Simulation 8Z32 Main | 
Attack Suit or Singleton?
|
 by Richard Pavlicek |
Recently I held the West* hand on lead against 6 
. Should I attack with a club or heart? Or lead my singleton hoping for a ruff? The presence of my two kings makes it less likely partner has the 
A or A to deliver a ruff, but leading either round suit could lose the setting trick. Or maybe a trump lead is best? At the table I guessed wrong and may have gone against the odds; hence this simulation to discover the best lead.
*Actually I was South. Deal is rotated to South declarer for my simulation format.
 | Both vul | | West | North | East | South
|
| 6 5 |  | | | | | 1
|
 K J 3 2 | | Pass | 1 NT | Pass | 3
|
| 2 | | Pass | 3 | Pass | 4
|
 K 9 8 7 4 3 | | Pass | 4 NT | Pass | 5
|
| 6 | | Pass | 6 | All Pass |
The auction, though not identical, was essentially as above with 1 NT forcing (6-12 HCP). The response to 4 NT (RKCB) showed three key cards. I will compare leads of all four suits, or more specifically, assuming the common expert agreement of “low from odd, third from even” in side suits, the 5, 3, 2 and 8.
For the simulation I created 10,000 random deals with the West hand fixed and these constraints: South, 19-21 points with 5+ spades, four diamonds, and three of [ A K A A A]; North, 12 points with three spades; and East with fewer than 6 playing tricks (else would be likely to bid). Results were determined with double-dummy play by both sides after the opening lead but with a restriction: When declarer has nine diamonds, he is forced to make the normal percentage play if the singleton is not led, i.e., losing a diamond trick when East has Q-x-x, Q-J-x, K-J-x or K-10-x (unless A-Q-J behind).
Below is the actual deal:
| South deals | K Q 3 | West | North | East | South
|
| Both vul | 6 4 | | | | 1
|
| J 10 9 8 4 | Pass | 1 NT | Pass | 3
|
| A 5 2 | Pass | 3 | Pass | 4
|
| 6 5 |  | 8 7 4 | Pass | 4 NT | Pass | 5
|
| K J 3 2 | Q 10 9 8 7 | Pass | 6 | All Pass
|
| 2 | Q 6 5
|
| K 9 8 7 4 3 | J 10
|
| A J 10 9 2
|
| A 5
|
| A K 7 3
|
| 6 South | Q 6 |
I led my singleton, which gave declarer 12 easy tricks. A club lead would also fail, as declarer would ride it to his queen. A heart or a trump lead would set it, because declarer would have no reason to finesse partner in diamonds, especially when he is longer in trumps. Disappointing at the time, but satisfying now. Despite occasions like this where it kills* partner’s holding, results show the 2 is the best lead. This brings to mind the sage advice of the great Benito Garozzo, “Always lead your singleton.”
*In the 10,000 deals there were 316 such cases, for which I awarded an extra defensive trick for any non-diamond lead. In the sample deals that follow, this adjustment is indicated by showing the actual double-dummy results in parentheses, e.g., see Deal 5.
Results are shown below. Set Percent shows how often the contract is defeated. Hold Percent shows how often the contract is made exactly, i.e., without an overtrick. Trick Average shows the average number of tricks won by the defense. The second table compares the leads according to the form of scoring, with the superior lead at IMPs 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 vul (red). Signed numbers indicate the net gain or loss over 10,000 deals.
Results for 10,000 Deals
| 6 South | Set Percent | Hold Percent | Trick Average
|
|---|
| 2 lead | 29.62 | 42.57 | 1.0733
|
| 5 lead | 24.29 | 50.02 | 1.0117
|
| 8 lead | 21.18 | 48.59 | 0.9362
|
| 3 lead | 20.96 | 45.45 | 0.8926 |
| Scoring Comparison | Win Percent | NV Net Score | NV Net IMPs | Vul Net Score | Vul Net IMPs
|
|---|
| 2 lead vs 5 | 52.96 | +557380 | +7809 | +838630 | +9694
|
| 2 lead vs 8 | 56.72 | +890830 | +12560 | +1327080 | +15338
|
| 2 lead vs 3 | 58.70 | +927470 | +13287 | +1378620 | +16179
|
| 5 lead vs 8 | 54.04 | +333450 | +4854 | +488450 | +5799
|
| 5 lead vs 3 | 56.10 | +370090 | +5619 | +539990 | +6691
|
| 8 lead vs 3 | 51.96 | +36640 | +737 | +51540 | +859 |
Note: Removing the decimal point in percents or averages shows the number of occurrences.
