Simulation 8Z31 Main | 
Long or Short Major?
|
 by Richard Pavlicek |
When leading against 3 NT from a weak hand, a common problem is whether to lead your long suit, or a short suit trying to hit partner. With all the variables involved, a general solution might be impossible, or at least a three-piper for Sherlock Holmes.
Eliminate the impossible and whatever remains, however improbable, must be the truth.
It is presumed, of course, that the bidding is unrevealing in regard to your choice of opening leads. For example, suppose you are West and on lead after this common auction:
 | E-W vul | | West | North | East | South
|
 10 2 |  | | | | | 1 NT
|
 J 8 6 5 4 | | Pass | 3 NT | Pass | Pass
|
 Q 4 2 | | Pass
|
 8 7 3 |
|
| 3 NT |
Should you lead your heart suit? Or a spade hoping partner has five or more spades? If one of the choices were safe, it would seem better (e.g., a spade with 10-9 or a heart with J-10-9-x-x) but either lead here could cost a trick. I thought it would be interesting to compare the choices with a simulation, and for completeness I’ll include both minors as well. Specifically I will compare leads of the 10, 5, 2 and 8.
The Game Is Afoot!
For a simulation I created 10,000 random deals with the West hand fixed and these constraints: South, a 15-17 HCP 1 NT opening per my strategy to allow a 5-card major only if the doubleton is at least J-x; North, no 4+ major (unless 4-3-3-3) with 10-15 HCP if no 5+ minor, 9-14 HCP with a 5-card minor, or 8-13 HCP with a 6-card minor; and East to pass 3 NT.* Results were determined with perfect play by both sides after the opening lead. While this would usually not occur in practice, differences tend to even out, as my studies show a close correlation between actual play and double-dummy.
*Besides ruling out extremely wild shapes where East would bid, I assumed the default expert agreement that double asks partner to lead his shorter or weaker major; hence I ruled out hands with 5+ spades headed by A-K-Q, A-K-J or A-Q-J; or with an outside ace, A-K or K-Q-J.
Results are shown below. Trick Average shows the average number of tricks won by the defense. Set Percent shows how often the contract is defeated. Hold Percent shows how often the contract is made exactly, i.e., without an overtrick. 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 with declarer vul (red). Signed numbers indicate the net gain or loss over 10,000 deals.
There is nothing more deceptive than an obvious fact.
As expected in a Holmesian episode, the intrigue goes on. With my specified West hand, a heart lead is a narrow favorite, but a slight change could flip the winner. For example, the Q could be an entry (favoring a heart lead) without which the 10 is probably better. Therefore, the general case must remain unsolved.
Also noteworthy is my exclusion of East hands that would double 3 NT; I first ran the simulation without this exclusion, and the 10 was a narrow winner. Another curiosity is that the 8 is better than the 10 (but not the 5) at matchpoints because of its higher trick average; while the 10 is better at IMPs because of its higher set percent.
Results for 10,000 Deals
| 3 NT South | Trick Average | Set Percent | Hold Percent
|
|---|
| 5 lead | 2.4444 | 7.18 | 11.07
|
| 10 lead | 2.3590 | 5.15 | 11.07
|
| 8 lead | 2.3644 | 4.45 | 11.77
|
| 2 lead | 2.2254 | 3.74 | 10.58 |
| Scoring Comparison | Win Percent | NV Net Score | NV Net IMPs | Vul Net Score | Vul Net IMPs
|
|---|
| 5 lead vs 10 | 51.43 | +110820 | +2411 | +161420 | +2814
|
| 5 lead vs 8 | 51.27 | +139520 | +2989 | +209920 | +3544
|
| 5 lead vs 2 | 56.56 | +211000 | +4935 | +299050 | +5626
|
| 10 lead vs 8 | 49.75 | +28700 | +592 | +48500 | +755
|
| 10 lead vs 2 | 55.41 | +100180 | +2548 | +137630 | +2839
|
| 8 lead vs 2 | 55.90 | +71480 | +2000 | +89130 | +2133 |
Note: Removing the decimal point in averages or percents shows the number of occurrences.
