Simulation 8Z15 Main

Stayman or Pass?

by Richard Pavlicek

Suppose South opens 1 NT (15-17) in first seat, West passes, and you have the North hand shown.

Kevin O’Dea (Ireland) asks, “If you bid 2 Stayman intending to pass opener’s 2 or 2 , will your matchpoint score, on average, be better or worse than passing 1 NT?”

I would think better, but for a definitive answer I’ll have to consult Madame Zoltar and get back to you.

J 7 6 3
J 8 7 4
7 4
A Q 5
Table

West

Pass North

? East
South
1 NT

This kind of problem is best solved by a simulation, as theoretical calculation would be a numerical zoo if even possible. Besides your options, it is also reasonable to invite game if a fit is found, so I’ll include that as well to make three options: (A) Pass 1 NT; (B) bid 2 then pass 2 or 2 , else bid 2 NT; or (C) bid 2 then raise to 3 or 3 , else bid 2 NT. Note that Options B and C both dictate the same invitational 2 NT when opener has no major.

This simulation is more complicated than most, because the contract will vary for Options B and C. Depending on the existence of a fit and opener’s strength, Option B will play 2 , 2 , 2 NT or 3 NT; and Option C will play 2 NT, 3 , 3 , 3 NT, 4 or 4 . (Option A will always play 1 NT.) Therefore, for each random deal, the appropriate contracts must be determined before comparison. The strain is straightforward: the major fit if any (hearts with both) else notrump. My criterion for a “maximum” will be 17 revalued points, a better yardstick than simply HCP, as it will include some hands of 16 HCP but reject others.

To determine the best option I created 10,000 random deals with the North hand fixed, and South constrained to open 1 NT: HCP 15-17; freakness less than 3 (balanced); with a 5-card major, doubleton must be J-x or better (my general guideline which is about mainstream). Further, to exclude most deals that would harbor interference, both West and East are constrained to HCP less than 15; freakness less than 6 or playing half-tricks less than 12; longest suit less than 6 or playing half-tricks less than 12.

As predicted, Option B is the clear winner at matchpoints. In fact Option A is dead last, losing to Option C as well.

At total points or IMPs, however, it’s a different story. Thanks to the game bonus, Option C is now the winner except nonvul at IMPs, where Option A noses out the field — evidently the only time that passing 1 NT is the winning strategy. Enlightening, to say the least.

Results for 10,000 Deals
Option Trick Avg Make Pct Matchpoints Nonvul TPs Nonvul IMPs Vul TPs Vul IMPs
A 7.893 90.92 17896 44.74 1036730 50.48 29477 53.22 1428730 46.10 37313 49.24
B 8.638 76.28 23620 59.05 921670 44.88 25532 46.09 1294070 41.76 32980 43.52
C 8.638 52.92 18484 46.21 1121920 54.63 28079 50.69 1925620 62.14 43368 57.23

Results for 10,000 Deals
Option	Trick Avg	Make Pct	Matchpoints	Nonvul TPs	Nonvul IMPs	Vul TPs	Vul IMPs
A	7.893	90.92	17896 44.74	1036730 50.48	29477 53.22	1428730 46.10	37313 49.24
B	8.638	76.28	23620 59.05	921670 44.88	25532 46.09	1294070 41.76	32980 43.52
C	8.638	52.92	18484 46.21	1121920 54.63	28079 50.69	1925620 62.14	43368 57.23

Trick Avg shows the average number of tricks won by declarer. Make Pct shows the percent of time the contract is made. Matchpoints shows the raw total (European style: 2 for a win, 1 for a tie) and effective scoring percent. Total Points and IMPs are shown similarly as raw totals and percents, with separate accountings for N-S nonvulnerable and N-S vulnerable. (Vulnerability does not affect matchpoints.)

Below are 100 of the 10,000 deals, including the first 10 and last 10, and selected deals in-between where the option chosen made a significant difference. The number of tricks won by declarer is shown for each contract, assuming double-dummy play by both sides.

Seed 7337A4B5 10000

1. J 7 6 3
J 8 7 4
7 4
A Q 5
K 10 5 4
Q 3 2
10 9 6 2
K 10 Table Q 9 2
9 6 5
A J 8 5
J 6 3
1 NT 9
3 NT 9
3 NT 9 A 8
A K 10
K Q 3
9 8 7 4 2

2. J 7 6 3
J 8 7 4
7 4
A Q 5
A 9 2
A 10 2
K J 8 6 5
9 4 Table Q 10 4
Q 6 5 3
9 3
10 8 6 3
1 NT 7
3 NT 7
3 NT 7 K 8 5
K 9
A Q 10 2
K J 7 2

3. J 7 6 3
J 8 7 4
7 4
A Q 5
K 10 9 5 4
9 5
A Q 5 2
8 7 Table 2
K 10
K 9 8 6 3
9 6 4 3 2
1 NT 8
2 10
4 10 A Q 8
A Q 6 3 2
J 10
K J 10

4. J 7 6 3
J 8 7 4
7 4
A Q 5
K 8 4
A K 6 2
9 2
10 7 6 2 Table Q 9
9 5
Q J 10 6 5
J 9 4 3
1 NT 9
2 9
4 9 A 10 5 2
Q 10 3
A K 8 3
K 8

5. J 7 6 3
J 8 7 4
7 4
A Q 5
8 2
K Q 2
9 8 6 5
K J 6 3 Table Q 5
9 6 5
K Q J 10 3
10 7 2
1 NT 9
2 10
4 10 A K 10 9 4
A 10 3
A 2
9 8 4

