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Simplified Advanced Hand Valuation (Core Card Count)
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Kaplan & Rubens CCCC (KnR) has become a benchmark for hand valuation, especially for balanced hands in constructive auctions.

 

The one major problem with KnR is the difficulty in applying it at the table, due to its complexity and 1/20th of a point granularity.  I have developed an approach that retains the main benefits of KnR, while making it easier to use in real time.  Think of it as a modified version of KnR, calibrated to be calculation-efficient for balanced hands (i.e. 4333s, 4432s & 5332s).

 

The key components of this valuation approach are:

  • the quite familiar base 4321 (HCP) count
  • positive adjustments for Aces & Pushers (Ts & 9s);
  • deductions for Kings & Quacks (Qs & Js);
  • a separate suit quality adjustment; and 
  • adjustments for shape where relevant (largely left out of scope of this post).

 

All together, the adjustments relative to 4321 count are highly correlated with those implicitly made by KnR.  I will tackle each of them in turn on the upcoming pages ...

The adjustments for Aces & Pushers are positive, with one exception.

 

Aces

  • if third or longer = +½ each
  • Ax = no adjustment
  • stiff A = -½

 

Tens

  • if third or longer w/ at least 2 of AKQJ9 = +½
  • if third or longer w/ at least 1 of AKQJ9 = +¼
  • other Ts = no adjustment

 

Nines

  • if third or longer w/ at least 2 of AKQJT8 = +¼
  • other 9s = no adjustment

The deductions for Kings and Quacks are generally negative.

 

Kings

  • if third or longer = no deduction
  • AK tight or Kx = -½
  • stiff K = -2

 

Queens

  • AKQ+ or AQx+ or KQx+ = -¼
  • Qxx+ (w/o A or K) = -½
  • AQ or KQ tight = -¾
  • Qx (w/o A or K) = -1
  • stiff Q = -1½

 

Jacks

  • if third or longer with at least 1 of AKQ = -¼
  • Jxx+ or AJ, KJ or QJ tight = -½
  • Jx = -¾
  • stiff J = -1

At first glance, the adjustments above may look like they require a decent amount of memorization. After practicing with it for a dozen hands or so (e.g. looking at hand records post-session or BW bidding polls), the scales for the devaluation of Qs & Js become intuitive and the combinations involving As/Ts/9s & Qs/Js become easier to handle.

 

The suggested approach for handling the ¼ point adjustments is to:

  • tally the total net number of such adjustments (+ or -) for each suit; and
  • divide that total by four.

 

The Suit Quality Adjustment (for 3+ card suits only) can be considered an optional refinement for balanced hands (i.e. 4333s, 4432s & 5332s) with scattered strength; it becomes more relevant for semi-balanced or unbalanced hands, or balanced hands with concentrated strength:

  • sum (4321 count * suit length) for all 3+ card suits
  • subtract HCP * 11 / 3 (the average suit length for a given honor in a balanced hand will be roughly 3.7)
  • divide net result by 10

 

One adjustment for shape (explicitly part of KnR) becomes relevant:

  • -½ for any 4333

Let's walk through a few examples of applying this method/process ...

 

Qxx Jxxx K9x QTx (8 hcp) would be adjusted as follows

  • by suit: -2 -2 +0 -1 = -5 / 4 = -1¼ point
  • suit quality: (2*3)+(1*4)+(3*3)+(2*3) = 25; 8x11 = 88 / 3 = 29; 25-29 = -4 / 10 = -0.4
  • shape: -½ (for a 4x3)
  • 8 - 1.25 - 0.4 -0.5 = 5.85, a "bad" 6 count

 

KTxx  Axx AT9x xx (11 hcp) would be adjusted

  • by suit:  +1 +2 +2 +0 = +5 / 4 = +1¼ points
  • suit quality:  (3*4)+(4*3)+(4*4) = 40; 11x11 = 121 / 3 = 40; 40-40 = no adj
  • shape: none
  • 11 + 1.25 + 0 +0 = 12.25, a "good" 12 count

 

AJx KQxxx KJx Qx (16 hcp) would be adjusted as follows

  • by suit:  +1 -1 -1 -4 = -3 / 4 = -¾ point
  • suit quality:  (5*3)+(5*5)+(4*3) = 52; 14x11 = 154 / 3 = 51; 52-51 = +1 / 10 = +0.1
  • shape: none
  • 16 - 0.75 + 0.1 +0 = 15.35, a "good" 15 count

 

Last notes:

  • This approach works best when both partners are making these adjustments.  If your partner is not, one can argue for reducing the overall adjustment, since his/her hand would on average be making an opposite adjustment about 1/3 as big as yours.  Of course, if your partner values his/her hands really well in general, make the full adjustment to your hand.
  • As soon as partner or your opponents speak, you have more information to value your hand.  Avoid getting too focused on applying a formula to your 13 cards, and use that info!
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