For example, the set percent of 7.18 translates to 718 sets in 10,000 deals.
| Simulation 8Z31 Main |  | Top Long or Short Major? |
Actual 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 3 NT by South.
| 1. | K 8 4
A Q 7 2
J 9 7
K 10 9
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 |  | Q 9 7 6 5
10 9
A 10 8 5
Q 6
|
5 → 1
10 → 1
8 → 1
2 → 1 | A J 3
K 3
K 6 3
A J 5 4 2 |
| 2. | 9 8 7
A 3 2
K 9 7
A Q 6 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A K 6 4 3
10
J 8 6 3
10 9 2
|
5 → 3
10 → 3
8 → 3
2 → 2 | Q J 5
K Q 9 7
A 10 5
K J 4 |
| 3. | 7 6 4
A
K 9 8 7 5
K J 5 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q J 9 5
K 9
6 3
Q 10 6 2
|
5 → 3
10 → 3
8 → 3
2 → 2 | A 8 3
Q 10 7 3 2
A J 10
A 9 |
| 4. | A 9 8 7
A Q 10
8 6 3
10 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 6 4
9 2
K 10 5
A K 9 6 4
|
5 → 3
10 → 3
8 → 4
2 → 3 | K Q 5 3
K 7 3
A J 9 7
Q J |
| 5. | J 9 6 4
K Q 7
A 9 8
A 9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 5 3
9 2
K 10 7 5
K 10 4 2
|
5 → 3
10 → 3
8 → 3
2 → 3 | A K 8 7
A 10 3
J 6 3
Q J 5 |
| 6. | Q J 6
Q 10 7
7 3
K Q 9 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 8 7 5 4
A 2
A 10 9 6
A 10 6
|
5 → 4
10 → 4
8 → 4
2 → 4 | A K 9 3
K 9 3
K J 8 5
J 4 |
| 7. | K J 9
A 10
J 10 9 7
K Q J 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 6 5 4 3
K Q 2
8 6 3
10 4
|
5 → 3
10 → 2
8 → 2
2 → 1 | A 8 7
9 7 3
A K 5
A 9 6 2 |
| 8. | Q J 7
K
K 9 8 7 6
J 10 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 8 6 5 3
A 9 7 3 2
A 10
A 9
|
5 → 6
10 → 5
8 → 5
2 → 4 | A K 9 4
Q 10
J 5 3
K Q 5 2 |
| 9. | 8 6 3
A Q 9 7
A K 10
Q 10 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K J 7 5
3 2
J 8 7
9 6 4 2
|
5 → 1
10 → 1
8 → 1
2 → 1 | A Q 9 4
K 10
9 6 5 3
A K J |
| 10. | Q 8 5
A Q 2
A J 10 9 8
10 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 9 6 4 3
10 3
K 5 3
K J 9 2
|
5 → 1
10 → 1
8 → 1
2 → 1 | A K J 7
K 9 7
7 6
A Q 5 4 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 11. | K 7
Q 10
A 9 7 3
J 6 5 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 9 8 6 5
A 9 7
K 10 8
Q 9
|
5 → 2
10 → 2
8 → 2
2 → 2 | A Q 4 3
K 3 2
J 6 5
A K 10 |
| 12. | J 7
7 3 2
K 10 7 6 5 3
A 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 9 8 4 3
A 9
J
K Q 10 6 4
|
5 → 1
10 → 2
8 → 3
2 → 1 | A K 6 5
K Q 10
A 9 8
J 9 5 |
| 13. | K J 9
A Q 7
6 5
10 6 5 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 6 4 3
K 9 3
K J 10 9 7
K
|
5 → 1
10 → 2
8 → 2
2 → 2 | A 8 7 5
10 2
A 8 3
A Q J 9 |
| 14. | K 8 7 4
A K 10
9 6 3
K 10 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 3
9 7 3
A J 8 5
Q J 6 4
|
5 → 2
10 → 2
8 → 2
2 → 2 | A Q 9 6 5
Q 2
K 10 7
A 9 5 |
| 15. | 9 6 3
7
A J 10 3
A K J 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 7 5 4
K Q 10 9
8 7 6
10 5
|
5 → 0
10 → 0
8 → 0
2 → 0 | A K J 8
A 3 2
K 9 5
Q 9 2 |
| 16. | K J
K 9 7
8 7 6 5