6. J 7 6 3
J 8 7 4
7 4
A Q 5
K Q 8 4
6 5 3
J 3
J 6 4 2 Table A 5 2
10 9
K Q 10 9 6
10 7 3
1 NT 8
2 10
4 10 10 9
A K Q 2
A 8 5 2
K 9 8

7. J 7 6 3
J 8 7 4
7 4
A Q 5
K 9 5
10 6
J 10 9
K 10 9 4 3 Table 10 8 4
A K 3
Q 8 6 5
J 8 7
1 NT 7
2 10
3 10 A Q 2
Q 9 5 2
A K 3 2
6 2

8. J 7 6 3
J 8 7 4
7 4
A Q 5
K Q 10 4
K 5
A 6 5
J 10 6 3 Table 9 8
Q 9 6 2
Q 10 9 8 3
9 7
1 NT 8
2 NT 8
2 NT 8 A 5 2
A 10 3
K J 2
K 8 4 2

9. J 7 6 3
J 8 7 4
7 4
A Q 5
9
Q 10 9 6 3 2
10 9 8 5
10 7 Table A Q 8 5 4
K
K J 6 3
9 6 4
1 NT 10
3 NT 10
3 NT 10 K 10 2
A 5
A Q 2
K J 8 3 2

10. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 8 5 4
K 10
Q J 6 3
J 8 2 Table A 2
9 6 5 2
9 8 5 2
K 9 6
1 NT 8
3 NT 8
3 NT 8 K 10 9
A Q 3
A K 10
10 7 4 3

Simulation 8Z15 Main Top Stayman or Pass?

14. J 7 6 3
J 8 7 4
7 4
A Q 5
9
10 6 2
Q 9 6 3 2
J 7 4 3 Table K Q 4
A Q 5 3
J 8 5
9 8 2
1 NT 10
2 11
4 11 A 10 8 5 2
K 9
A K 10
K 10 6

20. J 7 6 3
J 8 7 4
7 4
A Q 5
9
6 5
J 8 6 5 2
K 9 8 7 4 Table 10 5 2
A 10 9 2
A Q 9 3
J 6
1 NT 8
2 11
4 11 A K Q 8 4
K Q 3
K 10
10 3 2

22. J 7 6 3
J 8 7 4
7 4
A Q 5
9 4
10 9 6
Q 9 6 2
J 9 6 4 Table K Q 10 8 5
K
J 10 5 3
K 7 2
1 NT 10
2 11
4 11 A 2
A Q 5 3 2
A K 8
10 8 3

25. J 7 6 3
J 8 7 4
7 4
A Q 5
K 9 5 2
K
A 9 8 5
10 8 7 4 Table A 10
10 9 6 3 2
10 2
J 9 6 3
1 NT 9
3 NT 9
3 NT 9 Q 8 4
A Q 5
K Q J 6 3
K 2

26. J 7 6 3
J 8 7 4
7 4
A Q 5
—
10 9 6 5 3
J 10 9 8 5
10 8 6 Table K 10 9 5 2
Q 2
A Q 2
K 4 3
1 NT 9
2 10
4 10 A Q 8 4
A K
K 6 3
J 9 7 2

27. J 7 6 3
J 8 7 4
7 4
A Q 5
9 4 2
K Q 9 5
8 6 5 2
8 6 Table Q 5
A 6 3
Q J 10 9
J 9 4 2
1 NT 10
2 11
4 11 A K 10 8
10 2
A K 3
K 10 7 3

32. J 7 6 3
J 8 7 4
7 4
A Q 5
8 5
A 9 2
J 10 9 5
J 8 7 4 Table K Q 4
K 5 3
8 6 3
K 10 9 2
1 NT 7
2 9
4 9 A 10 9 2
Q 10 6
A K Q 2
6 3

44. J 7 6 3
J 8 7 4
7 4
A Q 5
10 8 4
10 2
J 10 6 5
J 9 7 6 Table Q
A K 6 3
A 9 3 2
10 4 3 2
1 NT 10
2 9
4 9 A K 9 5 2
Q 9 5
K Q 8
K 8

47. J 7 6 3
J 8 7 4
7 4
A Q 5
A 4
9 6 3
J 10 8 5
K 7 4 2 Table 8 5 2
Q 10 2
K Q 6 2
10 8 6
1 NT 9
2 10
4 10 K Q 10 9
A K 5
A 9 3
J 9 3

48. J 7 6 3
J 8 7 4
7 4
A Q 5
9
10 9 6 3
A Q J 9
J 10 9 6 Table 10 5 4 2
A K 2
10 8 3 2
7 4
1 NT 7
2 8
4 8 A K Q 8
Q 5
K 6 5
K 8 3 2

Simulation 8Z15 Main Top Stayman or Pass?

49. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 8 5
Q 6 3
K 9 6 3
K J 6 Table A 9 4
10 9 5
J 10 8 2
8 3 2
1 NT 9
3 NT 9
3 NT 9 K 10 2
A K 2
A Q 5
10 9 7 4

50. J 7 6 3
J 8 7 4
7 4
A Q 5
10 9 5
Q 6
J 9 6 5 3
9 7 2 Table 4 2
A K 9 3
K Q 8 2
10 6 3
1 NT 9
2 10
4 10 A K Q 8
10 5 2
A 10
K J 8 4

53. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 9 5
K 9
Q 6 3 2
K J 8 4 Table 10 2
10 5 3 2
K J 10 9
7 3 2
1 NT 8
2 10
4 10 A K 8 4
A Q 6
A 8 5
10 9 6

55. J 7 6 3
J 8 7 4
7 4
A Q 5
K Q 10 9 2
6 5
Q J 5
J 10 9 Table 5 4
K 9 3
K 10 3 2
8 7 6 4
1 NT 9
2 11
4 11 A 8
A Q 10 2
A 9 8 6
K 3 2

56. J 7 6 3
J 8 7 4
7 4
A Q 5
K 10 4 2
10 2
A 6 5 2
K 8 4 Table Q 9 5
Q 5
K 9 8 3
9 6 3 2
1 NT 9
2 10
4 10 A 8
A K 9 6 3
Q J 10
J 10 7

57. J 7 6 3
J 8 7 4
7 4
A Q 5
9 8 5 2
A 2
Q J 8 5
J 4 3 Table Q 10
Q 9 6 5
A 9 3 2
8 6 2
1 NT 9
3 NT 9
3 NT 9 A K 4
K 10 3
K 10 6
K 10 9 7

58. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 8 5 4
5 3
K 8 5
J 8 7 2 Table 10
K 10 9 2
Q J 10 2
K 10 6 3
1 NT 7
2 9
4 9 A K 9 2
A Q 6
A 9 6 3
9 4

60. J 7 6 3
J 8 7 4
7 4
A Q 5
A 9
9 5
Q 10 6 3
J 10 6 4 2 Table Q 10 8 4 2
K Q 6
J 8 2
9 7
1 NT 9
2 10
4 10 K 5
A 10 3 2
A K 9 5
K 8 3

62. J 7 6 3
J 8 7 4
7 4
A Q 5
10 2
K Q 9
10 8 6 5 3
J 8 6 Table A Q 9 4
6 3
J 9
K 10 7 4 2
1 NT 6
2 8
4 8 K 8 5
A 10 5 2
A K Q 2
9 3

64. J 7 6 3
J 8 7 4
7 4
A Q 5
K 2
A Q 10 2
J 10 9 6 2
7 4 Table 9 5 4
5 3
A Q 8 5
10 9 8 3
1 NT 6
2 8
4 8 A Q 10 8
K 9 6
K 3
K J 6 2

Simulation 8Z15 Main Top Stayman or Pass?

66. J 7 6 3
J 8 7 4
7 4
A Q 5
K Q 9 5
A K
Q 10 8 3
10 6 2 Table 10 2
Q 6 5 3 2
9 5 2
7 4 3
1 NT 9
3 NT 9
3 NT 9 A 8 4
10 9
A K J 6
K J 9 8

67. J 7 6 3
J 8 7 4
7 4
A Q 5
K 10 8 5
9 3
K Q J
K 10 8 2 Table Q 2
10 6 5
10 8 3 2
J 6 4 3
1 NT 9
2 10
4 10 A 9 4
A K Q 2
A 9 6 5
9 7

68. J 7 6 3
J 8 7 4
7 4
A Q 5
10 5
K Q 10 5
10 6 5 3
9 4 2 Table A 8 2
9 6 2
K Q 8
J 8 6 3
1 NT 9
2 10
4 10 K Q 9 4
A 3
A J 9 2
K 10 7

72. J 7 6 3
J 8 7 4
7 4
A Q 5
9 4
Q 9 6 2
9 6 5
K 8 6 3 Table K 10 2
K 10 5
K 10 8 2
J 10 7
1 NT 9
2 11
4 11 A Q 8 5
A 3
A Q J 3
9 4 2

76. J 7 6 3
J 8 7 4
7 4
A Q 5
10 8 2
A K 9 5
J 10 3
K 6 3 Table K 9
Q 10 3
9 8 6 2
10 9 8 7
1 NT 9
2 11
4 11 A Q 5 4
6 2
A K Q 5
J 4 2

77. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 5
K 2
K Q 9 2
J 8 7 4 3 Table A 4 2
10 9 3
J 8 6 3
10 9 6
1 NT 8
2 10
4 10 K 10 9 8
A Q 6 5
A 10 5
K 2

80. J 7 6 3
J 8 7 4
7 4
A Q 5
9 2
10 6 5 3
Q 10 8
10 9 3 2 Table Q 10 4
A Q
A J 9 3 2
8 7 4
1 NT 8
2 10
4 10 A K 8 5
K 9 2
K 6 5
K J 6

89. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 4 2
5
J 9 6 3
K 10 7 4 2 Table K 8 5
K Q 6 3
Q 10 2
J 9 3
1 NT 8
2 11
4 11 A 10 9
A 10 9 2
A K 8 5
8 6

90. J 7 6 3
J 8 7 4
7 4
A Q 5
9 5 4 2
K 10 5 2
3 2
K 9 3 Table Q 10
Q 9 3
A Q 10 8
10 8 7 6
1 NT 9
3 NT 9
3 NT 9 A K 8
A 6
K J 9 6 5
J 4 2

91. J 7 6 3
J 8 7 4
7 4
A Q 5
5 4
9 6 3
Q J 8 3
8 7 4 2 Table A K 10 2
Q 2
9 6 2
K 10 9 6
1 NT 9
2 10
4 10 Q 9 8
A K 10 5
A K 10 5
J 3

Simulation 8Z15 Main Top Stayman or Pass?