For example, the set percent of 29.62 translates to 2962 sets in 10,000 deals.
| Simulation 8Z32 Main |  | Top Attack Suit or Singleton? |
Sample Deals
Below are 100 of the 10,000 deals, including the first 20 and last 20. The 60 selected deals in between cycle through optimal gains for each lead. Numbers show tricks won by the defense with double-dummy play after that opening lead. Contract is always 6 by South.
| 1. | K 7 3
A 9 8 6 4
K 6 5
Q 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 9 2
Q 10 7
Q J 9 8 4
6 5
|
2 → 2
5 → 2
8 → 1
3 → 2 | A Q J 8 4
5
A 10 7 3
A J 10 |
| 2. | 9 8 2
A Q 8 7 6
10 5 3
A J
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q J 3
5 4
J 9 8 7 4
Q 10 6
|
2 → 1
5 → 0
8 → 1
3 → 0 | A K 10 7 4
10 9
A K Q 6
5 2 |
| 3. | A 8 4
10 6 5
K 10 9 6
A 10 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 9 7
9 8 7 4
8 7 4 3
Q 6
|
2 → 1
5 → 1
8 → 1
3 → 1 | K Q J 3 2
A Q
A Q J 5
J 2 |
| 4. | K 8 3
A 7 6 4
Q 5
Q J 6 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 9 4
Q 10 9
J 10 9 6 4 3
10
|
2 → 1
5 → 1
8 → 2
3 → 2 | A Q J 7 2
8 5
A K 8 7
A 2 |
| 5. | A 9 7
A 9 5
K 10 7 5 3
5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 4 3
10 8 7
Q 8 6
Q J 10 6
|
2 → 1
5 → 2 (1)
8 → 2 (1)
3 → 1 (0) | K Q J 8 2
Q 6 4
A J 9 4
A |
| 6. | K 4 3
A Q 10 6
Q 9 6
J 6 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 7
9 5 4
K 7 5 4 3
Q 10 2
|
2 → 0
5 → 0
8 → 0
3 → 0 | A Q 10 9 8 2
8 7
A J 10 8
A |
| 7. | J 7 2
Q 8 6
A K 9 8 6 4
10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 10 8
10 9 7 5 4
10 7
J 6 5
|
2 → 0
5 → 0
8 → 0
3 → 0 | A Q 9 4 3
A
Q J 5 3
A Q 2 |
| 8. | 8 7 3
7 6
A 9 6 5
A Q J 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q J 4
10 9 5 4
J 10 7 3
6 2
|
2 → 1
5 → 1
8 → 1
3 → 0 | A K 10 9 2
A Q 8
K Q 8 4
5 |
| 9. | 9 8 7
8
A K 10 9 8 6 4
Q J
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 4 3
10 9 6 5 4
J
A 10 6 5
|
2 → 0
5 → 0
8 → 1
3 → 0 | A K Q J 2
A Q 7
Q 7 5 3
2 |
| 10. | K J 10
Q 9 8 6 4
8 5 4
A J
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 4 2
7 5
Q J 9 7 6
Q 10 2
|
2 → 1
5 → 1
8 → 2
3 → 0 | A Q 8 7 3
A 10
A K 10 3
6 5 |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 11. | 9 3 2
A 6 5 4
K Q 10 9 7 5
—
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 10 4
Q 9 8
8 3
Q J 10 5 2
|
2 → 0
5 → 0
8 → 0
3 → 0 | A Q J 8 7
10 7
A J 6 4
A 6 |
| 12. | K 8 2
Q 10 9 7 6
Q 7 3
A 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 10 4
8 4
J 9 8 5 4
Q 10 5
|
2 → 1
5 → 1
8 → 1
3 → 0 | A Q 9 7 3
A 5
A K 10 6
J 2 |
| 13. | A 9 7
Q 9 8 4
6 4 3
A Q 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 8 2
7 6
