The level-1 opening is the main bidding space in Bridge. So, the spectrum of the level-1 opening is an important subject to understand. Because it shows the odds of it happening in regard to the whole possible hand. In particular, in the segment of 12-19 HCP range.
The “spectrum” is the cross-section between the hand-pattern/hand-distribution probability and the high card point distribution probability. Knowing this detail, at least in a high-level perspective, will improve your Bridge result in the long run. Especially in order to accurately determined your partner’s hand via the bidding and also in designing more effective bidding system.
All the number is easily producible using simple combinatoric mathematic. But, no need to repeat the math as Richard Pavlicek1see High Card Expectancy and Against All Odds has done this work for all to see.
The spectrum of level-1 opening table
OK, below is the main spectrum table for HCP range 12-19 in regard to the probability of distribution. This is what called apriori probability. In essence, it is the probability before the hand has been dealt. It is the possibility of any possible hand combination.
| Level-1 Opening | Range (HCP) | 12 – 14 | 15 – 17 | 18-19 | ||
|---|---|---|---|---|---|---|
| Pattern | Probability | 20.6% | 10.1% | 2.6% | Sum | |
| 1 | 4-4-3-2 | 21.6% | 4.4% | 2.2% | 0.6% | 7.2% |
| 2 | 5-3-3-2 | 15.5% | 3.2% | 1.6% | 0.4% | 5.2% |
| 3 | 5-4-3-1 | 12.9% | 2.7% | 1.3% | 0.3% | 4.3% |
| 4 | 5-4-2-2 | 10.6% | 2.2% | 1.1% | 0.3% | 3.5% |
| 5 | 4-3-3-3 | 10.5% | 2.2% | 1.1% | 0.3% | 3.5% |
| 6 | 6-3-2-2 | 5.6% | 1.2% | 0.6% | 0.1% | 1.9% |
| 7 | 6-4-2-1 | 4.7% | 1.0% | 0.5% | 0.1% | 1.6% |
| 8 | 6-3-3-1 | 3.4% | 0.7% | 0.3% | 0.1% | 1.2% |
| 9 | 5-5-2-1 | 3.2% | 0.7% | 0.3% | 0.1% | 1.1% |
| 10 | 4-4-4-1 | 3.0% | 0.6% | 0.3% | 0.1% | 1.0% |
| 11 | 7-3-2-1 | 1.9% | 0.4% | 0.2% | 0.0% | 0.6% |
| 12 | 6-4-3-0 | 1.3% | 0.3% | 0.1% | 0.0% | 0.4% |
| 13 | 5-4-4-0 | 1.2% | 0.3% | 0.1% | 0.0% | 0.4% |
| 14 | 5-5-3-0 | 0.9% | 0.2% | 0.1% | 0.0% | 0.3% |
| 15 | 6-5-1-1 | 0.7% | 0.1% | 0.1% | 0.0% | 0.2% |
| 16 | 6-5-2-0 | 0.7% | 0.1% | 0.1% | 0.0% | 0.2% |
| 17 | 7-2-2-2 | 0.51% | 0.11% | 0.05% | 0.01% | 0.17% |
| 18 | 7-4-1-1 | 0.39% | 0.08% | 0.04% | 0.01% | 0.13% |
| 19 | 7-4-2-0 | 0.36% | 0.07% | 0.04% | 0.01% | 0.12% |
Much lower probability
| Level-1 Opening | Range (HCP) | 12 – 14 | 15 – 17 | 18-19 | ||
|---|---|---|---|---|---|---|
| Pattern | Probability | 20.6% | 10.1% | 2.6% | Sum | |
| 20 | 7-3-3-0 | 0.27% | 0.05% | 0.03% | 0.01% | 0.09% |
| 21 | 8-2-2-1 | 0.19% | 0.04% | 0.02% | 0.01% | 0.06% |
| 22 | 8-3-1-1 | 0.12% | 0.02% | 0.01% | 0.00% | 0.04% |
| 23 | 7-5-1-0 | 0.109% | 0.022% | 0.011% | 0.003% | 0.036% |