96. J 7 6 3
J 8 7 4
7 4
A Q 5
10 5 4 2
10 6 5
8 6 3
K 9 2 Table A Q 9
K 9 2
K 9 5
J 8 4 3
1 NT 10
3 NT 10
3 NT 10 K 8
A Q 3
A Q J 10 2
10 7 6

97. J 7 6 3
J 8 7 4
7 4
A Q 5
A K Q
10 9 5 3
9 8 5
10 7 4 Table 10 8 4 2
6
A Q 6 3 2
J 3 2
1 NT 9
2 10
4 10 9 5
A K Q 2
K J 10
K 9 8 6

100. J 7 6 3
J 8 7 4
7 4
A Q 5
K 10
Q 2
Q 6 5 3
J 10 9 8 7 Table 5 4 2
K 9 6
K J 10 9 2
3 2
1 NT 8
2 10
4 10 A Q 9 8
A 10 5 3
A 8
K 6 4

101. J 7 6 3
J 8 7 4
7 4
A Q 5
A 8 4
9 2
A 10 9 8 5
J 6 3 Table 5
A Q 6 3
J 3 2
10 9 8 7 2
1 NT 7
2 10
4 10 K Q 10 9 2
K 10 5
K Q 6
K 4

102. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 5 2
9 6
A 10 6
9 8 7 6 2 Table 10 9 8 4
A K 5
K 9 8 2
4 3
1 NT 8
2 8
4 8 A K
Q 10 3 2
Q J 5 3
K J 10

105. J 7 6 3
J 8 7 4
7 4
A Q 5
8 5
Q 6 5
K 9 8
10 8 7 6 3 Table A Q 10 4 2
A 9 3
10 6 5
J 2
1 NT 9
3 NT 9
3 NT 9 K 9
K 10 2
A Q J 3 2
K 9 4

106. J 7 6 3
J 8 7 4
7 4
A Q 5
10 9 8
Q 5 3
10 8 3 2
J 8 3 Table A Q 5 2
A 6 2
K 9 5
10 9 2
1 NT 9
3 NT 9
3 NT 9 K 4
K 10 9
A Q J 6
K 7 6 4

108. J 7 6 3
J 8 7 4
7 4
A Q 5
K 9 8 4 2
10 6
J 3
K J 10 7 Table 5
5 3 2
A K 10 8 6
8 4 3 2
1 NT 9
2 10
4 10 A Q 10
A K Q 9
Q 9 5 2
9 6

111. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 4
9 6 3
J 10 8 6 5 3
4 3 Table 10 9 8 2
K Q
A Q 2
J 8 7 2
1 NT 9
2 11
4 11 A K 5
A 10 5 2
K 9
K 10 9 6

115. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 10 4 2
K 3 2
J 10 6 2
K 7 Table 9 8 5
A 10
Q 9 8 5
J 8 6 3
1 NT 8
2 10
4 10 A K
Q 9 6 5
A K 3
10 9 4 2

Simulation 8Z15 Main Top Stayman or Pass?

116. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 8 4
5 3 2
J 10 9 2
J 10 9 Table A 10 9 5
Q
A Q 6 5
8 7 3 2
1 NT 9
2 11
4 11 K 2
A K 10 9 6
K 8 3
K 6 4

118. J 7 6 3
J 8 7 4
7 4
A Q 5
8 5 4 2
Q
Q 10 6 3 2
K 4 3 Table K Q
K 10 6 3
J 9 8
10 7 6 2
1 NT 9
2 10
4 10 A 10 9
A 9 5 2
A K 5
J 9 8

119. J 7 6 3
J 8 7 4
7 4
A Q 5
A 4 2
K 10
10 9 6 2
K 10 6 4 Table K 9 8
9 6 5
Q J 8 5 3
9 7
1 NT 7
2 9
4 9 Q 10 5
A Q 3 2
A K
J 8 3 2

121. J 7 6 3
J 8 7 4
7 4
A Q 5
8 5 4
K Q 9 5 3
Q 8
J 9 4 Table K 9
10 6
A J 10 6 2
8 7 3 2
1 NT 9
2 11
4 11 A Q 10 2
A 2
K 9 5 3
K 10 6

128. J 7 6 3
J 8 7 4
7 4
A Q 5
4 2
Q 10 9 5 3
K 6
K 9 7 3 Table 10 8 5
K
Q J 10 9 5 3
J 10 6
1 NT 9
2 10
4 10 A K Q 9
A 6 2
A 8 2
8 4 2

130. J 7 6 3
J 8 7 4
7 4
A Q 5
10 9 4 2
5 3
A Q 10
J 7 6 3 Table K 8
Q 9 2
K J 9 8
10 9 8 2
1 NT 9
2 11
4 11 A Q 5
A K 10 6
6 5 3 2
K 4

139. J 7 6 3
J 8 7 4
7 4
A Q 5
9 8 5 4 2
Q 5
A 9 5 2
7 3 Table K
10 3 2
K Q 10 6 3
J 10 4 2
1 NT 8
2 11
4 11 A Q 10
A K 9 6
J 8
K 9 8 6

142. J 7 6 3
J 8 7 4
7 4
A Q 5
8 4
5 2
J 6 5 2
J 10 8 4 2 Table A Q 10 5 2
K Q 9 3
K 3
7 3
1 NT 9
3 NT 9
3 NT 9 K 9
A 10 6
A Q 10 9 8
K 9 6

144. J 7 6 3
J 8 7 4
7 4
A Q 5
A 10 9 2
9 5
J 9 5
10 9 8 4 Table K 8 5
Q 6 2
A 8 6 3
J 7 3
1 NT 9
2 10
4 10 Q 4
A K 10 3
K Q 10 2
K 6 2

146. J 7 6 3
J 8 7 4
7 4
A Q 5
9 5 4 2
A Q 10
K 10 5
10 8 2 Table 8
9 6 3
Q 9 8 6 3 2
K J 7
1 NT 6
2 8
4 8 A K Q 10
K 5 2
A J
9 6 4 3

Simulation 8Z15 Main Top Stayman or Pass?

