A Modified Long Suit Evaluator

by Stig Holmquist

The Karpin method of hand evaluation is based on the Work point count plus adding one point for each card over four in any suit. It does not differentiate between honor rich and honor poor long suits. E. Kaplan addressed this question in 1982 with his Four C's method. It was however too complicated to use at the table by ordinary mortal players, although some experts are able to do so. It's the aim here to propose a simplified method to obtain nearly identical values using plain arithmetic. The method will take into account the 10 card but not the 9- nor the 8-spot card. It's based on assigning "inverted" losing trick counts to honors. Specifically, an A counts as 1.5, a K as 1, a Q as 0.5. To these is added 0.25 for the J. If these values are doubled one gets 3-2-1-0.5, the same as the old Four Aces point count, to which one must add 0.25 for the T. Doubling these one gets 6-4-2-1-0.5, which is the Work point scale with 2-1-points (A = 2, K = 1) added. A long suit is then evaluated by multiplying its Four Aces count by the appropriate suit-length factor and then dividing by 3.

For example, the 6-card suit AQTxxx would count as 6(3+1+0.25)/3=8.5. Two computer implementations (Th. Andrews and J. Goldsmith) of the Four C's method yields 8.45. There are 31 six-card combinations of 1,2,3,4 or 5 honor cards listed in the table that follows, with the suit counts calculated to show that this simple method yields pointcounts that are on average only 5 percent higher than obtained with the Four C's count. One would need to do a comprehensive computer simulation with double-dummy analysis to determine if this difference matters in real bidding. The data in this table for six-card suits can be used to evaluate any long suit, L, by multiplying with (L+/-0.5)/6, so that for 5-card suits the factor would be 5.5/6 ~0.9 and for 7-card suits it would be 6.5/6~1.1. And 8-card suits could be evaluated with 7/6~1.2 as a factor.

3 | 2 | 1 | 0.5 | 0.25 | Sum | 2x | 4C | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A | K | Q | J | T | 3 | 1 | 1 | 1 | 1 | 1 | 6.75 | 13.5 | 12.6 |