| 24 | 8-3-2-0 | 0.109% | 0.022% | 0.011% | 0.003% | 0.036% |
| 25 | 6-6-1-0 | 0.072% | 0.015% | 0.007% | 0.002% | 0.024% |
| 26 | 8-4-1-0 | 0.045% | 0.009% | 0.005% | 0.001% | 0.015% |
| 27 | 9-2-1-1 | 0.018% | 0.004% | 0.002% | 0.000% | 0.006% |
| 28 | 9-3-1-0 | 0.0100% | 0.0021% | 0.0010% | 0.0003% | 0.0033% |
| 29 | 9-2-2-0 | 0.0082% | 0.0017% | 0.0008% | 0.0002% | 0.0027% |
| 30 | 7-6-0-0 | 0.0056% | 0.0012% | 0.0006% | 0.0001% | 0.0019% |
| 31 | 8-5-0-0 | 0.00310% | 0.00064% | 0.00031% | 0.00008% | 0.00103% |
| 32 | 10-2-1-0 | 0.00110% | 0.00023% | 0.00011% | 0.00003% | 0.00037% |
| 33 | 9-4-0-0 | 0.00097% | 0.00020% | 0.00010% | 0.00003% | 0.00032% |
| 34 | 10-1-1-1 | 0.000396% | 0.000082% | 0.000040% | 0.000010% | 0.000132% |
| 35 | 10-3-0-0 | 0.000155% | 0.000032% | 0.000016% | 0.000004% | 0.000052% |
| 36 | 11-1-1-0 | 0.0000249% | 0.0000051% | 0.0000025% | 0.0000007% | 0.0000083% |
| 37 | 11-2-0-0 | 0.00001150% | 0.00000237% | 0.00000116% | 0.00000030% | 0.00000384% |
| 38 | 12-1-0-0 | 0.00000032% | 0.00000007% | 0.00000003% | 0.00000001% | 0.00000011% |
| 39 | 13-0-0-0 | 0.00000006% | 0.00000001% | 0.00000001% | 0.000000002% | 0.00000002% |
| ALL | Sum | 100.0% | 20.6% | 10.1% | 2.6% | 33.4% |
How you interpret the table above? The column is the HCP range. The total of the individual range is at the top. For example, the probability of 15-17 HCP with ANY distribution is 10.1%
As you can see in the bottom right of the table, the spectrum of level-1 opening that’s a total probability of 33.4%. Therefore, we need to breakdown it further for all the opening bid for level-1: 1NT, 1-minor opening (1C/1D) and 1-Major opening (1H/1S)
1NT opening’s spectrum
Let us start with the easiest opening bid in this spectrum. 1NT opening would only be limited to 3 hand distributions: (4432), (5332) and (4432). (Note: the distribution within parentheses denotes that it is not suit-specific). Therefore:
- If you use Strong 1NT opening, see the 15-17 HCP column. The total possible distribution is: 2.2%+1.6%+1.1% = 4.9%. Hence, the other level-1 openings have 10.1%-4.9%=5.1% chances for 15-17 HCP range.
- If you use Weak 1NT opening, the total possible distribution is 4.4%+3.2%+2.2%=9.8%. So, in this case, the odd for the other level-1 opening is 20.6%-9.8%=10.8%
The split between 1-minor and 1-Major Opening
Probability for 1-Major opening in EVERY HCP Range
| Pattern | # out of | Probability | Specific Distribution | ||
|---|---|---|---|---|---|
| 1 | 4-4-3-2 | 0 | 12 | 0.00000% | |
| 2 | 5-3-3-2 | 6 | 12 | 7.75840% | 5532 5323 5233 3532 3523 2533 |
| 3 | 5-4-3-1 | 12 | 24 | 6.46535% | 5431 5413 5341 5314 5143 5134 4513 4531 3541 3514 1534 1543 |
| 4 | 5-4-2-2 | 6 | 12 | 5.28985% | 5422 5244 5224 4522 2542 2524 |
