Simulation 8Z15 Main

Stayman or Pass?

by Richard Pavlicek

Suppose North opens 1 NT (15-17) in first seat, East passes, and you have this hand:

West
North
1 NT East
Pass South
? J 7 6 3
J 8 7 4
7 4
A Q 5

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 can’t offer a definite answer. Trying to solve this by theoretical calculation would be a numerical nightmare, if even possible. The only practical solution is to run a simulation, so we’ll consult Madame Zoltar for the answer.

Kevin suggests two options: (A) Pass 1 NT, or (B) bid 2 then pass 2 or 2 . For interest sake I will include a third: (C) Bid 2 then raise 2 or 2 to invite game. Note that Options B and C both require a 2 NT follow-up over 2 when opener denies a major.

The final contract for Options B and C will vary according to the presence of a major fit and opener’s strength. More specifically, Option B will have North declaring 2 , 2 , 2 NT or 3 NT; and Option C will have North declaring 2 NT, 3 , 3 , 3 NT, 4 or 4 . Determining the strain is easy; either North has a major or he doesn’t, and with both he bids 2 . My criterion for a maximum will be 17 revalued points, a better yardstick than simply HCP, as it includes some hands of 16 HCP but rejects others.

For a simulation I created 10,000 random deals with the South hand fixed. North: 15-17 HCP; balanced; 5-card major allowed if doubleton is J-x or better. East was constrained not to have any appropriate action (bid or double) over 1 NT. No constraints were placed on West (no turn yet).

Results are shown below. Trick Average shows the average number of tricks won by declarer. Make Percent shows how often the contract is made (including with overtrick) and Overtrick Percent how often an overtrick is made. The second table compares the options directly, with the better option leftmost. Net W-L (matchpoints or board-a-match verdict) counts +1 for a win and -1 for a loss. Net Score and Net IMPs are calculated twice, first with declarer nonvul (green) then with declarer vul (red). Plus values show the net gain over 10,000 deals.

As predicted, Option B is the winner at matchpoints, and perhaps surprisingly, at IMPs as well. In fact the only loss for Option B is at total points vulnerable to Option C, but this can be ignored with the obsolete scoring method. The case for runner-up is a mixed bag: Option C tops Option A at total points and IMPs vulnerable but loses at matchpoints and IMPs nonvulnerable. Enlightening or bewildering [pick one].

Results for 10,000 Deals
Option Trick Average Make Percent Overtrick Percent
A. Pass 1 NT 7.8917 89.87 67.11
B. 2 then pass 8.6619 77.05 50.21
C. 2 then raise 8.6619 52.39 13.66

Results for 10,000 Deals
Option	Trick Average	Make Percent	Overtrick Percent
A. Pass 1 NT	7.8917	89.87	67.11
B. 2 then pass	8.6619	77.05	50.21
C. 2 then raise	8.6619	52.39	13.66

Comparison Net W-L NV Net Score NV Net IMPs Vul Net Score Vul Net IMPs
B. vs. A. +2488 +132,920 +4389 +218,970 +6108
B. vs. C. +1174 +88,340 +2970 -58,460 +34
C. vs. A. -547 +44,580 -726 +277,430 +3104

Comparison	Net W-L	NV Net Score	NV Net IMPs	Vul Net Score	Vul Net IMPs
B. vs. A.	+2488	+132,920	+4389	+218,970	+6108
B. vs. C.	+1174	+88,340	+2970	-58,460	+34
C. vs. A.	-547	+44,580	-726	+277,430	+3104

Actual Deals

Below are 100 of the 10,000 deals, including the first 20, last 20, and 60 in-between with the greatest IMP gains (20 for each option). Contracts shown are for Options A, B and C. Numbers after each contract show the tricks won by declarer with double-dummy play all-around.

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

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

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

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

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

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

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

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

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

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

Simulation 8Z15 Main Top Stayman or Pass?

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

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

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

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

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

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

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

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

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

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

Simulation 8Z15 Main Top Stayman or Pass?

