14. A K 9 x

Improvements on the Suit Combination section of

The Official Encyclopedia of Bridge, 5th edition

Jeroen Warmerdam

July, 1998

email: narcis45@wxs.nl

Improvements of declarer play

Dummy

Declarer

Tricks

Chance of Success

Tricks per Deal

22.

A K 9 x x

Q 10

Max

Cash the queen, lead the ten to the king and cash the ace

4.48

72.

A K x x

J 9 8

Run the jack and then the nine, hoping West has Q10x or Qxxxx

Max

Run the jack; if it is covered run the nine; if it loses to the queen, cash ace and king

2.85

Run the nine is worse for four tricks if West falsecards the queen from Q10x.

Run the nine produces 2.8506 tricks per deal if West is not capable of a falsecard from Q10x. Run the jack guarantees 2.8537 tricks per deal.

88.

A K 9 8 7 x

J x

Cash the ace, and then run the jack

89.

A K 9 8 x x

Cash the ace, and then run the jack

J x

Max

Run the jack, guessing what to do next if is covered or cash the ace, and then run the jack

5.01

90.

A K 9 x x x

J x

Lead small to the jack; then cash the ace and king or Lead to the nine. If it loses, cash ace and king; if West plays the ten, run the jack next

Max

Lead to the nine. If it loses, cash ace and king; if West plays the ten, run the jack next

4.96

95.

A K 7 6 x

J 9 8

Max

Run the jack. If it is covered, finesse the nine; if it loses, cash ace and king

4.14

Run the jack guarantees 4.14 tricks per deal, no matter how the defenders play. See 93.

98.

A K x x x

J 9 x

Max

Play the ace and king, unless the ten drops from West. In that case lead the jack and only cash the king if West follows suit

4.01

150.

A Q 9 8 x

J x

Lead small to the queen, and if it holds run the jack next

160.

A Q 9 x

J x x

Max

Lead small to the nine, and finesse the queen next

2.77

The treatment for "Max" in the encyclopedia gives 2.71 tricks per deal only.

209.	A Q 8 x x x J x x	Max		Run the jack; if it is covered and the ten or nine drops from East, finesse the eight next			5.21
	Dummy Declarer		Tricks		Chance of Success			Tricks per Deal
243A	A 10 9 x x K x	3 Max		Play the king, then finesse the nine or ten, unless an honor drops from East		94	3.59

289.

K Q 9 x

J x x

Lead low to the king. If it holds, lead low to the queen; if it loses cash jack and queen

369.

A Q x x x

10 x x

Max

Lead to the ace, and unless West plays the king lead small to the queen. If West plays the jack, finesse the queen immediately*

(*It has been assumed that West plays the jack from KJ. If West is good enough to play the king from KJ, also lead small to the queen on the second round, in case West plays the king)

3.41

3.38

The treatment of the encyclopedia produces 3.3791 tricks per deal if West always plays the king from KJ. Small to the queen if West plays the king is slightly better: 3.3848 tricks per deal.

381.

10 x x x x

A Q x

Max

Lead small to A Q x. Finesse the queen if East plays the jack, otherwise play the ace and lead small to the queen

3.50

477.

A J 8

10 x x

Run the ten; if it is covered win the ace and finesse the eight next; if it loses finesse the jack next* (* And if West is tempted to duck with Qx(x)(x) or Kx(x)(x))

487.

A J 9 x

x x x

Finesse the nine. If it loses to the ten, finesse the jack next. If it loses to the queen or king, cash the ace

537.

K 10 8 x

J x x

Finesse the ten. If it loses to the queen, lead small to the king; if the ten loses to the ace, finesse the eight next

541.

K x x x

J 9 x

Lead small to the nine. If it loses to the ten or queen, lead low to the king; if it holds or loses to the ace, lead low to the jack. If an honor appears from East, lead low to the nine* (* And if West does not falsecard with AQ)

I do not understand "47% chance of success" in the encyclopedia. With best defense 40% chance of success is maximum for two tricks.

543.

K 10 8 x x

J x x

Max

Finesse the ten. If the loses to the ace, finesse the eight

3.15

548.