A K 6 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 8 7 6 5 3
10 3
K 9 3
J 9
|
5 → 1
10 → 1
8 → 1
2 → 1 | A 9 4
A Q 2
A J 10
Q 10 5 4 |
| 17. | 9 8 7
9 7
A 10 5
K Q 10 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q J 5
A Q 3 2
K J 9 3
9 6
|
5 → 4
10 → 3
8 → 3
2 → 4 | A K 6 4 3
K 10
8 7 6
A J 4 |
| 18. | 8 6 5
Q 10
K 10 8 7 6
A 10 9
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 7
A 7 2
J 3
K Q 6 5 4
|
5 → 2
10 → 2
8 → 3
2 → 1 | A Q J 4 3
K 9 3
A 9 5
J 2 |
| 19. | A K 3
K Q 9 7
8 7 6
10 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q J 9 6 4
10 3
A J 10 5
6 5
|
5 → 1
10 → 2
8 → 2
2 → 2 | 8 7 5
A 2
K 9 3
A K Q J 9 |
| 20. | A 8 4
Q 9 2
8 6
A Q J 6 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 7 6 5
K 10 3
J 7 5 3
4
|
5 → 3
10 → 3
8 → 3
2 → 2 | J 9 3
A 7
A K 10 9
K 10 9 5 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 29. | J 8 7
A
K 10 9 6 3
J 10 9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 9 5 3
K 10 9 3
J 7 5
A K 2
|
5 → 4
10 → 3
8 → 3
2 → 2 | A K Q 6 4
Q 7 2
A 8
Q 5 4 |
| 33. | K 7 4
Q 10
K 10 6 3
A Q 10 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q J 9 8
9 7 3
A 9 7 5
9 2
|
5 → 2
10 → 3
8 → 2
2 → 1 | A 6 5 3
A K 2
J 8
K J 5 4 |
| 34. | J 8 3
A 7
K 10 9 3
A 9 5 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 7 5
9 2
A 7 5
K 10 6 2
|
5 → 2
10 → 2
8 → 3
2 → 2 | A Q 6 4
K Q 10 3
J 8 6
Q J |
| 42. | K J 9 3
A Q 7
10 9 3
J 6 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A 8 7 5
10 9
A J 8 7
Q 10 5
|
5 → 2
10 → 2
8 → 2
2 → 4 | Q 6 4
K 3 2
K 6 5
A K 9 4 |
| 79. | A 5 4
K 3 2
A J 9 8 3
J 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 9 7 6 3
A Q
7 6
10 9 4 2
|
5 → 2
10 → 1
8 → 1
2 → 1 | K Q 8
10 9 7
K 10 5
A K Q 6 |
| 129. | K Q
A 3
10 9 8 7 6 5
10 9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A 9 8 6 5 4
10 2
J 3
A Q J
|
5 → 4
10 → 5
8 → 4
2 → 4 | J 7 3
K Q 9 7
A K
K 5 4 2 |
| 149. | A J 4
9 2
A 9 8 5
Q 10 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 9 8 7 5 3
Q 10
J 10 6
K J
|
5 → 2
10 → 2
8 → 3
2 → 2 | K 6
A K 7 3
K 7 3
A 9 5 2 |
| 164. | A J 8
A Q 10 9
10 8 7
Q 6 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 9 5
7 2
A 6 5 3
J 9 5 4
|
5 → 2
10 → 2
8 → 2
2 → 3 | K 7 6 4 3
K 3
K J 9
A K 10 |
| 169. | K 5 4
Q
J 10 9 5 3
A J 9 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 9 7 6
K 10 7 3
A 8
Q 6 4
|
5 → 5
10 → 3
8 → 4
2 → 4 | A J 8 3
A 9 2
K 7 6
K 10 5 |
| 173. | J 7
A K 3
9 6 5 3
A K 10 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 9 6 5 3
10 9 2
7
J 4 2
|
5 → 1
10 → 2
8 → 1
2 → 0 | A 8 4
Q 7
A K J 10 8
Q 9 5 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 176. | Q J 5
A K 7
10 9 5 3
Q 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A 9 8 7 6
10 3 2
8
A 10 9 4
|
5 → 3
10 → 3
8 → 4
2 → 2 | K 4 3
Q 9
A K J 7 6
K J 6 |
| 181. | 8 7 3
K 3 2
J 7 3
A Q J 9
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K J 9