K 9 8 7 5
6 5 2
|
2 → 0
5 → 1
8 → 1
3 → 0 | K Q 10 4 3
A 10 5
A Q J 10
J |
| 14. | K J 3
Q 9 7 4
A J 7 4
J 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 7 2
10 5
Q 10 9 6
Q 6 5 2
|
2 → 2
5 → 2
8 → 2
3 → 2 | A Q 9 8 4
A 8 6
K 8 5 3
A |
| 15. | 7 4 2
A 8 4
A K 5 4 3
10 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 9 8
10 9 7 6
J 7 6
Q J 2
|
2 → 1
5 → 1
8 → 1
3 → 0 | A K Q J 3
Q 5
Q 10 9 8
A 6 |
| 16. | J 10 7
6
Q J 10 8 3
A Q 6 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 3
A Q 9 8 7 4
9 6 5
J 2
|
2 → 0
5 → 0
8 → 0
3 → 1 | A K Q 8 4 2
10 5
A K 7 4
10 |
| 17. | Q 10 9
Q 10 9
10 9 7 5
A Q J
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 7
8 7 6
K 8 6 3
10 6 5 2
|
2 → 1
5 → 1
8 → 0
3 → 0 | A J 8 4 3 2
A 5 4
A Q J 4
— |
| 18. | A Q 3
Q 7
Q J 5 4
J 10 6 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 7 4 2
10 8 6 5 4
A 10 8 3
5
|
2 → 3
5 → 2
8 → 2
3 → 2 | K J 10 9 8
A 9
K 9 7 6
A Q |
| 19. | A Q 7
10 7 5
10 6 5 3
A J 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 4 2
Q 8 4
J 8 7 4
10 6 2
|
2 → 1
5 → 1
8 → 1
3 → 1 | K J 9 8 3
A 9 6
A K Q 9
Q |
| 20. | 10 9 7
A 10 7 5 4
A J
J 10 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 4 2
Q 8
Q 9 8 6 4 3
6 5
|
2 → 2
5 → 2
8 → 1
3 → 2 | A K Q 8 3
9 6
K 10 7 5
A Q |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 48. | J 10 8
A Q 9 7
Q J 9 8 7
Q
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | A 4 2
6 5 4
5 4 3
J 10 6 2
|
2 → 2
5 → 1
8 → 1
3 → 1 | K Q 9 7 3
10 8
A K 10 6
A 5 |
| 437. | Q 9 2
A 9 5
10 7 6 5
A Q 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 8
10 7 4
Q J 4 3
J 10 6 5
|
2 → 0
5 → 1
8 → 0
3 → 0 | A K J 7 4 3
Q 8 6
A K 9 8
— |
| 470. | 10 7 2
9
A K J 10 7 4
Q 6 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 8 4
10 8 7 6 5
8 3
A 10 5
|
2 → 0
5 → 0
8 → 1
3 → 0 | A K Q 9 3
A Q 4
Q 9 6 5
J |
| 471. | K 9 2
8 6
K Q J 9 7 5 3
10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 4 3
A Q 9 7 5 4
4
J 5 2
|
2 → 0
5 → 0
8 → 0
3 → 1 | A Q 10 8 7
10
A 10 8 6
A Q 6 |
| 473. | 10 3 2
A Q 10
K 10 8 5
Q 10 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | A 9 4
9 7 4
9 7 6 4
J 6 5
|
2 → 2
5 → 1
8 → 1
3 → 1 | K Q J 8 7
8 6 5
A Q J 3
A |
| 507. | K 7 3
A 8 7 4
K 9 8 5
Q 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 4
Q 10 9 6
Q J 10 7
J 10 6 2
|
2 → 1
5 → 2
8 → 1
3 → 1 | A Q J 10 9 8 2
5
A 6 4 3
A |
| 514. | K J 2
9 5
J 10 9 4
A Q 5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 8 4
8 7 6 4
K 7 6 5
J 6
|
2 → 0
5 → 0
8 → 1
3 → 0 | A Q 9 7 3
A Q 10
A Q 8 3
10 |
| 563. | K 7 2
9 6
A Q 5 4 3
Q 10 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 9