K 10 8 x

J x x x

Max

Finesse the ten. If this loses to the queen, lead small to the jack; if the ten loses to the ace, finesse the eight

2.19

568.

A 10 x x

9 x x

Lead small to the nine. If this loses to West, cash the ace. If an honor appears from East on the first round, run the 9 and if it loses finesse the ten

Dummy

Declarer

Tricks

Chance of Success

Tricks per Deal

589.

Q J x x x

9 x

Lead small to the 9. If it loses to the ten, duck the next round

601.

Q x x x x

J 9 x

Lead small to the jack. If it loses to West, lead towards the queen but only play the queen in case the ten appears from West

617.

K 10 x x

9 x x

Lead small to the ten. If this loses to the queen or jack, lead small towards the king but only play the king in case the jack or queen appears from West

622.

K 10 x x x

9 x x

Max

Finesse the ten. If this loses to the queen or jack, lead small towards the king but only play the king in case the jack or queen appears from West

2.59

639.

Q 10 x x

x x x

Lead to the ten. If it loses to the jack, lead to the queen. If it loses to the ace or king, duck one round and then lead to the queen

Improvements of defense

Dummy

Declarer

Tricks

Chance of Success

Tricks per Deal

82.

J x x x

A K 9

Max

Cash the ace and king unless the queen drops from West*

(*But if West is good enough to falsecard from QT, we have to play the king, even if the queen falls under the ace)

2.90

2.89

See 81.

190.

Q J 9 x x

A x x

Lead the Queen. If it holds, lead the jack; if it is covered, cash the jack*

(*This assumes that East would duck the queen at least 2/3 of the time with Kx, which is the best defense. If East would cover with Kx, finesse the nine if the queen is covered.

The treatment in the encyclopedia produces 10% chance of success if East would not cover the queen with Kx. I do not see a reason to assume that East will cover half the time.

201.

A 9 8 x

Q J x x

Lead the Queen. If it is covered cash the jack; if it holds, lead the jack. Hope that West has Kxx, K10, or Kxxx*

(*It has been assumed that, if the queen is led, West will cover at most 1/3 of the time with Kx. This is the best defense)

The remark about K10xx with East is not relevant. If West would always duck with Kx, the defense is also optimal. For Max: also "at most" could be added to "cover 1/3 of the time".

203.

Q J 9 x

A x x x

Lead the queen. If it holds, lead the jack; if it is covered, cash the jack*

(*This assumes that East ducks the queen at least 2/3 of the time with Kx, which is the best defense. If East would cover with Kx, finesse the nine if the queen is covered)

The treatment in the encyclopedia produces 10% chance of success if East would not cover the queen with Kx. I do not see a reason to assume that East will cover half the time.

251.

A 10 x x x x

K 9

Max

Lead small to the nine. If East inserts an honor, win the king and run the nine*

(*But if West would cover the nine on the next round with Qxxx or Jxxx, we can win the ace, if the nine is not covered, and win 6 tricks in case East has doubleton QJ)

4.80

4.83

266.

A K 8 x x x

10 x x

Max

Lead the ten, and play the ace whatever happens; then play the king. This line saves a trick if West is tempted to cover with QJ9x

5.31+

See 271.

	Dummy Declarer		Tricks		Chance of Success		Tricks per Deal
430.	K Q 10 9 x x	4		Finesse the ten* (*But if West is good enough to play the jack from AJ(x), we can not duck the next round)		14 13
		Max		Finesse the ten* (*But if West is good enough to play the jack from AJ(x), we can not duck the next round)			2.82 2.81

437.

K Q 10 8 x x

Finesse the ten. If the jack appears from West, duck the next round*

(*But if West is good enough to play the jack from AJ(x), we can not duck the next round)

Max

Finesse the ten*

(*But if West is good enough to play the jack from AJ(x), we can not duck the next round)

3.82

3.80

496.

