Suit combinations - K10 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 king and ten but possess the ace, 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 five cards combined

Declarer - dummy	Tricks required	Line of play	POS
x - AQJ9	4	Finesse the nine (mp)	0.003
x - AQJ9	3	Finesse the nine (mp)	0.523
x - AQJ8	3	Finesse the queen (mp)	0.122
x - AQJx	3	Finesse the queen (mp)	0.112
J - AQ98	4	Run the jack (mp)	0.003
J - AQ98	3	Run the jack (mp)	0.243
J - AQ92	3	Run the jack (mp)	0.223
J - AQ82	3	Run the jack (mp)	0.057
J - AQ72	3	Run the jack (mp)	0.008
xx - AQJ	3	Finesse the queen (mp)	0.500
Jx - AQ9	3	Run the jack (mp)	0.242
Jx - AQx	3	Finesse the queen (mp)	0.004
Ax - QJ9	3	Run the queen (mp)	0.020

[edit] Declarer and dummy hold six cards combined

Declarer - dummy	Tricks required	Line of play	POS
x - AQJ98	5	Finesse the nine (mp)	0.007
x - AQJ98	4	Finesse the nine (mp)	0.408
x - AQJ97	4	Finesse the nine (mp)	0.333
x - AQJ97	3	Finesse the nine (mp)	0.900
x - AQJ96	3	Finesse the nine (mp)	0.867
x - AQJ9x	4	Finesse the nine (mp)	0.318
x - AQJ9x	3	Finesse the nine (mp)	0.859
x - AQJ87	4	Finesse the queen (mp)	0.171
x - AQJ87	3	Finesse the eight	0.867
x - AQJ8x	4	Finesse the queen (mp)	0.142
x - AQJ8x	3	Duck a round	0.733
x - AQJ86	3	Finesse the eight	0.760
x - AQJxx	4	Finesse the queen (mp)	0.133
x - AQJxx	3	Duck a round	0.719
xx - AQJ9	4	Finesse the queen (mp)	0.517
xx - AQJ9	3	Finesse the queen (mp)	0.682
xx - AQJ8	4	Finesse the queen (mp)	0.089
xx - AQJ8	3	Finesse the queen (mp)	0.552
xx - AQJ7	3	Finesse the queen (mp)	0.509
xx - AQJx	3	Finesse the queen (mp)	0.500
Jx - AQ98	4	Run the jack; if covered, take the ace and finesse the 9 next; if it holds, finesse the queen next; if it loses, play the ace next (mp)	0.052
Jx - AQ98	3	Run the jack; if covered, take the ace and finesse the 9 next; if it holds, finesse the queen next; if it loses, play the ace next (mp)	0.682
3	Play to the jack; next finesse the nine (mp)	0.556

[edit] Declarer and dummy hold seven cards combined

Declarer - dummy	Tricks required	Line of play	POS
xx - AQJ98	5	Finesse the queen (mp)	0.194
xx - AQJ98	4	Finesse the queen (mp)	0.715
xx - AQJ9x	5	Finesse the queen (mp)	0.194
xx - AQJ9x	4	Finesse the queen (mp)	0.678
xx - AQJ97	3	Finesse the nine (mp)	0.956
xx - AQJ9x	3	Finesse the nine (mp)	0.944
xx - AQJ87	4	Finesse the queen (mp)	0.171
xxx - AQJ9	4	Finesse the queen (mp)	0.278
xxx - AQJ9	3	Finesse the queen (mp)	0.783
xxx - AQJ8	4	Finesse the queen (mp)	0.194
xxx - AQJ8	3	Play the ace, then finesse the queen	0.720
xxx - AQJx	4	Finesse the queen (mp)	0.178
xxx - AQJx	3	Play the ace, then finesse the queen	0.690

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

Suit combinations in contract bridge