Q 9
10 9 8 6 5
K 6 5
|
5 → 2
10 → 2
8 → 2
2 → 3 | A Q 6 5 4
A 10 7
A K
10 4 2 |
| 188. | K 7 3
10 2
A J 8 7
K 10 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 6 5 4
K Q 3
10 5 3
A 9 2
|
5 → 3
10 → 1
8 → 1
2 → 1 | A J 9 8
A 9 7
K 9 6
Q J 5 |
| 213. | 9 4
K Q 3
A 10 8 3
Q J 10 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 7 6 3
A 7
9 6 5
K 9 5 4
|
5 → 1
10 → 2
8 → 1
2 → 1 | A Q J 8 5
10 9 2
K J 7
A 6 |
| 217. | Q J 6
K Q 9
J 9 8 7
Q 9 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A K 9 5
10 7 3
10 5
K 10 6 5
|
5 → 4
10 → 4
8 → 5
2 → 3 | 8 7 4 3
A 2
A K 6 3
A J 2 |
| 234. | J 6 5
A 9 7
9 8 5
A Q J 9
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 8
Q 3 2
J 10 7 6
10 6 2
|
5 → 2
10 → 1
8 → 2
2 → 3 | A 9 7 4 3
K 10
A K 3
K 5 4 |
| 247. | J 8 5
3
A J 10 9 8
Q J 10 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A 9 6 3
K Q 2
7 3
K 9 6 4
|
5 → 3
10 → 2
8 → 2
2 → 2 | K Q 7 4
A 10 9 7
K 6 5
A 5 |
| 263. | Q 8 3
A 7
A J 3
10 9 5 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K J 9 5 4
3 2
9 7 6
A Q J
|
5 → 2
10 → 3
8 → 2
2 → 2 | A 7 6
K Q 10 9
K 10 8 5
K 6 |
| 310. | 7 5
10 9 7
A K 8 6 3
A Q 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 9 3
3 2
10 9 5
K 10 5 2
|
5 → 2
10 → 2
8 → 3
2 → 1 | A J 8 6 4
A K Q
J 7
J 9 6 |
| 325. | Q J 9 6
A Q 2
8 5 3
A 10 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 8 4 3
10 9 3
A K 9 6
J 5 4
|
5 → 2
10 → 2
8 → 2
2 → 4 | A K 7 5
K 7
J 10 7
K Q 9 6 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 329. | 9 8 4
A Q 10
A J 7 5 3
5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 7 6 5
K 3 2
10 9
A 9 6 4
|
5 → 2
10 → 1
8 → 1
2 → 1 | A K J 3
9 7
K 8 6
K Q J 10 |
| 334. | K 7 5
A Q 7 3
K 9 3
10 6 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q J 8 6 4
K 2
A 10 7 6
9 4
|
5 → 3
10 → 4
8 → 3
2 → 2 | A 9 3
10 9
J 8 5
A K Q J 2 |
| 339. | K 8 4
7
A J 10 7 3
J 9 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A 5 3
A 10 9 2
8 5
K Q 10 4
|
5 → 3
10 → 3
8 → 4
2 → 3 | Q J 9 7 6
K Q 3
K 9 6
A 6 |
| 357. | A J 8 5
K 7 2
6 5 3
K 10 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 9 7
A 10 3
K J 10 8
Q J 9 6
|
5 → 3
10 → 3
8 → 3
2 → 4 | K Q 6 4 3
Q 9
A 9 7
A 4 2 |
| 358. | J 4 3
K Q
7 6 3
A K 10 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A K 9 7
10 9 7 3
9 8 5
Q 2
|
5 → 3
10 → 2
8 → 2
2 → 2 | Q 8 6 5
A 2
A K J 10
J 9 5 |
| 368. | Q 9
9 7
A 9 7 3
K Q J 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A K 8 7 6 5 3
Q 10
10 8 5
10
|
5 → 3
10 → 7
8 → 3
2 → 2 | J 4
A K 3 2
K J 6
A 9 6 4 |
| 379. | K 6 4
Q 9 2
A J 10 8 5
J 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 8 7 3
A 3
6 3
K Q 10 9 5 4
|
5 → 1
10 → 1
8 → 2
2 → 1 | A Q J 9 5
K 10 7
K 9 7
A 2 |
| 388. | A J 9 5
K 9 7
6 5 3
K 6 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 8 7 6 3
Q
A K 10 9
J 10 9 4
|
5 → 3