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

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

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

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

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

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

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

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

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

1714. A Q 5 2
K Q
Q 5 2
K J 6 4
K 9 8 4
9 3 2
A K 10 9 8 3
— Table 10
A 10 6 5
J 6
10 9 8 7 3 2
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

Simulation 8Z15 Main Top Stayman or Pass?

2018. A K Q 4
6 5 2
K 5
K 10 4 3
10 9 8 2
K 3
J 8 3 2
9 6 2 Table 5
A Q 10 9
A Q 10 9 6
J 8 7
1 NT → 4
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

2047. K Q 2
A K Q 2
10 8
K 6 4 3
10 5
9 3
K Q J 9 6 3
J 9 2 Table A 9 8 4
10 6 5
A 5 2
10 8 7
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

2119. A K Q 8
K Q 3
8 6
K 6 3 2
9 5
A 9 6 5
Q J 2
J 10 7 4 Table 10 4 2
10 2
A K 10 9 5 3
9 8
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

2207. 10 5 4
K Q 9 2
K Q J
K J 10
A 9
10 5
A 10 9 8 6 5 3
9 3 Table K Q 8 2
A 6 3
2
8 7 6 4 2
1 NT → 8
2 → 6
3 → 6 J 7 6 3
J 8 7 4
7 4
A Q 5

2462. K 8 5 2
K 9 3
A Q J 2
K 10
—
A 2
10 9 8 3
J 9 8 7 6 4 2 Table A Q 10 9 4
Q 10 6 5
K 6 5
3
1 NT → 8
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

2477. A K Q 9 5
Q 10 3
K 9
K 10 4
8 2
K 9 6 5
10 8 2
J 8 7 6 Table 10 4
A 2
A Q J 6 5 3
9 3 2
1 NT → 5
2 → 9
4 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

2515. A Q 10 9 8
A Q 9
Q 8
K 4 2
5 4 2
K 10 3 2
A J
J 10 8 7 Table K
6 5
K 10 9 6 5 3 2
9 6 3
1 NT → 6
2 → 11
4 → 11 J 7 6 3
J 8 7 4
7 4
A Q 5

2722. A K Q 10 8
K 5 2
J 8 5
K 9
9
3
A K Q 10 6 3 2
J 10 3 2 Table 5 4 2
A Q 10 9 6
9
8 7 6 4
1 NT → 4
2 → 8
4 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

2848. A K 2
A Q 3 2
6 5
K J 8 6
9 8 4
K 10 5
K J 9 2
9 7 3 Table Q 10 5
9 6
A Q 10 8 3
10 4 2
1 NT → 8
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

2897. K Q 8
A 6 5 2
K J 9 6
K 4
9 2
K 10 9 3
8 5 2
J 10 8 2 Table A 10 5 4
Q
A Q 10 3
9 7 6 3
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

Simulation 8Z15 Main Top Stayman or Pass?

3061. A K 8 2
A K 5 2
Q 6
J 9 7
Q 5 4
3
A K J 10 9 8 5 3
K Table 10 9
Q 10 9 6
2
10 8 6 4 3 2
1 NT → 5
2 → 9
4 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

3175. K Q 9 5 2
K Q 9
Q 2
K 8 4
4
A 10 6
K J 10 9 8 6 5
9 3 Table A 10 8
5 3 2
A 3
J 10 7 6 2
1 NT → 4
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

3672. A K 9 8 5
A 10 6
Q 2
K 10 7
Q 10 2
K 5 3 2
J 5
9 8 6 3 Table 4
Q 9
A K 10 9 8 6 3
J 4 2
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

3866. K Q
A K 6 3
Q J 8
10 9 7 2
A 10 9 8 4 2
—
K 9 5 2
K 8 4 Table 5
Q 10 9 5 2
A 10 6 3
J 6 3
1 NT → 7
2 → 6
3 → 6 J 7 6 3
J 8 7 4
7 4
A Q 5

