Introducing the concept of “Bridge Spectrum” as a tool for bridge analysis. This is where the High Card Point (HCP) meets with the hand pattern distribution. The concept is pretty straightforward and easy to understand. This is the basic concept if you want to compare a specific hand-distribution in an HCP range to another HCP range or even other distribution.
We already know about the 39 Hand Distribution in Bridge and its statistic (if you are unfamiliar with it, please read that first). So, now let us take a look at the expectancy of having a certain HCP range. For example, what is the chance of you get a 15-17HCP? Or what is the chance to get 21+ HCP?
High Card Distribution
In the history of Bridge, there was a time when the level-2 openings were all of a strong variation. Google “Acol” and you will find a good example of this. But, because then people realize that the chance of getting strong hand is way less than getting the weak hand. In other words, all those good strong level-2 opening were hardly being used. Maybe very rarely. And people who play the weak-two opening bid were dominating the result.
As a result, we see today in the more “modern” era, the opposite is true. The “Standard” system which is dominating the world of Bridge currently, crams all the strong hand to just 1 bid 2C. And the rest os level-2 opening are usually all kind of weak variation, a combination of weak and strong and everything in between.
The HCP range probability table
Richard Pavlicek has published the result of the chance of High Card Point distribution here. I do not want to repeat the comprehensive here, but we do want to use the statistic to help us get better in Bridge. Based on his work, we can have the HCP range probability as follows:
| HCP Range | Percentage |
|---|---|
| 0 – 5 | 14.0% |
| 6 – 9 | 32.8% |
| 10 – 11 | 18.3% |
| 12 – 14 | 20.6% |
| 15 – 17 | 10.1% |
| 18-19 | 2.6% |
| 20-22 | 1.2% |
| 23+ | 0.2% |
| Total | 100.0% |
Some example of information that we can derive from the table above:
- You got about twice the chance of getting 12-14 HCP hand than 15-17 hand
- Getting a 24+ HCP is average at 1 in 500 hands
- The chance of you have a 6-11 HCP (weak two range) is 65%.
- The odds of getting 18+ HCP hand is only ~4% (1 in 25 hands)
So, you can see why using the strong level-2 opening is not that good. It is only catered for a small percentage of hand that is less frequent than a weak two hand that is way more frequent to happen.
Bridge Spectrum: the introduction
Now, we can go one step deeper for a good Bridge analysis. For example, what is the odds of getting a (4441) in 18-19 HCP range?
This is what Bridge Spectrum is about. It is just a cross-section of the hand distribution vs HCP distribution probability. So, in this case, from the 39-hand distribution statistic, we know that the odds of having a (4441) distribution is 3%, And from that table above, having an 18-19 HCP is 2.6%. Then the spectrum of (4441) with 18-19 is 2.6% x 3% = 0.08%
As a comparison, say you want to know what is the odds for a (5440) distribution for 12-14 HCP. The odds of (5440) is 1.2%. Then the spectrum of a hand with (5440) 12-14 HCP = 20.6% x 1.2% = 0.25%. Therefore, having (5440) in the 12-14 range is (0.255/0.08%=)~ 3 times more likely.
So, with the bridge spectrum, you can compare different hand distributions in different point range.
