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If the KR Evaluator Could Upgrade
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Experts are upgrade crazy these days. You getting your share? Say you had a bucket-load of randomly dealt and balanced 14-HCP hands. What proportion of them would you upgrade to open 1NT (your range is 15-17)? What are the key factors that make a hand upgrade-worthy?

The Kaplan Rubens Evaluator (for link see end of post) is probably an excellent proxy for an expert's judgement. It makes similar adjustments to HCP that the expert 'eyeballing' does, so is a good stand-in. KR adjusts as follows: positives for honors combined, for five-card suits, for aces and kings, for chunky spots, for tens in combination with honors, and negatives for isolated queens and jacks, for 4333 shape, for doubleton honors like KJ alone, and so on. I'll call those tweaked points KRP.

For this exercise we need to deal a lot of hands and calculate a lot of KRPs, so the KR web calculator won’t do. Consequently, as a public service, I built a hand generator which can deal a bunch of hands in the shape and HCP range I specify, and calculate their KR score. So for some bridge fun, I can query 'deal 10000 hands all with precisely 5332 shape, exactly 14 HCP, and report back with some KRP information'. Next is that report.

Remember, we’re dealing with 10000 random 5332 hands, each with 14 HCP. The KRPs are distributed as follows, in 0.25 KRP brackets.

KRP <= 12.00 = 99 deals

KRP > 12.00 and <= 12.25 = 104

> 12.25 = 157

> 12.50 = 225

> 12.75 = 403

> 13.00 = 533

> 13.25 = 643

> 13.50 = 803

> 13.75 = 902

> 14.00 = 945

> 14.25 = 996

> 14.50 = 950

> 14.75 = 808

> 15.00 = 812

> 15.25 = 642

> 15.50 = 410

> 15.75 = 263

> 16.00+ = 305

The average KRP for these 14-HCP hands was 14.23. The KRP for 61.3% of the hands was higher than 14. There is a span of 6+ KRP for the 14-HCP hands, from less than 11.50 to more than 17.50.

10000 deals is enough to make the results statistically significant. For example, a second run same size shows 61.7% hands higher than 14 (compared to 61.3% above).

So how often might this proxy expert upgrade? If he was an aggressive upgrader, he might 'round up' to 15, and upgrade with any hand 14.50 or higher. That suggests he would upgrade ~42% of his hands (950 + 808 + etc).

If he was more conservative, he might upgrade just those hands with 15+ KRP, or ~24%.

On this evidence it seems that an upgrade proportion for 5332 hands in the 1/4 to 1/3 range would be reasonable.

There is a dark side too; the oft-whispered but never actually consummated downgrade omigod. If your notrump range is 14-16, note that 10-15% of these hands have KRPs less than 13 or so, and are serious candidates for downgrading. As if.

We looked at 5332 hands, what about 4432? I'll spare you the dirty details this time.

Average KRP is exactly (a trifle weirdly too) 14.00, a little short of the 5332 average of 14.23. That 5-card suit makes a difference.

Doing the same kind of arithmetic, an aggressive upgrader might upgrade 32% of his hands, a conservative upgrader something in the 15% range.

So for 4432 hands, an upgrade ratio of approximately 1 in 4 looks sensible.

Some 15% or so are, theoretically anyway, downgrade-worthy. I won’t hold my breath.

KR subtracts a full half-point for 4333 hands, so combined with only one 'long suit', you will be upgrading fewer of those. I also did not consider the ‘semi-balanced’ 5422 hands because KR adds a point for the second doubleton, not entirely applicable to a valuation for notrump hands. Of your balanced hands, 45% will be 4432, 33% will be 5332, and 22% will be 4333.

I repeated the exercise for upgrading 19-HCP hands to 20, with these results.

For 5332 hands, aggressively upgrade ~56% of hands (19.5+ KRP), more conservatively ~33% (20.0+ KRP). Wow.

For 4432 hands, aggressively upgrade ~47%, conservatively ~24%.

It's pretty clear you should seriously consider upgrading a healthy chunk of your 19-HCP hands.