147. J 7 6 3
J 8 7 4
7 4
A Q 5
K 10 9
9 3
9 8 6 3
J 10 8 4 Table 5 2
K Q 6 5
A 10 5
K 9 7 6
1 NT 7
2 9
4 9 A Q 8 4
A 10 2
K Q J 2
3 2

149. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 5
A 9 6 5
10 3 2
K J 7 6 Table K 8 2
Q 2
Q 9 6 5
10 9 8 2
1 NT 9
2 10
4 10 A 10 9 4
K 10 3
A K J 8
4 3

150. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 8 4
5 3 2
J 6 5 3
K 9 8 Table K 10 9 2
Q 6
K Q 9
10 7 6 4
1 NT 8
2 10
4 10 A 5
A K 10 9
A 10 8 2
J 3 2

151. J 7 6 3
J 8 7 4
7 4
A Q 5
10 9 5
Q 9 5 3
10 3
7 6 3 2 Table Q 4 2
A
A Q J 8 5
J 10 9 8
1 NT 8
2 10
4 10 A K 8
K 10 6 2
K 9 6 2
K 4

152. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 9 8 4 2
5 3
10 6 5
6 3 2 Table A 10
K 10 9 6
A K 8 2
10 9 4
1 NT 9
3 NT 9
3 NT 9 K 5
A Q 2
Q J 9 3
K J 8 7

159. J 7 6 3
J 8 7 4
7 4
A Q 5
A 8 5 4
Q 6
Q 5 2
K J 8 2 Table 9 2
10 9 3 2
K 9 8
7 6 4 3
1 NT 9
3 NT 9
3 NT 9 K Q 10
A K 5
A J 10 6 3
10 9

163. J 7 6 3
J 8 7 4
7 4
A Q 5
10 4
K 6 5 2
K Q 6 2
K 7 2 Table Q 8 5
Q 10 9
10 5 3
10 8 4 3
1 NT 9
2 10
4 10 A K 9 2
A 3
A J 9 8
J 9 6

164. J 7 6 3
J 8 7 4
7 4
A Q 5
9 4 2
A 3 2
J 8
K 10 4 3 2 Table K 10 5
Q 10 9 5
Q 10 9 5
7 6
1 NT 9
3 NT 9
3 NT 9 A Q 8
K 6
A K 6 3 2
J 9 8

165. J 7 6 3
J 8 7 4
7 4
A Q 5
K 10 2
A 5 3
9 6 5 2
10 4 2 Table A Q 5
Q 10 9 2
10 8
J 8 7 6
1 NT 9
3 NT 9
3 NT 9 9 8 4
K 6
A K Q J 3
K 9 3

167. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 10 8 4
A 9 6
Q J 2
9 8 7 Table 5
Q 5 3 2
9 8 6 5
K J 4 2
1 NT 7
2 9
4 9 A K 9 2
K 10
A K 10 3
10 6 3

Simulation 8Z15 Main Top Stayman or Pass?

171. J 7 6 3
J 8 7 4
7 4
A Q 5
10 8 5
10 9 3
A Q J 9 3
8 3 Table A 4
K Q 5 2
5 2
10 7 6 4 2
1 NT 7
2 9
4 9 K Q 9 2
A 6
K 10 8 6
K J 9

175. J 7 6 3
J 8 7 4
7 4
A Q 5
9 5
Q 10 6 2
A 9 5 3 2
8 6 Table 8 4 2
K 9 5
K Q J
9 4 3 2
1 NT 8
2 10
4 10 A K Q 10
A 3
10 8 6
K J 10 7

177. J 7 6 3
J 8 7 4
7 4
A Q 5
K 9 8
6 5 3
5 2
K 9 7 4 2 Table A 10 5 4
K Q 9
J 10 9 8 3
3
1 NT 9
3 NT 9
3 NT 9 Q 2
A 10 2
A K Q 6
J 10 8 6

182. J 7 6 3
J 8 7 4
7 4
A Q 5
K 8 5
10 9
J 9 8 3
10 9 8 7 Table Q 9 4 2
Q 2
A K 10 5
6 3 2
1 NT 9
2 10
4 10 A 10
A K 6 5 3
Q 6 2
K J 4

194. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 9 8 4
5 2
Q 8
K 10 9 7 2 Table A 5 2
Q 10 9 6
J 6 5 2
J 8
1 NT 9
3 NT 9
3 NT 9 K 10
A K 3
A K 10 9 3
6 4 3

197. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 8 4
A 10 6
A K 6 5
10 6 2 Table 10 9 5
Q 2
10 9 8 3 2
9 7 4
1 NT 6
2 8
4 8 A K 2
K 9 5 3
Q J
K J 8 3

204. J 7 6 3
J 8 7 4
7 4
A Q 5
K 10 9 8 2
9
Q 5 3 2
K 6 2 Table A 5
Q 10 6 3 2
J 10
10 8 7 3
1 NT 9
3 NT 9
3 NT 9 Q 4
A K 5
A K 9 8 6
J 9 4

