | 98.34 | 89.79
|
| 9-7-6-4 | 1.3471 | 1.4262 | = | 1.4239 | 1.3049 | 1.4399 | 98.34 | 89.79
|
| 9-7-6-3 | 1.3471 | 1.4262 | = | 1.4239 | 1.3049 | 1.4399 | 98.34 | 89.79
|
| 9-7-6-2 | 1.3471 | 1.4262 | = | 1.4239 | 1.3049 | 1.4399 | 98.34 | 89.79
|
| 9-7-5-4 | 1.3464 | 1.4183 | 1.4239 | = | 1.3049 | 1.4395 | 98.09 | 88.95
|
| 9-7-5-3 | 1.3464 | 1.4183 | 1.4239 | 1.4239 | 1.3049 | 1.4395 | 98.09 | 88.95
|
| 9-7-5-2 | 1.3464 | 1.4183 | 1.4239 | 1.4239 | 1.3049 | 1.4395 | 98.09 | 88.95
|
| 9-7-4-3 | 1.3452 | 1.4140 | 1.4239 | = | 1.3049 | 1.4392 | 98.13 | 89.37
|
| 9-7-4-2 | 1.3452 | 1.4140 | 1.4239 | 1.4239 | 1.3049 | 1.4392 | 98.13 | 89.37
|
| 9-7-3-2 | 1.3444 | 1.4119 | 1.4239 | = | 1.3049 | 1.4389 | 98.17 | 89.65
|
| 9-6-5-4 | 1.3066 | 1.4171 | = | = | 1.2981 | 1.4304 | 98.42 | 90.35
|
| 9-6-5-3 | 1.3066 | 1.4171 | = | 1.4171 | 1.2981 | 1.4304 | 98.42 | 90.35
|
| 9-6-5-2 | 1.3066 | 1.4171 | = | 1.4171 | 1.2981 | 1.4304 | 98.42 | 90.35
|
| 9-6-4-3 | 1.3066 | 1.4135 | 1.4171 | = | 1.2981 | 1.4303 | 98.42 | 90.35
|
| 9-6-4-2 | 1.3066 | 1.4135 | 1.4171 | 1.4171 | 1.2981 | 1.4303 | 98.42 | 90.35
|
| 9-6-3-2 | 1.3066 | 1.4119 | 1.4171 | = | 1.2981 | 1.4303 | 98.43 | 91.05
|
| 9-5-4-3 | 1.2909 | 1.4135 | = | = | 1.2947 | 1.4262 | 98.43 | 91.05
|
| 9-5-4-2 | 1.2909 | 1.4135 | = | 1.4135 | 1.2947 | 1.4262 | 98.43 | 91.05
|
| 9-5-3-2 | 1.2909 | 1.4119 | 1.4135 | = | 1.2947 | 1.4262 | 98.43 | 91.05
|
| 9-4-3-2 | 1.2862 | 1.4119 | = | = | 1.2934 | 1.4244 | 98.47 | 91.61 |
| x-x | Highest | Second | Third | Fourth | Partner | Declarer | Safety | Percentile
|
|---|
| 8-7-6-5 | 1.3446 | = | = | = | 1.2197 | 1.3446 | 100.00 | 96.22
|
| 8-7-6-4 | 1.3446 | = | = | 1.3419 | 1.2197 | 1.3446 | 100.00 | 96.22
|
| 8-7-6-3 | 1.3446 | = | = | 1.3419 | 1.2197 | 1.3446 | 100.00 | 96.22
|
| 8-7-6-2 | 1.3446 | = | = | 1.3419 | 1.2197 | 1.3446 | 100.00 | 96.22
|
| 8-7-5-4 | 1.3439 | = | 1.3419 | = | 1.2197 | 1.3446 | 99.90 | 95.24
|
| 8-7-5-3 | 1.3439 | = | 1.3419 | 1.3419 | 1.2197 | 1.3446 | 99.90 | 95.24
|
| 8-7-5-2 | 1.3439 | = | 1.3419 | 1.3419 | 1.2197 | 1.3446 | 99.90 | 95.24
|
| 8-7-4-3 | 1.3428 | = | 1.3419 | = | 1.2197 | 1.3446 | 99.74 | 94.69
|
| 8-7-4-2 | 1.3428 | = | 1.3419 | 1.3419 | 1.2197 | 1.3446 | 99.74 | 94.69
|
| 8-7-3-2 | 1.3420 | = | 1.3419 | = | 1.2197 | 1.3446 | 99.64 | 93.29
|
| 8-6-5-4 | 1.3052 | 1.3418 | = | = | 1.2197 | 1.3439 | 99.68 | 93.43
|
| 8-6-5-3 | 1.3052 | 1.3418 | = | 1.3418 | 1.2197 | 1.3439 | 99.68 | 93.43
|
| 8-6-5-2 | 1.3052 | 1.3418 | = | 1.3418 | 1.2197 | 1.3439 | 99.68 | 93.43
|
| 8-6-4-3 | 1.3052 | 1.3409 | 1.3418 | = | 1.2197 | 1.3439 | 99.68 | 93.43
|
| 8-6-4-2 | 1.3052 | 1.3409 | 1.3418 | 1.3418 | 1.2197 | 1.3439 | 99.68 | 93.43
|
| 8-6-3-2 | 1.3052 | 1.3404 | 1.3418 | = | 1.2197 | 1.3439 | 99.68 | 93.43
|
| 8-5-4-3 | 1.2899 | 1.3409 | = | = | 1.2193 | 1.3428 | 99.72 | 94.27
|
| 8-5-4-2 | 1.2899 | 1.3409 | = | 1.3409 | 1.2193 | 1.3428 | 99.72 | 94.27
|
| 8-5-3-2 | 1.2899 | 1.3404 | 1.3409 | = | 1.2193 | 1.3428 | 99.72 | 94.27
|
| 8-4-3-2 | 1.2853 | 1.3404 | = | = | 1.2192 | 1.3420 | 99.76 | 95.10
|
| 7-6-5-4 | 1.3049 | = | = | = | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-6-5-3 | 1.3049 | = | = | 1.3049 | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-6-5-2 | 1.3049 | = | = | 1.3049 | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-6-4-3 | 1.3049 | = | 1.3049 | = | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-6-4-2 | 1.3049 | = | 1.3049 | 1.3049 | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-6-3-2 | 1.3049 | = | 1.3049 | = | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-5-4-3 | 1.2895 | 1.3049 | = | = | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-5-4-2 | 1.2895 | 1.3049 | = | 1.3049 | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-5-3-2 | 1.2895 | 1.3049 | 1.3049 | = | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 7-4-3-2 | 1.2849 | 1.3049 | = | = | 1.1890 | 1.3049 | 100.00 | 96.22
|
| 6-5-4-3 | 1.2895 | = | = | = | 1.1778 | 1.2895 | 100.00 | 96.22
|
| 6-5-4-2 | 1.2895 | = | = | 1.2895 | 1.1778 | 1.2895 | 100.00 | 96.22
|
| 6-5-3-2 | 1.2895 | = | 1.2895 | = | 1.1778 | 1.2895 | 100.00 | 96.22
|
| 6-4-3-2 | 1.2849 | 1.2895 | = | = | 1.1778 | 1.2895 | 100.00 | 96.22
|
| 5-4-3-2 | 1.2849 | = | = | = | 1.1757 | 1.2849 | 100.00 | 96.22 |
Take me to your leader!
“I would, but I didn’t know who my leader was.” -Jonathan Winters
| Study 8C05 Main | | Top Leading Authority |
© 2015 Richard Pavlicek