| 5 | 4-3-3-3 | 0 | 4 | 0.00000% | |
| 6 | 6-3-2-2 | 6 | 12 | 2.82125% | 6322 6232 6223 3622 2632 2623 |
| 7 | 6-4-2-1 | 12 | 24 | 2.35105% | 6421 6412 6241 6214 6142 6124 4612 4621 2641 2614 1624 1642 |
| 8 | 6-3-3-1 | 6 | 12 | 1.72410% | 6331 6313 6133 3631 3613 1633 |
| 9 | 5-5-2-1 | 10 | 12 | 2.64492% | 5521 5512 5251 5215 5152 5125 2551 2515 1552 1525 |
| 10 | 4-4-4-1 | 0 | 4 | 0.00000% | |
| 11 | 7-3-2-1 | 12 | 24 | 0.94040% | 7321 7312 7231 7213 7132 7123 3712 3721 2731 2713 1723 1732 |
| 12 | 6-4-3-0 | 12 | 24 | 0.66300% | 6430 6403 6340 6304 6043 6034 4603 4630 3640 3604 0634 0643 |
| 13 | 5-4-4-0 | 6 | 12 | 0.62165% | 5440 5404 5044 4540 4504 0544 |
| 14 | 5-5-3-0 | 10 | 12 | 0.74600% | 5530 5503 5350 5305 5053 5035 3550 3595 0553 0535 |
| 15 | 6-5-1-1 | 6 | 12 | 0.35265% | 6511 6151 6115 5611 1651 1615 |
| 16 | 6-5-2-0 | 12 | 24 | 0.32555% | 6520 6502 6250 6205 6052 6025 5602 5620 2650 2605 0625 0652 |
| 17 | 7-2-2-2 | 2 | 4 | 0.25650% | 7222 2722 |
| 18 | 7-4-1-1 | 6 | 12 | 0.19590% | 7411 7141 7114 4711 1741 1741 |
| 19 | 7-4-2-0 | 12 | 24 | 0.18085% | 7420 7402 7249 7204 7042 7924 4702 4720 2740 2704 0724 0742 |
Much lower probability
| Pattern | # out of | Probability | Specific Distribution | ||
|---|---|---|---|---|---|
| 20 | 7-3-3-0 | 6 | 12 | 0.13260% | 7330 7303 7033 3730 3703 0733 |
| 21 | 8-2-2-1 | 6 | 12 | 0.09620% | 8221 8212 8122 2821 2812 1822 |
| 22 | 8-3-1-1 | 6 | 12 | 0.05880% | 8311 8131 813 3811 1831 1813 |
| 23 | 7-5-1-0 | 12 | 24 | 0.05425% | 7510 7501 7150 7105 7051 7015 5701 5710 1750 1705 |
| 24 | 8-3-2-0 | 12 | 24 | 0.05425% | 8320 8302 8230 8203 8032 8023 3802 3820 2830 2803 0823 0832 |
| 25 | 6-6-1-0 | 10 | 12 | 0.06025% | 6610 6601 6160 6106 6061 6016 1660 1606 1066 0661 |
| 26 | 8-4-1-0 | 12 | 24 | 0.02260% | 8410 8401 8140 8104 8041 8014 4801 4810 1840 1804 0814 0841 |
| 27 | 9-2-1-1 | 6 | 12 | 0.00890% | 9211 9121 9112 2911 1921 1912 |
| 28 | 9-3-1-0 | 12 | 24 | 0.00500% | 9310 9301 9130 9103 9031 9013 3901 3910 1930 1903 0913 0931 |
| 29 | 9-2-2-0 | 6 | 12 | 0.00410% | 9220 9202 9022 2920 2902 0922 |
| 30 | 7-6-0-0 | 6 | 12 | 0.00280% | 7600 7060 7006 6700 0760 0706 |
| 31 | 8-5-0-0 | 6 | 12 | 0.00155% | 8500 8050 8005 5800 0850 0805 |
| 32 | 10-2-1-0 | 12 | 24 | 0.00055% | A210 A201 A120 A102 A021 A012 2A01 2A10 1A20 1A02 0A12 0A21 |
| 33 | 9-4-0-0 | 6 | 12 | 0.00049% | 9004 9040 9400 4009 0904 0940 |
| 34 | 10-1-1-1 | 2 | 4 | 0.00020% | A111 1A11 |
| 35 | 10-3-0-0 | 6 | 12 | 0.00008% | A300 A030 A003 3A00 0A30 0A03 |
| 36 | 11-1-1-0 | 6 | 12 | 0.00001% | B110 B101 B011 1B10 1B10 1B01 |
| 37 | 11-2-0-0 | 6 | 12 | 0.00001% | B200 B020 B002 2B00 0B20 0B02 |
| 38 | 12-1-0-0 | 6 | 12 | 0.00000% | C001 C010 C100 1C00 0C01 0C10 |