207. J 7 6 3
J 8 7 4
7 4
A Q 5
9 4
K 10 5 3
J 8 6 3
K 9 6 Table 10 8 5
A Q 6
K 5 2
10 8 4 2
1 NT 9
2 10
4 10 A K Q 2
9 2
A Q 10 9
J 7 3

210. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 8 5 4
Q 6 2
K 10 9
K 6 3 Table 10 9
K 10 9 5
Q J 8 6 2
10 2
1 NT 9
3 NT 9
3 NT 9 A K 2
A 3
A 5 3
J 9 8 7 4

215. J 7 6 3
J 8 7 4
7 4
A Q 5
10 9 8 4
Q 6
K J 8 6 2
10 4 Table K 2
A 10 9 5 3
Q
J 9 8 6 2
1 NT 9
3 NT 9
3 NT 9 A Q 5
K 2
A 10 9 5 3
K 7 3

Simulation 8Z15 Main Top Stayman or Pass?

221. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 9 5 2
10 5
10 5
K 10 8 7 2 Table A 10 8
A 9 3
Q J 8 3 2
9 3
1 NT 8
2 10
4 10 K 4
K Q 6 2
A K 9 6
J 6 4

222. J 7 6 3
J 8 7 4
7 4
A Q 5
A 10 5 4
K 9
J 8 3
10 8 3 2 Table Q
Q 6 5 3
Q 10 9 6 5 2
J 4
1 NT 9
2 10
4 10 K 9 8 2
A 10 2
A K
K 9 7 6

223. J 7 6 3
J 8 7 4
7 4
A Q 5
A 9 5 2
K 5 3 2
K J 2
9 3 Table 10 8
9 6
8 5 3
K J 10 8 7 2
1 NT 9
3 NT 9
3 NT 9 K Q 4
A Q 10
A Q 10 9 6
6 4

225. J 7 6 3
J 8 7 4
7 4
A Q 5
9 8 5 4
A 3
J 8 6 5
8 6 4 Table Q 10
K 9 6 2
A 9 3
J 10 9 7
1 NT 9
3 NT 9
3 NT 9 A K 2
Q 10 5
K Q 10 2
K 3 2

227. J 7 6 3
J 8 7 4
7 4
A Q 5
A Q 9 2
10 6 5 2
A K 8 3
7 Table 8
Q 9 3
9 6 5 2
10 9 8 3 2
1 NT 8
2 8
4 8 K 10 5 4
A K
Q J 10
K J 6 4

228. J 7 6 3
J 8 7 4
7 4
A Q 5
K 9 8
K 9 6 5
Q J 2
8 6 2 Table 10 4
A Q 2
10 9 8 6 3
7 4 3
1 NT 9
2 10
4 10 A Q 5 2
10 3
A K 5
K J 10 9

234. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 4
Q 5
9 3 2
J 8 7 6 4 2 Table 10 8 5
A 9 6 3
K Q J 10 6
10
1 NT 8
2 10
4 10 A K 9 2
K 10 2
A 8 5
K 9 3

236. J 7 6 3
J 8 7 4
7 4
A Q 5
10 4
10 5 3
K J 2
K 9 8 6 4 Table K Q 8
Q 9 6
10 9 5 3
J 3 2
1 NT 7
2 10
4 10 A 9 5 2
A K 2
A Q 8 6
10 7

237. J 7 6 3
J 8 7 4
7 4
A Q 5
9 4
5
A 9 8 5 3 2
10 9 6 3 Table 10 8 2
A Q 9 3 2
K Q 6
7 4
1 NT 6
2 8
4 8 A K Q 5
K 10 6
J 10
K J 8 2

240. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 8
K Q 10 9 5
K 10 8
10 6 2 Table 9 5 2
6 3
Q 9 6 3 2
K J 7
1 NT 7
2 9
4 9 A K 10 4
A 2
A J 5
9 8 4 3

Simulation 8Z15 Main Top Stayman or Pass?

9991. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 9 5
10 9 6
Q 8 6 3
9 8 6 Table A 8 2
A Q 3
J 9 5 2
7 4 3
1 NT 8
3 NT 8
3 NT 8 K 10 4
K 5 2
A K 10
K J 10 2

9992. J 7 6 3
J 8 7 4
7 4
A Q 5
8 5
K 9 5
J 10 8
J 10 9 7 4 Table 10 9 4
Q 10 2
A K Q 5 2
8 3
1 NT 8
2 9
3 9 A K Q 2
A 6 3
9 6 3
K 6 2

9993. J 7 6 3
J 8 7 4
7 4
A Q 5
A K Q 10
5 2
10 6 2
10 9 7 4 Table 9 5 4
Q 10 9 6
Q J 5
J 8 6
1 NT 9
3 NT 9
3 NT 9 8 2
A K 3
A K 9 8 3
K 3 2

9994. J 7 6 3
J 8 7 4
7 4
A Q 5
8 2
A Q 6 3
9 5 3
K 8 6 3 Table Q 9 5
10 5
K Q 8 6
J 10 4 2
1 NT 9
2 10
4 10 A K 10 4
K 9 2
A J 10 2
9 7

9995. J 7 6 3
J 8 7 4
7 4
A Q 5
A K 9
10 6 3
A 9 6 3
9 6 2 Table 8 2
9 5 2
K J 10 8
8 7 4 3
1 NT 7
2 9
4 9 Q 10 5 4
A K Q
Q 5 2
K J 10