The bridge spectrum table
| Full Spectrum | Range (HCP) | 0 – 5 | 6 – 9 | 10 – 11 | 12 – 14 | 15 – 17 | 18-19 | 20-22 | 23+ | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Pattern | Probability | 14.0% | 32.8% | 18.3% | 20.6% | 10.1% | 2.6% | 1.2% | 0.2% | Sum | |
| 1 | 4-4-3-2 | 21.6% | 3.0% | 7.1% | 4.0% | 4.4% | 2.2% | 0.6% | 0.3% | 0.05% | 21.6% |
| 2 | 5-3-3-2 | 15.5% | 2.2% | 5.1% | 2.8% | 3.2% | 1.6% | 0.4% | 0.2% | 0.03% | 15.5% |
| 3 | 5-4-3-1 | 12.9% | 1.8% | 4.2% | 2.4% | 2.7% | 1.3% | 0.3% | 0.2% | 0.03% | 12.9% |
| 4 | 5-4-2-2 | 10.6% | 1.5% | 3.5% | 1.9% | 2.2% | 1.1% | 0.3% | 0.1% | 0.02% | 10.6% |
| 5 | 4-3-3-3 | 10.5% | 1.5% | 3.5% | 1.9% | 2.2% | 1.1% | 0.3% | 0.13% | 0.02% | 10.5% |
| 6 | 6-3-2-2 | 5.6% | 0.8% | 1.9% | 1.0% | 1.2% | 0.6% | 0.1% | 0.07% | 0.012% | 5.6% |
| 7 | 6-4-2-1 | 4.7% | 0.7% | 1.5% | 0.9% | 1.0% | 0.5% | 0.1% | 0.06% | 0.010% | 4.7% |
| 8 | 6-3-3-1 | 3.4% | 0.5% | 1.1% | 0.6% | 0.7% | 0.3% | 0.1% | 0.04% | 0.007% | 3.4% |
| 9 | 5-5-2-1 | 3.2% | 0.4% | 1.0% | 0.6% | 0.7% | 0.3% | 0.08% | 0.04% | 0.007% | 3.2% |
| 10 | 4-4-4-1 | 3.0% | 0.4% | 1.0% | 0.5% | 0.6% | 0.3% | 0.08% | 0.04% | 0.006% | 3.0% |
| 11 | 7-3-2-1 | 1.9% | 0.3% | 0.6% | 0.3% | 0.4% | 0.2% | 0.05% | 0.02% | 0.004% | 1.9% |
| 12 | 6-4-3-0 | 1.3% | 0.2% | 0.4% | 0.2% | 0.3% | 0.13% | 0.04% | 0.02% | 0.003% | 1.3% |
| 13 | 5-4-4-0 | 1.2% | 0.2% | 0.4% | 0.2% | 0.3% | 0.13% | 0.03% | 0.02% | 0.003% | 1.2% |
Bridge Spectrum – part 2
| Full Spectrum | Range (HCP) | 0 – 5 | 6 – 9 | 10 – 11 | 12 – 14 | 15 – 17 | 18-19 | 20-22 | 23+ | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Pattern | Probability | 14.0% | 32.8% | 18.3% | 20.6% | 10.1% | 2.6% | 1.2% | 0.2% | Sum | |
| 14 | 5-5-3-0 | 0.9% | 0.1% | 0.3% | 0.2% | 0.2% | 0.09% | 0.02% | 0.011% | 0.002% | 0.9% |
| 15 | 6-5-1-1 | 0.7% | 0.10% | 0.23% | 0.13% | 0.15% | 0.07% | 0.02% | 0.009% | 0.002% | 0.7% |
| 16 | 6-5-2-0 | 0.7% | 0.09% | 0.21% | 0.12% | 0.13% | 0.07% | 0.02% | 0.008% | 0.0014% | 0.7% |
| 17 | 7-2-2-2 | 0.51% | 0.07% | 0.17% | 0.09% | 0.11% | 0.05% | 0.014% | 0.006% | 0.0011% | 0.5% |
| 18 | 7-4-1-1 | 0.39% | 0.05% | 0.13% | 0.07% | 0.08% | 0.04% | 0.010% | 0.005% | 0.0008% | 0.4% |
| 19 | 7-4-2-0 | 0.36% | 0.05% | 0.12% | 0.07% | 0.07% | 0.04% | 0.010% | 0.004% | 0.0008% | 0.4% |
| 20 | 7-3-3-0 | 0.27% | 0.04% | 0.09% | 0.05% | 0.05% | 0.03% | 0.007% | 0.003% | 0.0006% | 0.3% |
| 21 | 8-2-2-1 | 0.19% | 0.03% | 0.06% | 0.04% | 0.04% | 0.019% | 0.005% | 0.0024% | 0.0004% | 0.2% |
| 22 | 8-3-1-1 | 0.12% | 0.02% | 0.04% | 0.02% | 0.02% | 0.012% | 0.003% | 0.0014% | 0.0003% | 0.1% |
