Suit combinations - 10 missing

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Tables presented below indicate the best line of play in contract bridge for a single suit in isolation in which declarer and dummy lack the ten but possess the ace, king, queen and jack. The required minimum number of tricks is indicated as well as the probability of success (POS). The line of play that is optimal in matchpoint scoring (the line of play that beats other lines of play on as many lay-outs as possible) is marked with (MP). Best defense is assumed (including falsecarding where necessary). In all cases it is assumed declarer and dummy have enough entries via the orther suits. In the lay-out for declarer and dummy, irrelevant small cards are denoted by 'x', and the ten is denoted by 'T'. In the descriptions 'RHO' stands for 'right hand opponent' (the opponent sitting behind dummy), and 'LHO' stands for 'left hand opponent' (the opponent sitting behind declarer).

[edit] Declarer and dummy hold six cards combined

Declarer - dummy Tricks required Line of play POS
x - AKQJ9 5 Cash the top honours (mp) 0.719
x - AKQJ8 5 Cash the top honours (mp) 0.636
x - AKQJx 5 Cash the top honours (mp) 0.622

[edit] Declarer and dummy hold seven cards combined

Declarer - dummy Tricks required Line of play POS
x - AKQJ9x 6 Cash the top honours (mp) 0.864
5 Finesse the 9 0.993
xx - AKQJ9 5 Cash the top honours (mp) 0.871
Jx - AKQ9x 5 Cash the top honours (mp) 0.871
xx - AKQJx 5 Cash the top honours (mp) 0.840
Jx - AKQxx 5 Cash the top honours (mp) 0.840

[edit] Declarer and dummy hold eight cards combined

Declarer - dummy Tricks required Line of play POS
x - AKQJxxx 7 Cash the top honours (mp) 0.961
xx - AKQJ9x 6 Cash the top honours, but finesse the 9 if rho shows out in first round (mp) 0.980
xx - AKQJxx 6 Cash the top honours (mp) 0.961
xxx - AKQJ9 5 Cash the top honours, but finesse the 9 if rho shows out in the first round (mp) 0.980
xxx - AKQJ8 5 Cash the top honours, but repeat the finesse to the 8 if rho shows out in the first round (mp) 0.980
xxx - AKQJx 5 Cash the top honours (mp) 0.961


Suit combinations in contract bridge
Missing honours:

10 | J | Q | K | A

J10 | Q10 | QJ | K10 | KJ | KQ | A10 |AJ | AQ | AK

QJ10 | KJ10 | KQ10 | KQJ | AJ10 | AQ10 | AQJ | AK10 | AKJ | AKQ

KQJ10 | AQJ10 | AKJ10 | AKQ10 | AKQJ