Par contract is defined to be lowest contract such that there is no higher contract that either side can contract to improve its score. All contracts that are going down are assumed to be doubled. Examples: Both red, NS can make 9 tricks in clubs. EW cannot make any contract. Par contract is 1C with two overtricks. Both white, NS can make 4S+0(+420) and 5D+1(+420), and EW has no profitable sac available. Par contract is 4S+0. Both white, NS can make 4S+0(+420) and 5D+0(+400), but EW can sac in 5CX-2(+300). Par contract is 5D+0. The par contract results below use Matt Ginsburg double dummy library, which contains roughly 700,000 randomly dealt hands. The results are computed for each of the four possible vulnerabilities. The results for each each vulnerability contain the following. The first table is results sorted by contracts. The first column is the contract, followed by the number and frequency of that par contract, followed by the number and frequency of that par contract which is making. Next, there is a line that lists the % of par contracts that makes, as well as sacrifices sorted by vulnerability. The final table sorts the par contracts by the number of overtricks/undertricks. Par contracts for Vul None, Double always when down ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : Num Make P : 0 0.00% 0 0.00% 1C: 2063 0.29% 2063 100.00% 1D: 2000 0.28% 2000 100.00% 1H: 8098 1.13% 8098 100.00% 1S: 9609 1.34% 9609 100.00% 1N: 25995 3.63% 25995 100.00% 2C: 6646 0.93% 6646 100.00% 2D: 8367 1.17% 8367 100.00% 2H: 20851 2.91% 20851 100.00% 2S: 29175 4.07% 22293 76.41% 2N: 23802 3.32% 15270 64.15% 3C: 16218 2.26% 9313 57.42% 3D: 20433 2.85% 10158 49.71% 3H: 31844 4.44% 18359 57.65% 3S: 33859 4.72% 16858 49.79% 3N: 115657 16.13% 111450 96.36% 4C: 18003 2.51% 6668 37.04% 4D: 16926 2.36% 6103 36.06% 4H: 80415 11.21% 69430 86.34% 4S: 82522 11.51% 65674 79.58% 4N: 8374 1.17% 6417 76.63% 5C: 16706 2.33% 7551 45.20% 5D: 15068 2.10% 6472 42.95% 5H: 12743 1.78% 5419 42.53% 5S: 9542 1.33% 3803 39.86% 5N: 790 0.11% 637 80.63% 6C: 10184 1.42% 8403 82.51% 6D: 9521 1.33% 7377 77.48% 6H: 16846 2.35% 13991 83.05% 6S: 16140 2.25% 12364 76.60% 6N: 24213 3.38% 24161 99.79% 7C: 3171 0.44% 1707 53.83% 7D: 3122 0.44% 1700 54.45% 7H: 4080 0.57% 2897 71.00% 7S: 4213 0.59% 3057 72.56% 7N: 9906 1.38% 9901 99.95% Making contracts 76.85% White/Red Sacrifices 0.00% White/White Sacrifices 23.15% Red /Red Sacrifices 0.00% Red /White Sacrifices 0.00% Uptricks: -12: 0 0.00% -11: 0 0.00% -10: 0 0.00% -9: 0 0.00% -8: 0 