| 39 | 13-0-0-0 | 2 | 4 | 0.00000% | D000 0D00 |
| Sum | 33.84005% | ||||
So, from the table above, we can see that for each HCP range, the 1-Major opening accounts for 33.84% possibilities. However, you need to bid some of the balanced distribution via 1NT. Therefore, for Strong NT system, the 1-Major opening possibilities are reduced to 26.08%. (Removing (5332), (4333), and (4432) distribution) For weak NT, the same reduction happens in 12-14 HCP range. As a recap:
- For Strong NT system
- 12-14 HCP range: 20.6% x 33.84% = 7.0%
- 15-17 HCP range: 10.1% x 26.08% = 2.6%
- 18-19 HCP range: 2.6% x 33.84% = 0.9%
- Total for Strong NT 1-Major opening: 10.5%
- For Weak NT system
- 12-14 HCP range: 20.6% x 26.08% = 5.4%
- 15-17 HCP range: 10.1% x 33.84% = 3.4%
- 18-19 HCP range: 2.6% x 33.84% = 0.9%
- Total for Weak NT 1-Major opening: 9.7%
Probability for 1-minor opening in EVERY HCP Range
| Pattern | # out of | Probability | Specific Distribution | ||
|---|---|---|---|---|---|
| 1 | 4-4-3-2 | 12 | 12 | 21.55120% | 4432 4423 4342 4324 4243 4234 3442 3424 3244 2443 2434 2344 |
| 2 | 5-3-3-2 | 6 | 12 | 7.75840% | 3352 3325 3253 3235 2353 2335 |
| 3 | 5-4-3-1 | 12 | 24 | 6.46535% | 1354 1345 1453 1435 3145 3154 3415 3451 4153 4135 4351 4315 |
| 4 | 5-4-2-2 | 6 | 12 | 5.28985% | 4252 4225 2452 2425 2254 2245 |
| 5 | 4-3-3-3 | 4 | 4 | 10.53610% | 4333 3433 3343 3334 |
| 6 | 6-3-2-2 | 6 | 12 | 2.82125% | 3262 3226 2362 2326 2263 2236 |
| 7 | 6-4-2-1 | 12 | 24 | 2.35105% | 4216 4261 4126 4162 2461 2416 2164 2146 1426 1462 1246 1264 |
| 8 | 6-3-3-1 | 6 | 12 | 1.72410% | 3361 3316 3163 3136 1363 1336 |
| 9 | 5-5-2-1 | 2 | 12 | 0.52898% | 2155 1255 |
| 10 | 4-4-4-1 | 4 | 4 | 2.99320% | 4441 4414 4144 1444 |
| 11 | 7-3-2-1 | 12 | 24 | 0.94040% | 3217 3271 3127 3172 2371 2317 2173 2137 1327 1372 1237 1273 |
| 12 | 6-4-3-0 | 12 | 24 | 0.66300% | 4306 4360 4036 4063 3460 3406 3064 3046 0436 0463 0346 0364 |
| 13 | 5-4-4-0 | 6 | 12 | 0.62165% | 4450 4405 4054 4045 0454 0445 |
| 14 | 5-5-3-0 | 2 | 12 | 0.14920% | 3055 0355 |
| 15 | 6-5-1-1 | 6 | 12 | 0.35265% | 1165 1156 5161 5116 1561 1516 |
| 16 | 6-5-2-0 | 12 | 24 | 0.32555% | 5206 5260 5026 5062 2560 2506 2065 2056 0526 0562 0256 0265 |
| 17 | 7-2-2-2 | 2 | 4 | 0.25650% | 2272 2227 |
| 18 | 7-4-1-1 | 6 | 12 | 0.19590% | 4171 4117 1471 1417 1174 1147 |
| 19 | 7-4-2-0 | 12 | 24 | 0.18085% | 4207 4270 4027 4072 2470 2407 2074 2047 0427 0472 0247 0274 |
Much lower probability
| Pattern | # out of | Probability | Specific Distribution | ||
|---|---|---|---|---|---|
| 20 | 7-3-3-0 | 6 | 12 | 0.13260% | 3370 3307 3073 3037 0373 0337 |
| 21 | 8-2-2-1 | 6 | 12 | 0.09620% | 2281 2218 2182 2128 1282 1228 |
| 22 | 8-3-1-1 | 6 | 12 | 0.05880% | 3181 3118 1381 1318 1183 1138 |