3888. A Q 5 4
A Q 6
10 6
K J 8 7
K 10 9 8 2
10 5
A K Q 9
6 4 Table —
K 9 3 2
J 8 5 3 2
10 9 3 2
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

3939. A K Q 2
K Q 10 6
Q J 3
9 6
9 5
A 5
6 5 2
K J 8 7 4 2 Table 10 8 4
9 3 2
A K 10 9 8
10 3
1 NT → 5
2 → 9
4 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

4025. K 10 4 2
A K 10
Q J 10
K 10 8
Q 8
9 6 3
6 3
J 9 6 4 3 2 Table A 9 5
Q 5 2
A K 9 8 5 2
7
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

4034. A K 5 2
K 3
Q J 8 3
K J 8
8
Q 6 5
A 2
10 9 7 6 4 3 2 Table Q 10 9 4
A 10 9 2
K 10 9 6 5
—
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

4293. A K 4 2
A 9 2
K J 10 9
J 9
Q 10 9 5
K Q 10 6 5
3
K 10 2 Table 8
3
A Q 8 6 5 2
8 7 6 4 3
1 NT → 7
2 → 6
3 → 6 J 7 6 3
J 8 7 4
7 4
A Q 5

4385. K 10
Q 10 5 3 2
A K 2
K 10 4
A 9 4
A
Q J 8 6 5 3
J 6 3 Table Q 8 5 2
K 9 6
10 9
9 8 7 2
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

Simulation 8Z15 Main Top Stayman or Pass?

4457. A Q 8 5 4
A Q
J 6 3
K 9 8
9 2
K 10 9 6 5
Q 9
J 7 4 2 Table K 10
3 2
A K 10 8 5 2
10 6 3
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

4551. A 10 9
K Q 10 6 3
K 10
K 3 2
K Q 4
A 5 2
6 3 2
J 9 8 4 Table 8 5 2
9
A Q J 9 8 5
10 7 6
1 NT → 5
2 → 9
4 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

4945. A Q 9 5 2
A 10 2
K 10
K 4 2
10 4
Q 9 5
A J 9 5 3
10 9 3 Table K 8
K 6 3
Q 8 6 2
J 8 7 6
1 NT → 8
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

5203. A K Q 10
K Q 6
3 2
K 10 7 2
9 8 5
9 5 2
K 10 5
9 8 6 4 Table 4 2
A 10 3
A Q J 9 8 6
J 3
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

5219. A 9
A 6 5 2
K Q 6
K 7 4 2
K 10 4 2
K Q 10 9 3
A J
J 8 Table Q 8 5
—
10 9 8 5 3 2
10 9 6 3
1 NT → 8
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

5478. A Q 10 9 5
A Q 3
J 9 8
K 4
8 2
K 10 2
10 2
J 10 8 7 6 3 Table K 4
9 6 5
A K Q 6 5 3
9 2
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

5719. A K 8 5
K 9
K Q 9
J 9 7 2
—
A 10 6 5
A 10 6 5
K 10 8 6 4 Table Q 10 9 4 2
Q 3 2
J 8 3 2
3
1 NT → 8
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

5752. K Q 10 5 4
A Q 9
K 5
K 9 2
A 9 2
K 2
10 9 3
J 10 7 6 3 Table 8
10 6 5 3
A Q J 8 6 2
8 4
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

5756. K Q 10 4
A K Q 5
Q J 2
6 2
9 5 2
9 2
10 9 8 5
K 10 7 3 Table A 8
10 6 3
A K 6 3
J 9 8 4
1 NT → 5
2 → 9
4 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

5917. Q 9 2
A K Q 5
J 9 6
K 7 3
A 10 5
10
K Q 10 8 5 3 2
10 4 Table K 8 4
9 6 3 2
A
J 9 8 6 2
1 NT → 4
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

Simulation 8Z15 Main Top Stayman or Pass?