9996. J 7 6 3
J 8 7 4
7 4
A Q 5
10 9 5
A
A 8 6 3 2
9 8 7 2 Table A 8 4 2
9 6 5 3
Q 10
K 10 6
1 NT 8
2 9
3 9 K Q
K Q 10 2
K J 9 5
J 4 3

9997. J 7 6 3
J 8 7 4
7 4
A Q 5
A 10 9 4
6 5 2
K 8 3
K 7 3 Table 5
Q 10 9
Q J 9 6 5
9 6 4 2
1 NT 8
2 9
4 9 K Q 8 2
A K 3
A 10 2
J 10 8

9998. J 7 6 3
J 8 7 4
7 4
A Q 5
K Q 10 9 5 4
K 6
10 5 3
10 9 Table 8
A 5 3
K 8 6 2
J 8 7 4 2
1 NT 9
2 10
4 10 A 2
Q 10 9 2
A Q J 9
K 6 3

9999. J 7 6 3
J 8 7 4
7 4
A Q 5
K 2
5 3
8 6 5 3 2
J 10 7 6 Table A 10 9 8 5
Q 10 6
K Q J
9 3
1 NT 8
2 9
3 9 Q 4
A K 9 2
A 10 9
K 8 4 2

10000. J 7 6 3
J 8 7 4
7 4
A Q 5
Q 9 4 2
9 2
K Q 10 6
9 6 2 Table K 10 5
K Q 5
J 9 8 2
10 7 4
1 NT 9
2 10
4 10 A 8
A 10 6 3
A 5 3
K J 8 3

Simulation 8Z15 Main

Top Stayman or Pass?

1.	J 7 6 3 J 8 7 4 7 4 A Q 5
K 10 5 4 Q 3 2 10 9 6 2 K 10		Q 9 2 9 6 5 A J 8 5 J 6 3
1 NT 9 3 NT 9 3 NT 9	A 8 A K 10 K Q 3 9 8 7 4 2

2.	J 7 6 3 J 8 7 4 7 4 A Q 5
A 9 2 A 10 2 K J 8 6 5 9 4		Q 10 4 Q 6 5 3 9 3 10 8 6 3
1 NT 7 3 NT 7 3 NT 7	K 8 5 K 9 A Q 10 2 K J 7 2

3.	J 7 6 3 J 8 7 4 7 4 A Q 5
K 10 9 5 4 9 5 A Q 5 2 8 7		2 K 10 K 9 8 6 3 9 6 4 3 2
1 NT 8 2 10 4 10	A Q 8 A Q 6 3 2 J 10 K J 10

4.	J 7 6 3 J 8 7 4 7 4 A Q 5
K 8 4 A K 6 2 9 2 10 7 6 2		Q 9 9 5 Q J 10 6 5 J 9 4 3
1 NT 9 2 9 4 9	A 10 5 2 Q 10 3 A K 8 3 K 8

5.	J 7 6 3 J 8 7 4 7 4 A Q 5
8 2 K Q 2 9 8 6 5 K J 6 3		Q 5 9 6 5 K Q J 10 3 10 7 2
1 NT 9 2 10 4 10	A K 10 9 4 A 10 3 A 2 9 8 4

6.	J 7 6 3 J 8 7 4 7 4 A Q 5
K Q 8 4 6 5 3 J 3 J 6 4 2		A 5 2 10 9 K Q 10 9 6 10 7 3
1 NT 8 2 10 4 10	10 9 A K Q 2 A 8 5 2 K 9 8

7.	J 7 6 3 J 8 7 4 7 4 A Q 5
K 9 5 10 6 J 10 9 K 10 9 4 3		10 8 4 A K 3 Q 8 6 5 J 8 7
1 NT 7 2 10 3 10	A Q 2 Q 9 5 2 A K 3 2 6 2

8.	J 7 6 3 J 8 7 4 7 4 A Q 5
K Q 10 4 K 5 A 6 5 J 10 6 3		9 8 Q 9 6 2 Q 10 9 8 3 9 7
1 NT 8 2 NT 8 2 NT 8	A 5 2 A 10 3 K J 2 K 8 4 2

9.	J 7 6 3 J 8 7 4 7 4 A Q 5
9 Q 10 9 6 3 2 10 9 8 5 10 7		A Q 8 5 4 K K J 6 3 9 6 4
1 NT 10 3 NT 10 3 NT 10	K 10 2 A 5 A Q 2 K J 8 3 2

10.	J 7 6 3 J 8 7 4 7 4 A Q 5
Q 8 5 4 K 10 Q J 6 3 J 8 2		A 2 9 6 5 2 9 8 5 2 K 9 6
1 NT 8 3 NT 8 3 NT 8	K 10 9 A Q 3 A K 10 10 7 4 3

14.	J 7 6 3 J 8 7 4 7 4 A Q 5
9 10 6 2 Q 9 6 3 2 J 7 4 3		K Q 4 A Q 5 3 J 8 5 9 8 2
1 NT 10 2 11 4 11	A 10 8 5 2 K 9 A K 10 K 10 6

20.	J 7 6 3 J 8 7 4 7 4 A Q 5
9 6 5 J 8 6 5 2 K 9 8 7 4		10 5 2 A 10 9 2 A Q 9 3 J 6
1 NT 8 2 11 4 11	A K Q 8 4 K Q 3 K 10 10 3 2