Now let's get real. The KR calculation is messy and tricky and nobody is going to use it literally at the table. Is there a shortcut to all that arithmetic? When the expert eyeballs, what is important to him? Looks to me there are two general principles. The dominant principle can be summarized as have a good potential source of tricks.

Consider KJ6xx/Axx/KQJ/xx, with a KRP of 14.15. You shouldn't consider upgrading it, because the primary suit needs a lot of help. However add some spade texture KJT9x, and the KRP leaps to 15.05, a great candidate to upgrade. Or take Kxx/Axx/Kxxxx/Ax, prime HCP but no good source of tricks, with a KRP of 14.4. Add a little texture to those diamonds, KT9xx, and the KRP is now 15.15. Heck, just beef up those short majors KT9/AT9/Kxxxx/Ax for a KRP of 15.5. Or combine two of those honors making the hand Kxx/xxx/AKxxx/Ax, with a nice 15.2 KRP. Or combine honors plus add texture to reach 15.85 KRP for Kxx/xxx/AKTxx/Ax.

A secondary principle would be your minor honors should be supportive. This average hand has 13.95 KRP AKxx/Axxx/Qxx/Jx. But if those quacks instead play a supporting role, AKJx/AQxx/xxx/xx becomes upgrade-worthy at 15.10 KRP, or AKxx/AQJx/xxx/xx the same 15.10, or AKQJ/Axxx/xxx/xx at 15.00, you get the picture.

A third might be nines and tens are your friends. A previous hand, amended to AKJT/AQT9/xxx/xx, grows to 16.35 KRP.

There is nothing earth-shattering in any of this, but it's interesting to see the upgrades quantified.

So remember: have a potentially good source of tricks, with minor honors supportive. Me? I like an 11-14 range and might cease and desist opening 1NT with crappola like Qxx/KQx/Jxx/Kxxx and its 8.85 KRP. But on the other hand, this '10' pointer AKTxx/xxx/xxx/Kx upgrades to 12.15!

What do these KRP differences look like in real life? Here are some random 14-HCP hands, grouped into four categories.


Don't even think about upgrading (< 13.50 KRP)

xxx KQxxx Qx AKx

QTx Kxx Qxxx AKx

ATxx Jxx Axx KQx

AQ AJx QJTxx xxx

QJxx KTxx Ax KJx

Qxxx Txxx AKx KQ

Axx xxxx KJx AQx

AKxx Qxx QJTx Qx

AJxx Qx Axx QJxx

Txxx KJx AKJx Qx



Here are some aggressive upgrades (KRP high 14's)

Kxx Ax QJTx AT98

AKx Kx KJ9xx xx

AKx Kxxxx Ax xxx

xxx Jx AKQxx Axx

xxxx AQxx Axx Ax

KJx Kx AKxxx xxx

Axx AKxx xxx Kxx

QT98 AKxx AJx xx

xxx JT Axxxx AKQ

Kxx JTx AKQJx xx



Here are some sure-thing upgrades (KRP in the 15's)

Axx Kx xxx AQJTx

Axx AQxx xx AT9x

JTx AKQx xx ATxx

xx AKTx AJTx Qxx

Ax AKJxx Txx QTx

Axx AKQxx J9 xxx

Kxx xx AKxxx Axx

AKTx xxx AKx xxx

AKxx Kx Axxx xxx

KTxx AKJx xx KTx



And even if you don't usually upgrade, upgrade these (KRP 16+)

AKTx xxx AKxx xx

Ax AQT9x Axx xxx

Axx AKTxx xx Kxx

xx AKT9x xxx AKx

etc, they have a similar look, aces and kings and a source of tricks

Here is the KR calculation site:

Here is the description of what goes on during the calculation:


You might find the odd discrepancy between a KRP I have quoted, and the KR-site calculation. For the most part they agree minutely, but occasionally they produce small differences. I would not be surprised if there was an anomaly or two in my calculations, and I know of at least one bug in the site calculations. But really, what can you expect, for quick and dirty computing as a public service? :-)

Edited to correct to "KR subtracts one-half point for 4333 hands" (originally said one full point)

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