6508. K Q 9 4
A K 10 5
J 10 9
K 4
A 10 8 5
3
A Q 8 5
J 10 9 2 Table 2
Q 9 6 2
K 6 3 2
8 7 6 3
1 NT → 8
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

6700. A 9 4
A K Q 6 3
K J
7 6 2
K Q 10 8 5
10 2
9 6 5
K 10 8 Table 2
9 5
A Q 10 8 3 2
J 9 4 3
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

6885. A 9 5
K Q 5 3 2
K 6
K 3 2
K 10 8 2
A 10 6
Q 10 8
10 9 8 Table Q 4
9
A J 9 5 3 2
J 7 6 4
1 NT → 4
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

7016. Q 10 5 2
A K 10 9
Q J 10
K 3
A K 9 8 4
2
A 9 8 2
10 7 6 Table —
Q 6 5 3
K 6 5 3
J 9 8 4 2
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

7032. A K 9
K Q 10 9
6 3
K J 9 8
10 8 5 2
6
Q J 10 9 8 5
10 2 Table Q 4
A 5 3 2
A K 2
7 6 4 3
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

7422. A K 9
A Q 9 5
9 5
K 10 6 4
Q
10 2
A K Q J 8 6 3 2
J 7 Table 10 8 5 4 2
K 6 3
10
9 8 3 2
1 NT → 5
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

7722. Q 8 5 2
A Q 9 2
K 2
K J 7
A K 9 4
6 5 3
J 9
9 4 3 2 Table 10
K 10
A Q 10 8 6 5 3
10 8 6
1 NT → 4
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

7885. A Q 2
K Q 3 2
K Q 6 3
J 7
10 9 5 4
—
J 8 5
K 10 9 8 4 2 Table K 8
A 10 9 6 5
A 10 9 2
6 3
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

8009. A K Q 4
A Q 3
5 2
J 8 7 6
8
10 9 6 2
A K Q J 10 9 6
10 Table 10 9 5 2
K 5
8 3
K 9 4 3 2
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

8295. A K Q 10
A K 3
5 3
J 10 8 2
9
6 5
A K Q J 8 6 2
9 6 4 Table 8 5 4 2
Q 10 9 2
10 9
K 7 3
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

Simulation 8Z15 Main Top Stayman or Pass?

8390. A 8 5
K Q 6 5
Q J
K 10 7 3
Q 10
10 2
A K 8 6 5 3 2
8 4 Table K 9 4 2
A 9 3
10 9
J 9 6 2
1 NT → 4
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

8669. K Q 10 2
Q 10 5
A J
K 9 6 4
8 5
A K 6 3
Q 5
J 10 7 3 2 Table A 9 4
9 2
K 10 9 8 6 3 2
8
1 NT → 4
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

8810. 10 4 2
A Q 6 3
A Q 10
K J 10
K Q 9 5
2
8 6 5 3
8 7 3 2 Table A 8
K 10 9 5
K J 9 2
9 6 4
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

9071. 10 2
A K Q 2
K 6 3
K J 9 2
A K 8 5 4
10 9
9 8
10 7 4 3 Table Q 9
6 5 3
A Q J 10 5 2
8 6
1 NT → 4
2 → 9
4 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

9319. K Q 10 5
A K 9 6
Q J
J 4 3
A 9 8 4
Q 10 2
9 8
K 10 8 6 Table 2
5 3
A K 10 6 5 3 2
9 7 2
1 NT → 4
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

9388. A K 2
K Q 6 5 2
Q 9 2
K 4
Q 10 9
A 10 9
K 10
10 9 7 6 2 Table 8 5 4
3
A J 8 6 5 3
J 8 3
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

9537. A Q 5 2
K Q 9 5
A J
9 6 4
K 10 8 4
A 6 2
9 6 5
K 10 2 Table 9
10 3
K Q 10 8 3 2
J 8 7 3
1 NT → 7
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

9551. A K Q
K 10 9 6 3
A J
7 6 4
10 4
A Q
K 9 8 5 3
K 10 8 2 Table 9 8 5 2
5 2
Q 10 6 2
J 9 3
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