0.00% -7: 0 0.00% -6: 879 0.12% -5: 525 0.07% -4: 6357 0.89% -3: 2859 0.40% -2: 39273 5.48% -1: 116147 16.20% 0: 349169 48.69% 1: 154128 21.49% 2: 46661 6.51% 3: 1104 0.15% 4: 0 0.00% 5: 0 0.00% 6: 0 0.00% 7: 0 0.00% 8: 0 0.00% 9: 0 0.00% 10: 0 0.00% 11: 0 0.00% Par contracts for Vul NS, Double always when down ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : Num Make P : 0 0.00% 0 0.00% 1C: 4181 0.58% 4181 100.00% 1D: 4298 0.60% 4298 100.00% 1H: 18403 2.57% 18403 100.00% 1S: 20585 2.87% 20585 100.00% 1N: 33637 4.69% 33637 100.00% 2C: 9358 1.30% 9358 100.00% 2D: 10986 1.53% 10986 100.00% 2H: 26824 3.74% 26824 100.00% 2S: 30668 4.28% 27178 88.62% 2N: 17578 2.45% 13228 75.25% 3C: 15025 2.10% 11553 76.89% 3D: 16458 2.30% 11328 68.83% 3H: 24809 3.46% 18060 72.80% 3S: 24499 3.42% 15959 65.14% 3N: 107267 14.96% 105134 98.01% 4C: 13895 1.94% 6196 44.59% 4D: 12485 1.74% 5242 41.99% 4H: 74629 10.41% 66972 89.74% 4S: 78557 10.95% 62748 79.88% 4N: 9844 1.37% 7429 75.47% 5C: 17074 2.38% 7233 42.36% 5D: 16255 2.27% 6293 38.71% 5H: 14001 1.95% 5306 37.90% 5S: 10945 1.53% 3865 35.31% 5N: 1358 0.19% 1076 79.23% 6C: 10789 1.50% 8093 75.01% 6D: 10114 1.41% 7131 70.51% 6H: 14997 2.09% 11543 76.97% 6S: 15463 2.16% 10333 66.82% 6N: 22657 3.16% 22532 99.45% 7C: 4807 0.67% 1427 29.69% 7D: 4640 0.65% 1463 31.53% 7H: 5112 0.71% 2672 52.27% 7S: 4966 0.69% 3036 61.14% 7N: 9938 1.39% 9901 99.63% Making contracts 81.05% White/Red Sacrifices 17.28% White/White Sacrifices 0.00% Red /Red Sacrifices 0.00% Red /White Sacrifices 1.67% Uptricks: -12: 0 0.00% -11: 0 0.00% -10: 0 0.00% -9: 0 0.00% -8: 654 0.09% -7: 540 0.08% -6: 4982 0.69% -5: 5582 0.78% -4: 3430 0.48% -3: 32799 4.57% -2: 20130 2.81% -1: 67782 9.45% 0: 341015 47.55% 1: 173339 24.17% 2: 63484 8.85% 3: 3365 0.47% 4: 0 0.00% 5: 0 0.00% 6: 0 0.00% 7: 0 0.00% 8: 0 0.00% 9: 0 0.00% 10: 0 0.00% 11: 0 0.00% Par contracts for Vul EW, Double always when down ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : Num Make P : 0 0.00% 0 0.00% 1C: 4071 0.57% 4071 100.00% 1D: 4351 0.61% 4351 100.00% 1H: 18587 2.59% 18587 100.00% 1S: 20613 2.87% 20613 100.00% 1N: 33623 4.69% 33623 100.00% 2C: 9374 1.31% 9374 100.00% 2D: 10790 1.50% 10790 100.00% 2H: 26698 3.72% 26698 100.00% 2S: 31065 4.33% 27673 89.08% 2N: 17579 2.45% 13397 76.21% 3C: 14945 2.08% 11512 77.03% 3D: 16607 2.32% 11462 69.02% 3H: 24890 3.47% 18154 72.94% 3S: 24279 3.39% 15818 65.15% 3N: 107091 14.93% 105017 98.06% 4C: 13782 1.92% 6016 43.65% 4D: 12567 1.75% 5299 42.17% 4H: 74792 10.43% 66999 89.58% 4S: 78923 