Simulation 8Z29 Main

Nine Solid Clubs

by Richard Pavlicek

Patrick Chye of Alameda, California, asked about the following hand at IMP scoring with both sides vulnerable. More specifically, after partner passes and RHO opens 1 , he was curious how often 6 would make.

West

North Pass

East 1

South ?

K 3 A K — A K Q J 10 9 8 5 3

My guess was about 60 percent, as partner might have the Q; or the 7 entry (or any two clubs with a 1-1 split, or 3+ clubs) with East likely to hold the A. There is also a remote chance partner has the A (with a diamond lead), or even the A, which would fuel the postmortem on how to reach seven. In any case, I thought it would be interesting to compare the merit of 6 versus the ultraconservative 5 .

In my system I would start with a three-level cue-bid (3 ) to show any strong one-suiter except the cue-bid suit. I plan to gamble 6 , but there’s an off chance of accurately bidding seven: Partner’s response of 4 would show no diamond stopper and one ace (bingo); or if he bids 3 NT with a stopper, 4 by me would ask him to show a specific ace (4 NT = none).

There are tactical considerations as well. Bidding accurately to 6 or 7 would be in vain if the opponents found a cheap sacrifice, so an immediate 6 might work better. In my experience, however, a brash bid often spurs aggressive action that an opponent otherwise wouldn’t take; so I think science wins out in the long run.

For a simulation I created 10,000 random deals with the South hand fixed. North was constrained to have an original pass, and East to have a natural 1 opening per my method of evaluation. Results are determined with perfect play by both sides, which may not occur in practice, but differences tend to even out.* My studies show a close correlation between actual play and double-dummy.

*For example, actual play would fare better if North has the A, because West will usually lead a diamond; certainly not at double-dummy. In contrast, double-dummy play would fare better if North has J-10 and a club entry by knowing to finesse when East has the Q instead of the ace.

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 times with overtrick(s). Overtrick Pct shows how often the contract is made with one or more overtricks. The second table compares the contracts per form of scoring, with the superior contract shown first (leftmost). Win Percent delivers the verdict for matchpoints or board-a-match. Net Score and Net IMPs are calculated first with declarer nonvul (green) then with declarer vul (red) but only the latter applies to the actual case. Signed numbers indicate the net gain or loss over 10,000 deals.

No surprises, though the success of 6 is better than I thought, making 65.88 percent of the time, with an enormous gain of 44,997 IMPs, or almost 4.5 IMPs per deal.

Results for 10,000 Deals

Contract	Trick Average	Make Percent	Overtrick Pct
6 S	11.7679	65.88	11.29
5 S	11.7679	99.67	65.88

Scoring Comparison	Win Percent	NV Net Score	NV Net IMPs	Vul Net Score	Vul Net IMPs
6  vs 5	65.88	+1771800	+38612	+2572400	+44997

Simulation 8Z29 Main

Top Nine Solid Clubs

Actual Deals

Below are 100 of the 10,000 deals, including the first 20 and last 20. Selected deals in between alternate between maximal gains for each option. Numbers show the tricks won by declarer with double-dummy play.

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

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

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

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

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

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

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

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

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

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

Simulation 8Z29 Main

Top Nine Solid Clubs

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

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

13.	10 8 6 7 5 3 9 5 4 3 2 7 6
Q J 9 4 J 10 8 6 4 2 K 10 8 —		A 7 5 2 Q 9 A Q J 7 6 4 2
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

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

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

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

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

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

19.	8 7 4 Q 9 5 2 A J 5 7 4 2
Q J 10 9 6 5 J 3 8 7 4 2 6		A 2 10 8 7 6 4 K Q 10 9 6 3 —
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

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

Simulation 8Z29 Main

Top Nine Solid Clubs

29.	10 8 4 2 9 6 5 4 3 3 2 7 2
Q 9 6 Q J 8 7 A J 9 7 6 6		A J 7 5 10 2 K Q 10 8 5 4 4
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