22.	J 7 6 3 J 8 7 4 7 4 A Q 5
9 4 10 9 6 Q 9 6 2 J 9 6 4		K Q 10 8 5 K J 10 5 3 K 7 2
1 NT 10 2 11 4 11	A 2 A Q 5 3 2 A K 8 10 8 3

25.	J 7 6 3 J 8 7 4 7 4 A Q 5
K 9 5 2 K A 9 8 5 10 8 7 4		A 10 10 9 6 3 2 10 2 J 9 6 3
1 NT 9 3 NT 9 3 NT 9	Q 8 4 A Q 5 K Q J 6 3 K 2

26.	J 7 6 3 J 8 7 4 7 4 A Q 5
— 10 9 6 5 3 J 10 9 8 5 10 8 6		K 10 9 5 2 Q 2 A Q 2 K 4 3
1 NT 9 2 10 4 10	A Q 8 4 A K K 6 3 J 9 7 2

27.	J 7 6 3 J 8 7 4 7 4 A Q 5
9 4 2 K Q 9 5 8 6 5 2 8 6		Q 5 A 6 3 Q J 10 9 J 9 4 2
1 NT 10 2 11 4 11	A K 10 8 10 2 A K 3 K 10 7 3

32.	J 7 6 3 J 8 7 4 7 4 A Q 5
8 5 A 9 2 J 10 9 5 J 8 7 4		K Q 4 K 5 3 8 6 3 K 10 9 2
1 NT 7 2 9 4 9	A 10 9 2 Q 10 6 A K Q 2 6 3

44.	J 7 6 3 J 8 7 4 7 4 A Q 5
10 8 4 10 2 J 10 6 5 J 9 7 6		Q A K 6 3 A 9 3 2 10 4 3 2
1 NT 10 2 9 4 9	A K 9 5 2 Q 9 5 K Q 8 K 8

47.	J 7 6 3 J 8 7 4 7 4 A Q 5
A 4 9 6 3 J 10 8 5 K 7 4 2		8 5 2 Q 10 2 K Q 6 2 10 8 6
1 NT 9 2 10 4 10	K Q 10 9 A K 5 A 9 3 J 9 3

48.	J 7 6 3 J 8 7 4 7 4 A Q 5
9 10 9 6 3 A Q J 9 J 10 9 6		10 5 4 2 A K 2 10 8 3 2 7 4
1 NT 7 2 8 4 8	A K Q 8 Q 5 K 6 5 K 8 3 2

49.	J 7 6 3 J 8 7 4 7 4 A Q 5
Q 8 5 Q 6 3 K 9 6 3 K J 6		A 9 4 10 9 5 J 10 8 2 8 3 2
1 NT 9 3 NT 9 3 NT 9	K 10 2 A K 2 A Q 5 10 9 7 4

50.	J 7 6 3 J 8 7 4 7 4 A Q 5
10 9 5 Q 6 J 9 6 5 3 9 7 2		4 2 A K 9 3 K Q 8 2 10 6 3
1 NT 9 2 10 4 10	A K Q 8 10 5 2 A 10 K J 8 4

53.	J 7 6 3 J 8 7 4 7 4 A Q 5
Q 9 5 K 9 Q 6 3 2 K J 8 4		10 2 10 5 3 2 K J 10 9 7 3 2
1 NT 8 2 10 4 10	A K 8 4 A Q 6 A 8 5 10 9 6

55.	J 7 6 3 J 8 7 4 7 4 A Q 5
K Q 10 9 2 6 5 Q J 5 J 10 9		5 4 K 9 3 K 10 3 2 8 7 6 4
1 NT 9 2 11 4 11	A 8 A Q 10 2 A 9 8 6 K 3 2

56.	J 7 6 3 J 8 7 4 7 4 A Q 5
K 10 4 2 10 2 A 6 5 2 K 8 4		Q 9 5 Q 5 K 9 8 3 9 6 3 2
1 NT 9 2 10 4 10	A 8 A K 9 6 3 Q J 10 J 10 7

57.	J 7 6 3 J 8 7 4 7 4 A Q 5
9 8 5 2 A 2 Q J 8 5 J 4 3		Q 10 Q 9 6 5 A 9 3 2 8 6 2
1 NT 9 3 NT 9 3 NT 9	A K 4 K 10 3 K 10 6 K 10 9 7

58.	J 7 6 3 J 8 7 4 7 4 A Q 5
Q 8 5 4 5 3 K 8 5 J 8 7 2		10 K 10 9 2 Q J 10 2 K 10 6 3
1 NT 7 2 9 4 9	A K 9 2 A Q 6 A 9 6 3 9 4

60.	J 7 6 3 J 8 7 4 7 4 A Q 5
A 9 9 5 Q 10 6 3 J 10 6 4 2		Q 10 8 4 2 K Q 6 J 8 2 9 7
1 NT 9 2 10 4 10	K 5 A 10 3 2 A K 9 5 K 8 3

62.	J 7 6 3 J 8 7 4 7 4 A Q 5
10 2 K Q 9 10 8 6 5 3 J 8 6		A Q 9 4 6 3 J 9 K 10 7 4 2
1 NT 6 2 8 4 8	K 8 5 A 10 5 2 A K Q 2 9 3

64.	J 7 6 3 J 8 7 4 7 4 A Q 5
K 2 A Q 10 2 J 10 9 6 2 7 4		9 5 4 5 3 A Q 8 5 10 9 8 3
1 NT 6 2 8 4 8	A Q 10 8 K 9 6 K 3 K J 6 2