Q 8 7 5 4
K 10 8
J 6 2
|
2 → 1
5 → 1
8 → 1
3 → 2 | A Q J 8 4 3
A 10
J 9 7 6
A |
| 576. | 9 7 4
Q 7 6
K J 4
A Q 6 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | A J
10 8 5 4
10 9 8 5 3
J 2
|
2 → 2
5 → 1
8 → 1
3 → 1 | K Q 10 8 3 2
A 9
A Q 7 6
10 |
| 1345. | A 8 3
Q 8 4
A 10 9 6 5
Q 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 4 2
10 9 7 5
Q 8 3
J 6 5
|
2 → 1
5 → 2 (1)
8 → 1 (0)
3 → 1 (0) | K Q J 10 7
A 6
K J 7 4
A 10 |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 1360. | K 10 4
9
K Q J 8 7 6 3
10 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 8 3
8 7 6 5 4
9
A Q J 2
|
2 → 0
5 → 0
8 → 1
3 → 0 | A Q 9 7 2
A Q 10
A 10 5 4
5 |
| 1364. | K 10 2
A 5
10 8 6 5
Q J 10 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 8 7
Q 10 9 7 4
Q 9 7 4
5
|
2 → 1
5 → 1
8 → 1
3 → 2 | A J 9 4 3
8 6
A K J 3
A 6 |
| 1374. | Q 9 4
A Q 8 6 5
9 3
Q J 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 10
10 9 7
A J 10 8 6 5
5 2
|
2 → 2
5 → 1
8 → 1
3 → 1 | A K 8 7 3 2
4
K Q 7 4
A 6 |
| 2255. | 8 4 3
A 10 9 8 6 5
A J 10
5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 7 2
Q 4
Q 8 6 5 3
Q J 6
|
2 → 0
5 → 1
8 → 0
3 → 0 | A K Q J 10
7
K 9 7 4
A 10 2 |
| 2264. | J 9 4
A Q 5 4
Q 10 7 3
Q J
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 3
10 9 7 6
J 9 6 5
A 6 2
|
2 → 1
5 → 1
8 → 2
3 → 1 | A K Q 8 7 2
8
A K 8 4
10 5 |
| 2266. | J 4 2
10 9
Q J 7 3
A Q J 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 3
A Q 8 7 5 4
10 8 6 4
5
|
2 → 0
5 → 0
8 → 0
3 → 1 | A K Q 10 8 7
6
A K 9 5
10 2 |
| 2283. | K J 2
A 7 6 4
K 9 5 4
J 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 8 4 3
10 9 8 5
Q J 10 8
10 5
|
2 → 3
5 → 2
8 → 2
3 → 2 | A Q 10 9 7
Q
A 7 6 3
A Q 2 |
| 2326. | J 10 2
A Q 10 8 7 6 4
Q 6 4
—
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 8
9 5
K J 8 7 5
A J 5 2
|
2 → 1
5 → 2
8 → 1
3 → 0 | A K Q 7 4 3
—
A 10 9 3
Q 10 6 |
| 2368. | Q 7 4
10 8 6
A K J 8 6 4
10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 2
9 7 5 4
9 5
A Q J 6 2
|
2 → 0
5 → 0
8 → 1
3 → 0 | A K J 9 8 3
A Q
Q 10 7 3
5 |
| 2369. | Q J 2
9 8 7 4
A Q J 6 5
2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 10 4
Q 10 6
9 7 3
J 10 6 5
|
2 → 1
5 → 1
8 → 1
3 → 2 | A 9 8 7 3
A 5
K 10 8 4
A Q |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 2379. | A 10 9
—
Q 8 6 5 4 3
Q J 10 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 8 3
Q 10 8 7 6 5 4
A 9
6
|
2 → 2
5 → 1
8 → 1
3 → 1 | K Q 7 4 2
A 9
K J 10 7
A 2 |
| 2400. | K Q 8
10 8 7 6
7
A J 10 6 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 4 3
9 5 4
K Q 10 9 8 4 3
Q
|
2 → 1
5 → 2
8 → 1
3 → 0 | A J 10 9 7 2
A Q
A J 6 5