A J x x x x

10 x

Lead small to the ten. If it loses to West, cash the ace; if East plays an honor on the first round, run the ten next (best) or Run the ten. If West covers, duck the next round; if East wins the first round, finesse the jack*

(*It has been assumed the East will duck about of 2/3 of the time with Kx or Qx, which is optimal defense. If East would always duck, lead small to the ten and cash the ace on the next round even if East plays an honor. If East would always play an honor from Kx or Qx, lead small to the ten and finesse the next round even if the first round loses to West. It has also been assumed the West would cover the ten about 2/3 of the time with Kxx or Qxx, which is optimal defense. If West would always cover, run the ten. If West covers, duck the next round, but if East wins the first round, cash the ace. If West would always duck, run the ten and play low to the jack on the next round)

Max

Lead small to the ten. If it loses to West, cash the ace; if East plays an honor on the first round, run the ten next*

(*It has been assumed that East will play an honor at most 1/12 of the time from Kx or Qx. If East would always play an honor from Kx or Qx, finesse the jack if the first round loses to West. It has also been assumed that West will cover at most 21/52 of the time with Kxx or Qxx when the 10 is led from South. If West would always cover, run the ten and play low to the jack on the next round)

4.06

4.24

4.14

The lines in the encyclopedia for 5 tricks produces at most 17% if the defense if optimal. The line for "Max" produces 4.04 tricks per deal if East plays low from Kx or Qx.

Dummy

Declarer

Tricks

Chance of Success

Tricks per Deal

498.

A 9 x x x x

J x

Max

Lead small to the jack. If an honor wins from East, run the jack next; otherwise cash the ace*

(*But if East omits to falsecard with K10 or Q10, finesse the nine, if East plays the ten on the first round)

3.74

3.76

590.

Q J 9 8

x x x

Max

Lead small to the queen and unless West inserts an honor, finesse the nine next*

(*This assumes East would duck with Kx or Ax half the time, which is the best defense. If East would always win with Kx or Ax, lead to the jack if the first round holds. If East would always duck with Kx or Ax, lead to the jack if the first round loses)

1.58

1.63

591.

Q J 9 x

x x x

Max

Lead small to the queen and then lead to the jack*

(*This assumes East would duck with Kx or Ax half the time, which is the best defense. If East would always win with Kx or Ax, finesse the nine if the first round loses to East. If East would always duck with Kx or Ax, finesse the nine if the first round holds)

1.43

1.46

1.47

595.

Q x x x

J 9 x

Max

Lead small to the nine. If it loses to a high honor from West, lead small to the queen; otherwise lead small to the jack*

(*If East would play the ten from A10, K10, and 10xxx, which is the best defense, we have to play low to the nine if on the first round the ten is played by East and West wins this trick. Hence we only get one trick if East holds 10xxx)

1.30

1.29

Miscellaneous bridge remarks

14. A K 9 x - Q x

Missing percentage: 10%

31. A 9 x x - K Q x

Chance of Success should be 47%. Unlike (26) it is not possible to pick up J 10 x x x in West.

34. A K Q 9 x x - x x

Line for "Max" is missing:

Play off the top honors (with the same remark) Tricks per Deal: 5.64

38. A K 10 x - Q 9 x x

If the eight could be a false-card then there is 89% chance of success. This number could be added.

64A. K J 9 x x - A x

If East is capable of a falsecard from 10 x x then the Chance of Success is 19.38%. Why is this number not rounded to a whole percentage? If East is capable of a falsecard then the number of Tricks per Deal is 3.83.

69. A K 9 8 - J x x

Right play but wrong Tricks per Deal; it should be 3.03.

91. A J 8 x x x - K 9

There is no need for a safety play for 4 tricks. "Cash the king" will succeed as well.

102. J 9 8 x x - A K x

"If not, run the jack." should be "If not, run the nine".

For 5 tricks and "Max":

Cash the ace and king Chance of Success: 30% Tricks per Deal: 4.18.

133A. K x x x x x - A J 9 8

Missing percentage: 89

186a. A Q 6 x x - J 9 x

The correct Chance of Success is 82%.

243A. A 10 9 x x - K x

The given treatment for 4 tricks and for "Max" produces 65% Chance of Success and 3.57 Tricks per Deal. The given treatment for 3 tricks produces 94% Chance of Success. The line for Max can be improved. See above.