39.	9 4 2 J 8 7 5 4 3 9 2 6 4
A 10 8 7 6 Q 9 6 10 7 5 7 2		Q J 5 10 2 A K Q J 8 6 4 3 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

49.	10 8 4 J 7 5 4 3 K 7 5 2 7
J 9 6 5 9 8 6 2 Q J 9 8 3 —		A Q 7 2 Q 10 A 10 6 4 6 4 2
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

63.	10 5 2 J 10 8 6 5 3 8 7 6 6
A Q 9 7 6 4 Q 7 4 9 5 7 4		J 8 9 2 A K Q J 10 4 3 2 2
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

72.	10 5 4 2 Q J 9 5 4 3 2 4 2
9 8 7 9 8 7 6 4 2 K 7 6 7		A Q J 6 J 10 5 3 A Q 10 8 6
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

82.	10 9 8 7 5 10 7 6 5 3 2 8 4 —
Q 6 4 Q K 10 6 5 3 2 6 4 2		A J 2 J 9 8 4 A Q J 9 7 7
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

91.	9 7 6 5 4 J 4 10 8 7 6 6 4
Q J 10 8 2 8 7 6 5 J 4 2 7		A Q 10 9 3 2 A K Q 9 5 3 2
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

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

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

125.	9 5 4 2 9 8 4 2 8 7 3 2 6
A 8 6 Q 6 5 3 10 9 6 7 4 2		Q J 10 7 J 10 7 A K Q J 5 4 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

Simulation 8Z29 Main

Top Nine Solid Clubs

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

151.	9 6 5 4 J 9 8 4 2 9 3 2 6
Q 10 2 10 6 5 3 K Q 6 5 7 4		A J 8 7 Q 7 A J 10 8 7 4 2
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

160.	8 6 5 Q J 10 8 6 7 5 3 7 4
Q 10 7 9 7 4 3 Q 8 4 2 6 2		A J 9 4 2 5 2 A K J 10 9 6 —
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

172.	9 4 10 8 7 2 10 9 7 5 4 2 6
A J 10 6 2 J 9 6 5 8 3 4 2		Q 8 7 5 Q 4 3 A K Q J 6 7
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

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

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

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

211.	10 9 8 6 2 9 7 6 5 2 Q 8 3 —
7 4 Q 8 3 K J 9 5 4 6 4 2		A Q J 5 J 10 4 A 10 7 6 2 7
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

220.	8 5 4 2 7 5 4 K 10 7 6 5 7
J 7 6 9 8 6 3 2 A 3 2 6 2		A Q 10 9 Q J 10 Q J 9 8 4 4
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

229.	5 4 J 7 2 Q 9 7 5 4 2 6 2
J 9 8 6 2 Q 10 8 5 K J 7 4		A Q 10 7 9 6 4 3 A 10 8 6 3 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

Simulation 8Z29 Main

Top Nine Solid Clubs

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

247.	10 8 5 4 2 9 6 5 4 2 Q 3 6
Q J 7 6 Q 8 K 7 5 4 2 4 2		A 9 J 10 7 3 A J 10 9 8 6 7
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

256.	10 9 4 J 9 8 7 6 5 6 4 7 6
Q 8 7 5 Q 10 4 3 K Q 8 7 4		A J 6 2 2 A J 10 9 5 3 2 2
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

266.	10 9 7 6 2 10 7 5 4 K 7 4 3 —
J 8 5 Q 9 8 6 Q 10 9 5 7 2		A Q 4 J 3 2 A J 8 6 2 6 4
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

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

290.	9 8 7 6 4 2 8 6 5 3 9 6 4 —
Q J 5 J 10 4 K 10 2 7 6 4 2		A 10 Q 9 7 2 A Q J 8 7 5 3 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

299.	8 5 J 10 6 J 8 6 4 2 6 4 2
A J 9 2 9 8 7 5 4 3 10 3 7		Q 10 7 6 4 Q 2 A K Q 9 7 5 —
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