| 23 | 7-5-1-0 | 12 | 24 | 0.05425% | 5107 5170 5017 5071 1570 1507 1075 1057 0517 0571 0157 0175 |
| 24 | 8-3-2-0 | 12 | 24 | 0.05425% | 3208 3280 3028 3082 2380 2308 2083 2038 0328 0382 0238 0283 |
| 25 | 6-6-1-0 | 2 | 12 | 0.01205% | 1066 0166 |
| 26 | 8-4-1-0 | 12 | 24 | 0.02260% | 4108 4180 4018 4081 1480 1408 1084 1048 0418 0481 0148 0184 |
| 27 | 9-2-1-1 | 6 | 12 | 0.00890% | 2191 2119 1291 1219 1192 1129 |
| 28 | 9-3-1-0 | 12 | 24 | 0.00500% | 3109 3190 3019 3091 1390 1309 1093 1039 0319 0391 0139 0193 |
| 29 | 9-2-2-0 | 6 | 12 | 0.00410% | 2290 2209 2092 2029 0292 0229 |
| 30 | 7-6-0-0 | 6 | 12 | 0.00280% | 6070 6007 0670 0607 0076 0067 |
| 31 | 8-5-0-0 | 6 | 12 | 0.00155% | 5080 5007 0580 0508 0085 0058 |
| 32 | 10-2-1-0 | 12 | 24 | 0.00055% | 210A 21A0 201A 20A1 12A0 120A 10A2 102A 021A 02A1 012A 01A2 |
| 33 | 9-4-0-0 | 6 | 12 | 0.00049% | 4009 4090 0049 0094 0409 0490 |
| 34 | 10-1-1-1 | 2 | 4 | 0.00020% | 11A1 111A |
| 35 | 10-3-0-0 | 6 | 12 | 0.00008% | 30A0 300A 03A0 030A 00A3 003A |
| 36 | 11-1-1-0 | 6 | 12 | 0.00001% | 11B0 110B 10B1 101B 01B1 011B |
| 37 | 11-2-0-0 | 6 | 12 | 0.00001% | 20B0 200B 02B0 020B 00B2 002B |
| 38 | 12-1-0-0 | 6 | 12 | 0.00000% | 100C 10C0 001C 00C1 010C 01C0 |
| 39 | 13-0-0-0 | 2 | 4 | 0.00000% | 00D0 000D |
| Sum | 66.15961% | ||||
So, from the table above, we can see that for each HCP range, the 1-minor opening accounts for 66.16% possibilities. However, you need to bid some of the balanced distribution via 1NT. Therefore, the same as the Major-opening above, for Strong NT system, the 1-minor opening possibilities are reduced to 26.31%. (Removing (5332), (4333), and (4432) distribution) For weak NT, the same reduction happens in 12-14 HCP range. As a recap:
- For Strong NT system
- 12-14 HCP range: 20.6% x 66.16% = 13.6%
- 15-17 HCP range: 10.1% x 26.31% = 2.7%
- 18-19 HCP range: 2.6% x 66.16% = 1.7%
- Total for Strong NT 1-minor opening: 18.06%
- For Weak NT system
- 12-14 HCP range: 20.6% x 26.31% = 5.4%
- 15-17 HCP range: 10.1% x 66.16% = 6.7%
- 18-19 HCP range: 2.6% x 66.16% = 1.8%
- Total for Weak NT 1-minor opening: 13.9%
Summary for Strong NT System
Summarizing from all the above, the spectrum of level-1 opening for Strong NT System is:
- The chances of 1NT Opening is 4.9 %
- For 1-Major Opening, the odd is 10.5%
- Chances of 1-minor Opening 18.0%
- (Total: 33.4%)
Summary for Weak NT System
So, summarizing from all the above, The spectrum of level-1 opening for Weak NT System is:
- The chances of 1NT Opening 9.8 %
- For 1-Major Opening, the odd is 9.7%
- Chances of 1-minor Opening: 13.9%
- (Total: 33.4%)
The knowledge of the spectrum of level-1 opening as displayed above will be used for further detail analysis.