11.01% 63017 79.85% 4N: 9653 1.35% 7343 76.07% 5C: 17289 2.41% 7218 41.75% 5D: 16038 2.24% 6214 38.75% 5H: 13849 1.93% 5247 37.89% 5S: 10935 1.52% 3799 34.74% 5N: 1315 0.18% 1057 80.38% 6C: 10856 1.51% 8171 75.27% 6D: 9935 1.39% 7003 70.49% 6H: 14984 2.09% 11496 76.72% 6S: 15597 2.18% 10467 67.11% 6N: 22814 3.18% 22677 99.40% 7C: 4655 0.65% 1393 29.92% 7D: 4514 0.63% 1446 32.03% 7H: 5189 0.72% 2703 52.09% 7S: 4930 0.69% 3049 61.85% 7N: 9922 1.38% 9901 99.79% Making contracts 81.11% White/Red Sacrifices 17.25% White/White Sacrifices 0.00% Red /Red Sacrifices 0.00% Red /White Sacrifices 1.64% Uptricks: -12: 0 0.00% -11: 0 0.00% -10: 0 0.00% -9: 0 0.00% -8: 636 0.09% -7: 582 0.08% -6: 4933 0.69% -5: 5618 0.78% -4: 3244 0.45% -3: 32893 4.59% -2: 20181 2.81% -1: 67360 9.39% 0: 340873 47.53% 1: 173849 24.24% 2: 63607 8.87% 3: 3326 0.46% 4: 0 0.00% 5: 0 0.00% 6: 0 0.00% 7: 0 0.00% 8: 0 0.00% 9: 0 0.00% 10: 0 0.00% 11: 0 0.00% Par contracts for Vul Both, Double always when down ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : Num Make P : 0 0.00% 0 0.00% 1C: 6189 0.86% 6189 100.00% 1D: 6649 0.93% 6649 100.00% 1H: 28892 4.03% 28892 100.00% 1S: 31589 4.41% 31589 100.00% 1N: 41265 5.75% 41265 100.00% 2C: 12086 1.69% 12086 100.00% 2D: 13409 1.87% 13409 100.00% 2H: 32671 4.56% 32671 100.00% 2S: 32558 4.54% 32558 100.00% 2N: 11355 1.58% 11355 100.00% 3C: 13752 1.92% 13752 100.00% 3D: 12632 1.76% 12632 100.00% 3H: 17855 2.49% 17855 100.00% 3S: 14919 2.08% 14919 100.00% 3N: 111450 15.54% 111450 100.00% 4C: 8118 1.13% 5544 68.29% 4D: 6822 0.95% 4438 65.05% 4H: 72339 10.09% 69430 95.98% 4S: 78611 10.96% 65674 83.54% 4N: 8279 1.15% 6417 77.51% 5C: 16123 2.25% 7551 46.83% 5D: 15068 2.10% 6472 42.95% 5H: 12743 1.78% 5419 42.53% 5S: 9542 1.33% 3803 39.86% 5N: 790 0.11% 637 80.63% 6C: 10184 1.42% 8403 82.51% 6D: 9521 1.33% 7377 77.48% 6H: 13859 1.93% 11004 79.40% 6S: 15560 2.17% 10211 65.62% 6N: 23272 3.25% 23150 99.48% 7C: 4398 0.61% 1216 27.65% 7D: 4551 0.63% 1382 30.37% 7H: 5114 0.71% 2590 50.65% 7S: 5020 0.70% 3051 60.78% 7N: 9917 1.38% 9901 99.84% Making contracts 89.38% White/Red Sacrifices 0.00% White/White Sacrifices 0.00% Red /Red Sacrifices 10.62% Red /White Sacrifices 0.00% Uptricks: -12: 0 0.00% -11: 0 0.00% -10: 0 0.00% -9: 0 0.00% -8: 0 0.00% -7: 1122 0.16% -6: 879 0.12% -5: 6676 0.93% -4: 6357 0.89% -3: 2859 0.40% -2: 39273 5.48% -1: 18995 2.65% 0: 352023 49.09% 1: 200800 28.00% 2: 82531 11.51% 3: 5587 0.78% 4: 0 0.00% 5: 0 0.00% 6: 0 0.00% 7: 0 0.00% 8: 0 0.00% 9: 0 0.00% 10: 0 0.00% 11: 0 0.00%