311.	10 8 4 10 8 7 6 5 4 2 4 2 4
Q J 9 7 2 9 3 9 6 3 7 6 2		A 6 5 Q J A K Q J 10 8 7 5 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

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

329.	6 4 9 8 7 6 4 3 J 9 5 4 6
10 9 8 7 2 Q 5 2 K 8 7 2 7		A Q J 5 J 10 A Q 10 6 3 4 2
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

Simulation 8Z29 Main

Top Nine Solid Clubs

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

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

359.	9 4 2 10 6 2 J 5 4 7 6 4 2
Q 10 6 5 Q 9 8 5 4 K Q 3 2 —		A J 8 7 J 7 3 A 10 9 8 7 6 —
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

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

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

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

400.	9 8 5 4 10 4 Q 9 8 4 7 4 2
Q J 7 2 J 8 7 3 2 J 10 7 2 —		A 10 6 Q 9 6 5 A K 6 5 3 6
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

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

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

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

Simulation 8Z29 Main

Top Nine Solid Clubs

439.	10 8 7 2 Q 8 7 2 K 7 6 6 2
Q 6 5 10 6 5 4 3 J 10 5 3 4		A J 9 4 J 9 A Q 9 8 4 2 7
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

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

459.	9 7 6 4 Q 6 4 3 2 J 6 7 2
Q J 10 J 10 8 5 9 8 7 4 2 4		A 8 5 2 9 7 A K Q 10 5 3 6
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

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

481.	7 5 Q 7 3 2 Q 9 6 4 3 7 4
A 9 8 6 2 9 8 5 10 8 7 5 2 —		Q J 10 4 J 10 6 4 A K J 6 2
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

493.	10 9 7 J 8 5 4 2 J 8 7 6 2
A J 8 5 4 2 7 6 3 5 4 2 4		Q 6 Q 10 9 A K Q 10 9 6 3 7
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

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

511.	8 7 5 J 10 6 3 2 K 10 3 4 2
9 6 4 2 9 8 5 7 6 5 4 7 6		A Q J 10 Q 7 4 A Q J 9 8 2 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

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

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

Simulation 8Z29 Main

Top Nine Solid Clubs

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

549.	10 8 5 Q 7 6 K 10 6 5 4 3 4
J 9 7 6 10 8 5 4 3 2 J 7 2		A Q 4 2 J 9 A Q 9 8 7 2 6
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

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

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

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

593.	10 8 6 5 4 9 5 A 8 5 3 4 2
J 9 Q J 10 8 7 2 J 10 2 7 6		A Q 7 2 6 4 3 K Q 9 7 6 4 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

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

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

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

631.	9 5 4 Q J 10 5 3 2 6 4 2 6
A J 10 2 9 8 7 6 J 10 7 3 2		Q 8 7 6 4 A K Q 9 8 5 7 4
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

Simulation 8Z29 Main

Top Nine Solid Clubs

9981.	10 9 4 J 9 8 5 4 3 J 10 9 6
J 8 6 5 10 6 2 K 7 5 2 7 2		A Q 7 2 Q 7 A Q 8 6 4 3 4
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

9982.	Q J 5 2 8 3 J 10 5 4 3 7 2
9 7 4 Q 10 6 5 4 2 K 2 6 4		A 10 8 6 J 9 7 A Q 9 8 7 6 —
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

9983.	Q J 6 5 4 8 4 3 2 10 8 6 2
A 9 2 10 9 7 6 5 9 7 5 2 7		10 8 7 Q J A K Q J 4 3 6 4
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

9984.	Q 10 9 6 J 8 6 4 9 7 3 2 7
A 8 5 2 10 7 5 3 J 8 6 4 6		J 7 4 Q 9 2 A K Q 10 5 4 2
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

9985.	J 9 8 5 4 10 9 8 4 2 5 6 2
A 7 6 7 6 3 10 9 6 4 3 2 4		Q 10 2 Q J 5 A K Q J 8 7 7
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