9601. K Q 4
K Q 9 3
A 9
K 9 4 3
A 8 5 2
A 5 2
Q 8 3
8 7 2 Table 10 9
10 6
K J 10 6 5 2
J 10 6
1 NT → 6
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

9916. A K 10 9
A Q 3
10 9 5
K 9 8
—
9 6 2
Q J 6 3
J 10 7 4 3 2 Table Q 8 5 4 2
K 10 5
A K 8 2
6
1 NT → 8
2 → 7
4 → 7 J 7 6 3
J 8 7 4
7 4
A Q 5

Simulation 8Z15 Main Top Stayman or Pass?

9981. A Q 9 8
A K 2
K 10 8 5
J 6
10
10 6 3
9 3
K 10 9 8 7 4 3 Table K 5 4 2
Q 9 5
A Q J 6 2
2
1 NT → 8
2 → 9
4 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

9982. A Q 5 2
A 9 6
K Q 6 3
J 2
K 10 9 4
5 2
J 8 5
10 6 4 3 Table 8
K Q 10 3
A 10 9 2
K 9 8 7
1 NT → 7
2 → 9
3 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

9983. A 10 4
K Q 9 6
K Q J
9 8 3
K Q 8
3
A 8 6 5 2
K J 7 6 Table 9 5 2
A 10 5 2
10 9 3
10 4 2
1 NT → 7
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

9984. A Q 10 2
K Q 2
K 9
J 9 6 4
9 8 5
A 9 5
A Q J 10 6 5
7 Table K 4
10 6 3
8 3 2
K 10 8 3 2
1 NT → 7
2 → 9
3 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

9985. 10 9
A 10 9 3
A K J 6
K 8 4
A K Q 5 4
K Q 5
9 5 2
6 2 Table 8 2
6 2
Q 10 8 3
J 10 9 7 3
1 NT → 8
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

9986. 8 2
A K 9 6
A K 9
K 8 6 3
A K Q 9
5 3
J 10 8 5 3
10 2 Table 10 5 4
Q 10 2
Q 6 2
J 9 7 4
1 NT → 8
2 → 10
4 → 10 J 7 6 3
J 8 7 4
7 4
A Q 5

9987. A K 2
10 9 3
K J
K J 10 7 4
10 9 8 5
A K Q 6 5
10 5
9 6 Table Q 4
2
A Q 9 8 6 3 2
8 3 2
1 NT → 3
2 NT → 3
2 NT → 3 J 7 6 3
J 8 7 4
7 4
A Q 5

9988. K 9
A K 9
K Q J 5
10 8 3 2
Q 10 8 4
Q 2
A 9 8 6
K 7 6 Table A 5 2
10 6 5 3
10 3 2
J 9 4
1 NT → 8
3 NT → 8
3 NT → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

9989. A 5 2
A Q 5 2
A 10 5 3
K 6
K Q 10 9
9
9 6 2
10 9 8 4 3 Table 8 4
K 10 6 3
K Q J 8
J 7 2
1 NT → 8
2 → 9
4 → 9 J 7 6 3
J 8 7 4
7 4
A Q 5

9990. Q 10 8 4
A Q 5 3
K Q
K 10 3
K 5
—
A J 10 9 6 5 2
J 7 6 2 Table A 9 2
K 10 9 6 2
8 3
9 8 4
1 NT → 5
2 → 8
3 → 8 J 7 6 3
J 8 7 4
7 4
A Q 5

Simulation 8Z15 Main Top Stayman or Pass?

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

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

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

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

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

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

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

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

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

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

Simulation 8Z15 Main Top Stayman or Pass?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1714.	A Q 5 2 K Q Q 5 2 K J 6 4
K 9 8 4 9 3 2 A K 10 9 8 3 —		10 A 10 6 5 J 6 10 9 8 7 3 2
1 NT → 7 2 → 7 4 → 7	J 7 6 3 J 8 7 4 7 4 A Q 5