5 |
| 2423. | A J 7
Q 7
Q J 7 5 4
Q 6 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 8 4 3
8 6 5 4
9 8 3
A J 2
|
2 → 1
5 → 1
8 → 2
3 → 0 | K Q 10 9 2
A 10 9
A K 10 6
10 |
| 2498. | A Q J
6 4
Q 9 8 7 6 3
Q 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 8 7 2
A 9 8 7 5
J 10
10 6 2
|
2 → 1
5 → 1
8 → 0
3 → 2 | K 10 9 4 3
Q 10
A K 5 4
A J |
| 2522. | K 9 3
Q 10 7 6
K Q 10 9 6
Q
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | A 8 7
9 5 4
J 5 4
10 6 5 2
|
2 → 2
5 → 1
8 → 1
3 → 1 | Q J 10 4 2
A 8
A 8 7 3
A J |
| 2788. | 8 7 2
A 9 8
9 7
A Q J 10 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q J
7 6 5
Q 10 6 5 4 3
6 5
|
2 → 0
5 → 1
8 → 0
3 → 0 | A K 10 9 4 3
Q 10 4
A K J 8
— |
| 2790. | Q 7 4
Q 10 9 5
10 3
A Q J 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 10
8 7 4
K 9 7 6 5 4
6 5
|
2 → 0
5 → 0
8 → 1
3 → 0 | A J 9 8 3 2
A 6
A Q J 8
10 |
| 2801. | A 9 8
A 9 7 4
10 7 6
Q J 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 3 2
Q 8 5
Q 9 5 4 3
6 2
|
2 → 1
5 → 1
8 → 1
3 → 2 | K Q 10 7 4
10 6
A K J 8
A 5 |
| 2806. | K J 4
A 10 8 6 4
Q 10 4 3
Q
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 7 2
Q 5
J 9 8 6
J 10 5 2
|
2 → 2
5 → 1
8 → 1
3 → 1 | A Q 10 8 3
9 7
A K 7 5
A 6 |
| 3110. | 10 4 2
Q 9 8 7 5
A 8 7 6
A
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 8 3
10 6 4
Q J 10 9
10 6 5
|
2 → 1
5 → 2
8 → 1
3 → 1 | A K J 9 7
A
K 5 4 3
Q J 2 |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 3113. | 9 7 4
A 8 6
8 4
A Q J 5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 10 8
10 9 5 4
Q J 9 6 5 3
—
|
2 → 0
5 → 0
8 → 1
3 → 0 | A K Q 3 2
Q 7
A K 10 7
10 6 |
| 3115. | K 9 3
8 4
A Q J 6 5 4
10 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q J 2
Q 9 7 6 5
10 3
J 6 2
|
2 → 1
5 → 1
8 → 1
3 → 2 | A 10 8 7 4
A 10
K 9 8 7
A Q |
| 3127. | Q 8 3
Q 8 5 4
A Q 10 5 3
5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 9 2
10 9 7 6
7 6 4
A Q 6
|
2 → 2
5 → 1
8 → 1
3 → 1 | A K 10 7 4
A
K J 9 8
J 10 2 |
| 3217. | A 3 2
9 8 5 4
K 9 5 3
A 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 7
Q 7
J 10 8 4
Q J 10 5 2
|
2 → 1
5 → 2
8 → 1
3 → 1 | K Q J 9 8 4
A 10 6
A Q 7 6
— |
| 3222. | J 10 8
Q 6
Q 9 3
A Q J 6 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 9 4
10 9 7 4
J 8 7 6 4
10
|
2 → 0
5 → 0
8 → 1
3 → 0 | A Q 7 3 2
A 8 5
A K 10 5
2 |
| 3279. | 10 8 7
Q 10
Q 7 6
A Q J 10 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 3 2
A 9 8 6 4
J 10 9 8 4
6
|
2 → 1
5 → 1
8 → 1
3 → 2 | A K Q J 9 4
7 5
A K 5 3
5 |
| 3284. | Q 10 9
A Q 7
Q 7 5 4 3
Q 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | A 3 2
10 9 8 5 4
10 8 6
6 5
|
2 → 2