9986.	Q 8 4 J 9 7 6 4 3 2 10 8 4 —
A 9 6 5 10 9 7 6 5 3 2 7 6		J 10 7 2 Q 8 5 A K Q J 4 2
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

9987.	10 8 5 Q J 10 8 10 8 4 7 6 2
7 4 2 9 7 5 4 3 2 Q J 6 5 —		A Q J 9 6 6 A K 9 7 3 2 4
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

9988.	10 9 7 5 4 10 6 10 9 7 2 6 4
Q 8 2 Q 9 7 4 3 K J 5 4 7		A J 6 J 8 5 2 A Q 8 6 3 2
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

9989.	A 10 8 4 7 3 J 8 5 4 2 7 2
Q 9 5 2 Q J 8 6 5 10 9 6 4		J 7 6 10 9 4 2 A K Q 7 6 3 —
6 → 13 5 → 13	K 3 A K — A K Q J 10 9 8 5 3

9990.	A 8 2 J 8 2 J 10 9 8 3 6 4
J 10 9 7 6 4 10 7 4 3 Q 7 7		Q 5 Q 9 6 5 A K 6 5 4 2 2
6 → 13 5 → 13	K 3 A K — A K Q J 10 9 8 5 3

Simulation 8Z29 Main

Top Nine Solid Clubs

9991.	Q 9 8 7 6 4 Q 8 2 Q 4 7 4
10 J 10 7 6 3 J 10 9 7 6 5 6		A J 5 2 9 5 4 A K 8 3 2 2
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

9992.	Q 8 7 4 2 8 5 4 Q 10 7 4 7
J 10 9 5 10 9 7 6 8 6 2 4 2		A 6 Q J 3 2 A K J 9 5 3 6
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

9993.	10 9 7 6 2 8 2 Q 10 9 4 6 2
A Q J 5 4 10 9 7 5 3 J 8 7 —		8 Q J 6 4 A K 6 5 3 2 7 4
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

9994.	Q J 10 8 4 J 5 2 5 2 6 4 2
5 Q 10 9 8 6 3 A J 8 7 3 7		A 9 7 6 2 7 4 K Q 10 9 6 4 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

9995.	10 9 5 2 Q 9 6 4 A J 9 7 2
8 7 4 8 7 5 3 2 10 8 6 4 7		A Q J 6 J 10 K Q 5 3 2 6 4
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

9996.	J 10 9 7 6 4 J 7 6 9 8 3 2 —
5 2 Q 8 5 4 3 K 7 7 6 4 2		A Q 8 10 9 2 A Q J 10 6 5 4 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

9997.	Q 6 5 4 J 10 8 8 7 6 5 3 2 —
9 8 7 2 Q 9 5 4 3 Q 4 7 2		A J 10 7 6 2 A K J 10 9 6 4
6 → 12 5 → 12	K 3 A K — A K Q J 10 9 8 5 3

9998.	7 2 J 9 7 6 4 10 9 5 3 6 4
A 10 9 5 4 Q 8 3 Q 8 7 7 2		Q J 8 6 10 5 2 A K J 6 4 2 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

9999.	J 7 5 4 2 10 5 2 5 2 7 6 2
A 10 Q 8 4 3 Q 9 8 7 6 3 4		Q 9 8 6 J 9 7 6 A K J 10 4 —
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

10000.	9 7 4 2 J 8 7 4 Q 8 5 4 3 —
Q J 8 6 5 Q 9 3 2 10 9 7 2 —		A 10 10 6 5 A K J 6 7 6 4 2
6 → 11 5 → 11	K 3 A K — A K Q J 10 9 8 5 3

Extended search of 1,073,741,824 deals found 62,098,583 to fit constraints = 5.78338122 percent.

Simulation 8Z29 Main

Top Nine Solid Clubs

© 2025 Richard Pavlicek