| 23 | 7-5-1-0 | 0.109% | 0.02% | 0.04% | 0.02% | 0.02% | 0.011% | 0.003% | 0.0013% | 0.0002% | 0.1% |
| 24 | 8-3-2-0 | 0.109% | 0.02% | 0.04% | 0.02% | 0.02% | 0.011% | 0.003% | 0.0013% | 0.0002% | 0.1% |
| 25 | 6-6-1-0 | 0.072% | 0.010% | 0.024% | 0.013% | 0.015% | 0.007% | 0.002% | 0.0009% | 0.0002% | 0.1% |
| 26 | 8-4-1-0 | 0.045% | 0.006% | 0.015% | 0.008% | 0.009% | 0.005% | 0.0012% | 0.0006% | 0.00010% | 0.0% |
Bridge Spectrum – part 3
| Full Spectrum | Range (HCP) | 0 – 5 | 6 – 9 | 10 – 11 | 12 – 14 | 15 – 17 | 18-19 | 20-22 | 23+ | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Pattern | Probability | 14.0% | 32.8% | 18.3% | 20.6% | 10.1% | 2.6% | 1.2% | 0.2% | Sum | |
| 27 | 9-2-1-1 | 0.018% | 0.002% | 0.006% | 0.003% | 0.004% | 0.002% | 0.0005% | 0.0002% | 0.00004% | 0.0% |
| 28 | 9-3-1-0 | 0.0100% | 0.001% | 0.003% | 0.002% | 0.002% | 0.001% | 0.0003% | 0.00012% | 0.00002% | 0.0% |
| 29 | 9-2-2-0 | 0.0082% | 0.001% | 0.003% | 0.002% | 0.002% | 0.0008% | 0.0002% | 0.00010% | 0.00002% | 0.0% |
| 30 | 7-6-0-0 | 0.0056% | 0.0008% | 0.0018% | 0.0010% | 0.0012% | 0.0006% | 0.00015% | 0.00007% | 0.00001% | 0.0% |
| 31 | 8-5-0-0 | 0.00310% | 0.0004% | 0.0010% | 0.0006% | 0.0006% | 0.0003% | 0.00008% | 0.00004% | 0.000007% | 0.0% |
| 32 | 10-2-1-0 | 0.00110% | 0.0002% | 0.0004% | 0.0002% | 0.0002% | 0.00011% | 0.00003% | 0.000014% | 0.000002% | 0.0% |
| 33 | 9-4-0-0 | 0.00097% | 0.0001% | 0.0003% | 0.0002% | 0.0002% | 0.00010% | 0.00003% | 0.000012% | 0.000002% | 0.0% |
| 34 | 10-1-1-1 | 0.000396% | 0.00006% | 0.00013% | 0.00007% | 0.00008% | 0.00004% | 0.000010% | 0.000005% | 0.0000008% | 0.0% |
| 35 | 10-3-0-0 | 0.000155% | 0.00002% | 0.00005% | 0.00003% | 0.00003% | 0.00002% | 0.000004% | 0.000002% | 0.0000003% | 0.0% |
| 36 | 11-1-1-0 | 0.0000249% | 0.000003% | 0.000008% | 0.000005% | 0.000005% | 0.000003% | 0.0000007% | 0.0000003% | 0.00000005% | 0.0% |
| 37 | 11-2-0-0 | 0.00001150% | 0.000002% | 0.000004% | 0.000002% | 0.000002% | 0.000001% | 0.0000003% | 0.00000014% | 0.00000002% | 0.0% |
| 38 | 12-1-0-0 | 0.00000032% | 0.00000004% | 0.00000010% | 0.00000006% | 0.00000007% | 0.00000003% | 0.00000001% | 0.0000000039% | 0.0000000007% | 0.0% |
| 39 | 13-0-0-0 | 0.00000006% | 0.000000009% | 0.000000021% | 0.000000012% | 0.000000013% | 0.000000006% | 0.000000002% | 0.0000000008% | 0.0000000001% | 0.0% |
| * | Sum | 100.0% | 14.0% | 32.8% | 18.3% | 20.6% | 10.1% | 2.6% | 1.2% | 0.2% | 100.0% |
You will find that this “Bridge Spectrum” concept/term is being used throughout this website.