5 → 1
8 → 1
3 → 1 | K J 8 7 4
6
A K J 9
A J 10 |
| 3378. | K 7 2
Q 10 9 7 5 4
K J 9 7
—
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 4 3
8 6
Q 10 5 3
A J 6 5
|
2 → 1
5 → 2
8 → 1
3 → 1 | A Q J 9 8
A
A 8 6 4
Q 10 2 |
| 3389. | Q 9 7
Q 7 6 5
A K 8 4
10 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 4 2
9 8 4
10 9 7 3
Q J 5
|
2 → 1
5 → 1
8 → 2
3 → 1 | A J 10 8 3
A 10
Q J 6 5
A 6 |
| 3391. | K Q 4
10 7 6
A Q 7 5
J 10 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 8 2
Q 9 8 4
J 9 8 3
Q 5
|
2 → 1
5 → 1
8 → 1
3 → 2 | A J 10 7 3
A 5
K 10 6 4
A 6 |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 3405. | J 10 8
10
Q 10 4 3
A Q 6 5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 9 3
9 8 7 6 4
A 9 7 5
10
|
2 → 2
5 → 1
8 → 1
3 → 1 | A K 7 4 2
A Q 5
K J 8 6
J |
| 3485. | A Q 8
7 6
A J 10 9 3
6 5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 7 3 2
10 9 8 5 4
Q 8 6
J 10
|
2 → 1
5 → 2 (1)
8 → 1 (0)
3 → 1 (0) | K J 10 9 4
A Q
K 7 5 4
A Q |
| 3534. | 7 4 3
A Q 8 4
K 4
Q 10 5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 2
10 9 7 6
Q 9 7 6 5 3
A 6
|
2 → 0
5 → 0
8 → 1
3 → 0 | A K Q J 10 9 8
5
A J 10 8
J |
| 3535. | K 10 7
A 9 7 5
Q 7 4
Q J 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 9 3
Q 6 4
J 10 9 5 3
6 2
|
2 → 1
5 → 1
8 → 1
3 → 2 | A Q 8 4 2
10 8
A K 8 6
A 5 |
| 3540. | 10 7 3
4
K J 9 8 6
A Q 6 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | A Q 4
10 9 8 7 6
7 5 3
J 5
|
2 → 2
5 → 1
8 → 1
3 → 1 | K J 9 8 2
A Q 5
A Q 10 4
10 |
| 3547. | K 9 4
A 7 6 5 4
Q 4 3
Q J
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 3
Q 10 9 8
K 9 7 6 5
5 2
|
2 → 0
5 → 1
8 → 0
3 → 0 | A Q J 8 7 2
—
A J 10 8
A 10 6 |
| 3594. | J 9 3
A Q 9 6
K J 10 4
10 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 7 2
10 8 7 5 4
Q 8 7 5
A 5
|
2 → 1
5 → 1
8 → 2
3 → 1 | A K Q 10 8 4
—
A 9 6 3
Q J 2 |
| 3600. | J 9 7
A 9 6 4
A 9 4
Q J 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 8 4 3
Q 7
K 7 6 5 3
10 6 5
|
2 → 2
5 → 2
8 → 2
3 → 3 | A K Q 10 2
10 8 5
Q J 10 8
A |
| 3616. | J 8 7
A Q 10 9 8 4
Q 10 8 6
—
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | A 2
7 5
9 5 4 3
Q J 10 6 5
|
2 → 2
5 → 1
8 → 1
3 → 1 | K Q 10 9 4 3
6
A K J 7
A 2 |
| 3887. | A J 2
A 10 8 6
10 7 4 3
Q 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 7 4
Q 9 5 4
K J 9 8
10 6 5
|
2 → 2
5 → 3
8 → 2
3 → 2 | K Q 10 9 8 3
7
A Q 6 5
A J |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 3890. | K 7 2
6
K J 10 9 7 3
Q J 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 8 4
Q 10 8 7 5 4
5 4
A 6 2
|
2 → 0
5 → 0
8 → 1
3 → 0 | A Q J 10 9 3
A 9
A Q 8 6
10 |
| 3896. | 4 3 2
5