A | K | Q | J | 4 | 3 | 1 | 1 | 1 | 1 | 0 | 6.5 | 13 | 12 |

A | K | Q | T | 4 | 3 | 1 | 1 | 1 | 0 | 1 | 6.25 | 12.5 | 12 |

A | K | J | T | 4 | 3 | 1 | 1 | 0 | 1 | 1 | 5.75 | 11.5 | 10.9 |

A | Q | J | T | 4 | 3 | 1 | 0 | 1 | 1 | 1 | 4.75 | 9.5 | 9.3 |

K | Q | J | T | 4 | 3 | 0 | 1 | 1 | 1 | 1 | 3.75 | 7.5 | 7.7 |

A | K | Q | 4 | 3 | 2 | 1 | 1 | 1 | 0 | 0 | 6 | 12 | 11.4 |

A | K | J | 4 | 3 | 2 | 1 | 1 | 0 | 1 | 0 | 5.5 | 11 | 10.3 |

A | K | T | 4 | 3 | 2 | 1 | 1 | 0 | 0 | 1 | 5.25 | 10.5 | 10.05 |

A | Q | J | 4 | 3 | 2 | 1 | 0 | 1 | 1 | 0 | 4.5 | 9 | 8.7 |

A | Q | T | 4 | 3 | 2 | 1 | 0 | 1 | 0 | 1 | 4.25 | 8.5 | 8.45 |

A | J | T | 4 | 3 | 2 | 1 | 0 | 0 | 1 | 1 | 3.75 | 7.5 | 7.1 |

K | Q | J | 4 | 3 | 2 | 0 | 1 | 1 | 1 | 0 | 3.5 | 7 | 7.1 |

K | Q | T | 4 | 3 | 2 | 0 | 1 | 1 | 0 | 1 | 3.25 | 6.5 | 6.85 |

K | J | T | 4 | 3 | 2 | 0 | 1 | 0 | 1 | 1 | 2.75 | 5.5 | 5.5 |

Q | J | T | 4 | 3 | 2 | 0 | 0 | 1 | 1 | 1 | 1.75 | 3.5 | 3.65 |

A | K | 5 | 4 | 3 | 2 | 1 | 1 | 0 | 0 | 0 | 5 | 10 | 9.2 |

A | Q | 5 | 4 | 3 | 2 | 1 | 0 | 1 | 0 | 0 | 4 | 8 | 7.6 |

A | J | 5 | 4 | 3 | 2 | 1 | 0 | 0 | 1 | 0 | 3.5 | 7 | 6.25 |

A | T | 5 | 4 | 3 | 2 | 1 | 0 | 0 | 0 | 1 | 3.25 | 6.5 | 5.7 |

K | Q | 5 | 4 | 3 | 2 | 0 | 1 | 1 | 0 | 0 | 3 | 6 | 6 |

K | J | 5 | 4 | 3 | 2 | 0 | 1 | 0 | 1 | 0 | 2.5 | 5 | 4.65 |

K | T | 5 | 4 | 3 | 2 | 0 | 1 | 0 | 0 | 1 | 2.25 | 4.5 | 4.1 |

Q | J | 5 | 4 | 3 | 2 | 0 | 0 | 1 | 1 | 0 | 1.5 | 3 | 2.8 |

Q | T | 5 | 4 | 3 | 2 | 0 | 0 | 1 | 0 | 1 | 1.25 | 2.5 | 2.25 |

J | T | 5 | 4 | 3 | 2 | 0 | 0 | 0 | 1 | 1 | 0.75 | 1.5 | 1.2 |

A | 6 | 5 | 4 | 3 | 2 | 1 | 0 | 0 | 0 | 0 | 3 | 6 | 5.4 |

K | 6 | 5 | 4 | 3 | 2 | 0 | 1 | 0 | 0 | 0 | 2 | 4 | 3.8 |

Q | 6 | 5 | 4 | 3 | 2 | 0 | 0 | 1 | 0 | 0 | 1 | 2 | 1.95 |

J | 6 | 5 | 4 | 3 | 2 | 0 | 0 | 0 | 1 | 0 | 0.5 | 1 | 0.6 |

T | 6 | 5 | 4 | 3 | 2 | 0 | 0 | 0 | 0 | 1 | 0.25 | 0.5 | 0.3 |

The close agreement with Kaplan's Four C's count may seem surprising, considering that the latter is based on multiplying the HCP count in any suit by one tenth of the suit length. This method can also be used equally well for 4- and 3-card suits providing one uses 5/6 or 0.83 for 4-card suits and 4.5/6 or 0.75 for 3-card suits.

The method assigns fixed values to each secondary honor, queen, jack, and ten, in contrast with the Four C's method. A case can be made for counting the ten and the jack at different values unless they are combined with 3 HCP or two honor cards as is done with the Four C's method. The proper evaluation of jack and ten is debatable but tends to be rather trivial in the overall counting.

All aspects of hand evaluation should be based on trick-taking potential. Goren evaluated hand patterns by counting points for positive deviations from the the most balanced kind, 4-3-3-3; while Karpin assigned points for long suits only, and Kaplan counted no distribution point for 5-3-3-2 and only 1 for 6-3-2-2 and 4-4-4-1 and 2 for 7-2-2-2. The problem of shape evaluation deserves a separate discussion.

Let's see how this new method works with two six-card suits having the same hand pattern, 6=2=4=1 with identical 10 HCP and 1.5 quick tricks, viz.:

♠ x x x x x x ♥ K x ♦ Q J x x ♣ A

vs.

♠ A J x x x x ♥ K x ♦ Q x x x ♣ A

Standard hand evaluation would probably count each as 12 points. Four C's counts the first as 10.2 vs. 12.4 for the second, while my method would count them as 12 vs 14. How would a good player evaluate them?

The guru of bridge numbers, Danny Kleinman, has devised a method to evaluate suit quality in his article Thirty-Seven Points. He kindly previewed my idea and offered this comment about the close agreement between my approach and Kaplan's Four C's: "Let's see how this works without fractions. You use a 6-4-2-1 count, multiply by L, and divide by 12. Four C's uses a 4-3-2-1 count, multiplies by L, and divides by 10, then adds (roughly) a 3-2-1 count. What the two methods have in common is multilying by L. So let's ignore that to compare them. Let's transform your count to a 30-20-10-5 count multiplied by L/60, and the Four C's to a 24-18-12-6 count multiplied by L/60 plus (roughly) a 3-2-1 count. Now let's try it for L=5. Your count becomes a 30-20-10-5 count divided by 12. Four C's becomes a (24-18-12-6 count + 36-24-12-0 count) divided by 12, or a 60-42-24-6 count divided by 12. With an average mix of A, K, Q and J, the ratio of Four C's to your count becomes 132 to 65, or slightly more than 2-to-1. Surprise explained."

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