244. A K 10 9 - x x x

The given treatment for "Max" produces 3.02 Tricks per Deal.

257. A 10 x x x - K 8 x

The 100% safety play for 3 tricks could be added: "Play low to the eight."

287. K Q x x x - J 9

The given line produces 3.35 Tricks per Deal.

317. Q 10 9 - A x

The Chance of Success is 52.4989% and should be rounded to 52%. The number of Tricks per Deal is indeed 1.53 (1.5368).

339. Q x x x x - A 10

The given line for "Max" only produces 2.80 Tricks per Deal.

353. Q 10 9 8 - A x x

The given line for "Max" produces 2.70 Tricks per Deal.

361. A T 9 x x x - Q x

The given line for "Max" produces 4.56 Tricks per Deal.

The following could be added to the treatment "or lead small to the 9 and run the queen if it loses. The first line is better if East has singleton jack; the latter line is better is West has singleton king."

385. A Q x x - T x x x

There is no need for a separate safety play for 2 tricks. All lines will produce at least 2 tricks.

391A. Q x x x - A 10 8 7

The Chance of Success for 3 tricks is 62.6087%, so it should be rounded to 62.61% or better to 63%.

488. A J 8 x - 10 x x

The Chance of Success for 3 tricks is 27% instead of 26% (26.5031%).

503. A 9 8 7 x - J x x

Since the ten is also an honor, "This assumes that East will play an honor from K10 or Q10 about ..." should be "This assumes that East will play a high honor from K10 or Q10 about ...".

519. A 9 x x x x - 10 x x

"3.48 Tricks per Deal" should be "4.48 Tricks per Deal".

550. K x x x - J 10 8 x

Tricks per Deal missing: 1.97

Typing errors

"False-card" is sometimes written with a "-" and sometimes without, for instance 38 and 64A.

20. A K 10 9 x - Q x Missing space between K and 10

33. A K Q 10 x x x - x There is too much white space between "Max" and "Play"

42. A K Q 8 x x x - 9 x "J 10 x x x" should be "J 10 x x"

72. A K x x - J 9 8 Missing space between K and x

140. A Q 9 8 - J x "losses" should be "loses"

210. A Q 7 x x x - J 9 8 "J 9 8" too much to the right

221. A 9 8 x x - Q J x x "teh" should be "the"

226. Q J x x x - A x x x "20" is in the wrong column

247. A 10 x x - K 9 x "anbd" should be "and"

252. A K 10 9 x - x x x "tne" should be "the"

253. A K 9 x x - 10 x x Missing space between K and 9

276. K Q J 9 x - x Missing space between J and 9

289. K Q 9 x - J x x Missing space between the "xx" of "J x x"

291. K Q x x - J x x Missing space between K and Q.

"randmon" should be "random"; "nad" should be "and"

337. A Q x x x - 10 x Missing space between A and Q

338. A 10 9 x x - Q x The line for "Max" is given twice

345. A Q x x - 10 x x "21.0" should be "2.10"

369. A Q x x x - 10 x x Missing hand "10 x x"

386. A Q x x - x x x x "the ace," in the wrong place

401. A Q 10 x x x - x x x The suit combination is given twice.

The second line for 5 tricks is best

406. A x x x x x - Q T 9 "lsoes" should be "loses"

440. K Q x x x - 10 x Missing space between K and Q.

Missing space between AJ and "only"

444. K 10 x x - Q 9 x Missing space between AJ and "doubleton"

464. K 9 x x x - Q 10 x x "loses, or ..." too much to the left

488. A J 8 x - 10 x x Missing space between A and J.

"falsecard with 9xx" should be "falsecard with 9xxx"

489. A J x x - 10 x x "unelss" should be "unless"

509. A J 8 x - 10 x x x Missing space between J and 8

529. K J 9 8 - x x "A J 9 8" should be "K J 9 8"

540. K x x x - J 10 x Missing space between K and x

601. Q x x x x - J 9 x "241" should be "2.41"

609. Q J x x x - x x x x Missing "x" in South