A K 10 8 7 6
Q J 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 8
A 10 9 8 7 6 4
4 3
6 5
|
2 → 0
5 → 0
8 → 0
3 → 1 | A K J 10 9 7
Q
Q J 9 5
A 10 |
| 3900. | J 8 7
Q 7 6
K 10 4
A Q 10 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 4
10 8 5 4
A 8 7 6 5
J 2
|
2 → 2
5 → 1
8 → 1
3 → 1 | A K Q 10 3 2
A 9
Q J 9 3
5 |
| 3995. | Q 4 2
A 9 8
7 5 3
A Q 10 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 9
7 6 5
Q J 8 6 4
J 6 2
|
2 → 0
5 → 1
8 → 0
3 → 0 | A K J 8 7 3
Q 10 4
A K 10 9
— |
| 4003. | 9 4 3
10 9 6 4
A 8
A Q J 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 10 7
Q 8 7 5
J 10 7 6 5 4
—
|
2 → 0
5 → 0
8 → 1
3 → 0 | A K J 8 2
A
K Q 9 3
10 6 2 |
| 4035. | J 9 7
Q 6
K 5 4 3
A Q 5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10
A 9 8 7 5 4
10 8 7 6
10 6
|
2 → 0
5 → 0
8 → 0
3 → 1 | A K Q 8 4 3 2
10
A Q J 9
J |
| 4048. | 10 7 2
A Q 9 8 6
K J 10 7
Q
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 4
5 4
A 5 4 3
J 10 6 5 2
|
2 → 2
5 → 1
8 → 1
3 → 1 | A K Q J 8 3
10 7
Q 9 8 6
A |
| 4101. | 7 4 2
A 10 9 8 7 6 4
A J
Q
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 8 3
Q 5
Q 10 8 6 4 3
10 6
|
2 → 1
5 → 2
8 → 1
3 → 1 | A K J 10 9
—
K 9 7 5
A J 5 2 |
| 4105. | Q J 2
A Q 10 9 4
J 7 6 4
2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 8 7
8 7 6
10 9 8 3
A Q 10 6
|
2 → 0
5 → 0
8 → 1
3 → 0 | A K 10 9 4 3
5
A K Q 5
J 5 |
| 4112. | K 10 2
8 5 4
A Q 8
Q J 10 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 9 4
Q 10 9 6
10 7 5 4 3
2
|
2 → 1
5 → 1
8 → 1
3 → 2 | A J 8 7 3
A 7
K J 9 6
A 5 |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 9981. | K Q 9
A 9 8 7
J 9 8 4 3
J
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 8 4 2
Q 6 4
Q 7 6
10 6 5 2
|
2 → 0
5 → 1 (0)
8 → 1 (0)
3 → 1 (0) | A J 10 7 3
10 5
A K 10 5
A Q |
| 9982. | Q 10 3
10 8
A Q J 9 6 5 4
6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 7 4
A 9 6 5 4
7
J 10 5 2
|
2 → 0
5 → 0
8 → 0
3 → 2 | A K 9 8 2
Q 7
K 10 8 3
A Q |
| 9983. | K 4 3
9 5
K 6 5 4 3
A J 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 9 7
Q 10 8 6
10 8 7
10 5 2
|
2 → 0
5 → 0
8 → 0
3 → 0 | A J 10 8 2
A 7 4
A Q J 9
Q |
| 9984. | A 4 3
10 9 8 6
A Q 6 5 4
5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 8 2
Q 7 5
10 9 8
Q J 10 6
|
2 → 0
5 → 0
8 → 0
3 → 0 | K Q J 10 7
A 4
K J 7 3
A 2 |
| 9985. | Q 8 2
A 10 8 7 4
A 6
10 6 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 4 3
6 5
Q J 10 9 8 4
J 5
|
2 → 1
5 → 1
8 → 1
3 → 1 | A K J 10 7
Q 9
K 7 5 3
A Q |
| 9986. | Q 4 2
9
K J 7 6 3
A 6 5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 9
Q 10 7 6 4
10 5 4
Q J 10
|
2 → 0
5 → 0
8 → 0
3 → 0 | A J 10 8 7 3
A 8 5
A Q 9 8
— |
| 9987. | K Q 3
10 8 7 5
K Q J 5
J 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 10 4
A 9 6 4
8 7 6 4
10 5 2
|
2 → 2
5 → 2
8 → 1
3 → 2 | A J 9 8 7 2
Q
A 10 9 3
A Q |
| 9988. | K Q 7
Q 7 4
Q 10 8 6 5 4 3
—
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 9 8 3
A 10 8 6 5
7
Q J 5 2
|
2 → 0
5 → 0
8 → 0
3 → 1 | A J 10 4 2
9
A K J 9
A 10 6 |
| 9989. | 10 7 3
A 10 9 4
A Q 8 7
J 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 9 4
Q 8 6 5
9 5 4 3
Q 2
|
2 → 2
5 → 2
8 → 1
3 → 2 | A K J 8 2
7
K J 10 6
A 10 5 |
| 9990. | J 7 3
Q 10 9 7 5
K 4
A J 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K Q 4
8 6 4
J 10 9 8 7 3
6
|
2 → 2
5 → 1
8 → 1
3 → 1 | A 10 9 8 2
A
A Q 6 5
Q 5 2 |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
| 9991. | J 10 8
A 8 7 6 4
K Q 6 3
5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 9 2
Q 10 9 5
J 10 9 7
10 2
|
2 → 1
5 → 1
8 → 1
3 → 1 | A Q 7 4 3
—
A 8 5 4
A Q J 6 |
| 9992. | Q J 10
Q 9
A 8 6 5 4 3
Q J
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 7 4 2
10 7 6 5 4
10 9
A 10 2
|
2 → 1
5 → 1
8 → 2
3 → 0 | A K 9 8 3
A 8
K Q J 7
6 5 |
| 9993. | A 8 2
10 9 7
K 7 6 3
A J 5
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 4 3
8 6 5
Q 10 9 8
Q 10 6 2
|
2 → 1
5 → 1
8 → 1
3 → 1 | K Q J 10 9 7
A Q 4
A J 5 4
— |
| 9994. | Q 10 9
10 8 5
A J 5 4
A 5 2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 4 3 2
Q 9 7 4
Q 7 6 3
10 6
|
2 → 1
5 → 1
8 → 1
3 → 1 | A K J 8 7
A 6
K 10 9 8
Q J |
| 9995. | J 9 3
Q 10 9 8 4
A Q 10 9 5
—
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | K 7 4
7 5
K 4 3
Q 10 6 5 2
|
2 → 1
5 → 1
8 → 1
3 → 1 | A Q 10 8 2
A 6
J 8 7 6
A J |
| 9996. | 8 4 2
10 5
A 9 8 7
A Q J 6
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 9 3
Q 9 7 6
K 6 5 4
10 2
|
2 → 2
5 → 2
8 → 2
3 → 2 | A K Q 10 7
A 8 4
Q J 10 3
5 |
| 9997. | A 10 7
9 5
J 10 6 4 3
A J 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 4 3
Q 10 8 7
Q 9 5
Q 6 5 2
|
2 → 0
5 → 1 (0)
8 → 1 (0)
3 → 1 (0) | K Q J 9 8 2
A 6 4
A K 8 7
— |
| 9998. | 10 7 3
7 5 4
A K Q J 7 6
2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | 8 4
10 9 8 6
9 4
A J 10 6 5
|
2 → 0
5 → 0
8 → 1
3 → 0 | A K Q J 9 2
A Q
10 8 5 3
Q |
| 9999. | 8 4 3
A Q 9 7 6
8 4
A J 10
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | Q 2
5 4
Q 9 7 6 5 3
Q 6 2
|
2 → 0
5 → 0
8 → 0
3 → 0 | A K J 10 9 7
10 8
A K J 10
5 |
| 10000. | A Q 3
Q 9 8 7
Q 10 7 6 5
2
|
6 5
K J 3 2
2
K 9 8 7 4 3 | | J 7 2
A 10 5 4
9 8 3
J 10 5
|
2 → 1
5 → 1
8 → 0
3 → 1 | K 10 9 8 4
6
A K J 4
A Q 6 |
| Simulation 8Z32 Main | | Top Attack Suit or Singleton? |
© 2025 Richard Pavlicek