10 → 3
8 → 3
2 → 4 | K Q 4
A 10 3 2
J 8 7
A Q 2 |
| 393. | Q 8 5
K
K 8 6 3
K J 9 6 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 9 7 4 3
A Q 9 3
9 7
Q 5
|
5 → 5
10 → 1
8 → 1
2 → 1 | A K 6
10 7 2
A J 10 5
A 10 4 |
| 395. | A 8
10 3
A J 7 6 5
J 6 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 9 4 3
A 9 2
K 10 3
10 5
|
5 → 4
10 → 5
8 → 4
2 → 4 | J 7 6 5
K Q 7
9 8
A K Q 9 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 407. | Q J 9
A 7 2
K J 6
Q 6 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 7 5 4
Q 3
9 7 3
K J 10 5
|
5 → 1
10 → 1
8 → 2
2 → 1 | A 8 6 3
K 10 9
A 10 8 5
A 9 |
| 414. | 8 7 5
A Q
9 8 6
A Q J 9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 6 4 3
9 7 2
K 7 3
K 10 2
|
5 → 1
10 → 1
8 → 1
2 → 2 | A K J 9
K 10 3
A J 10 5
5 4 |
| 421. | K Q 3
9
A 9 8 7
Q 10 9 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 9 7 5 4
K 10 3
J 5 3
A K 2
|
5 → 3
10 → 2
8 → 2
2 → 2 | A J 8 6
A Q 7 2
K 10 6
J 5 |
| 430. | A 4
9 3 2
K 10 9 7 5
Q 10 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q J 7 5
10 7
J 8 3
K J 9
|
5 → 3
10 → 5
8 → 4
2 → 2 | 9 8 6 3
A K Q
A 6
A 6 5 4 |
| 441. | A 8 4 3
K 10 7
10 6 3
K Q 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 6 5
2
9 7 5
A J 10 9 2
|
5 → 3
10 → 3
8 → 4
2 → 2 | Q J 7
A Q 9 3
A K J 8
6 4 |
| 447. | J 8
K 9 7
A J 10
A 10 6 5 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 9 6 5
Q 10 3
K 8 6 3
J 9
|
5 → 1
10 → 1
8 → 1
2 → 2 | A K 7 4 3
A 2
9 7 5
K Q 2 |
| 450. | Q J 6
A 3
J 10 7 6 5 3
9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 8 7 5
K 10 7 2
K
A 10 2
|
5 → 5
10 → 3
8 → 3
2 → 3 | A 4 3
Q 9
A 9 8
K Q J 5 4 |
| 457. | Q 9 4
3
K 10 7 6 3
K J 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A K 8 7 6
K 10 9
J 8 5
Q 10
|
5 → 3
10 → 4
8 → 3
2 → 2 | J 5 3
A Q 7 2
A 9
A 9 5 2 |
| 494. | A J 8
K Q 10 3
9 8 7
Q 10 9
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 9 6 5 4
2
J 10 6 5
A K J 2
|
5 → 3
10 → 3
8 → 4
2 → 3 | K Q 7 3
A 9 7
A K 3
6 5 4 |
| 509. | 8 6 3
K Q 3
A J 8 3
5 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A 7 5 4
9 2
K 10 7 5
A 10 6
|
5 → 3
10 → 3
8 → 3
2 → 4 | K Q J 9
A 10 7
9 6
K Q J 9 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 515. | K Q 9
3 2
10 5
K 10 9 6 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A J 6 4 3
K Q 10 9
A 9 7 3
—
|
5 → 6
10 → 5
8 → 5
2 → 5 | 8 7 5
A 7
K J 8 6
A Q J 4 |
| 527. | K 6 3
Q 10
A J 8 7 5
J 10 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A Q J 8
9 7 2
10 9 3
A 9 4
|
5 → 2
10 → 4
8 → 2
2 → 2 | 9 7 5 4
A K 3
K 6
K Q 5 2 |
| 530. | Q J 9 8
Q 9 3
K 9 5
Q J 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 6 5 4 3
K 10
A 7 3
K 10 9 6
|
5 → 2
10 → 2
8 → 3
2 → 2 | A K 7
A 7 2
J 10 8 6
A 4 2 |
| 567. | K 9 8
A 10 2
9 5 3
K J 9 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 6 5
9 7
A K 10 7 6
Q 6 5
|
5 → 1
10 → 1
8 → 1
2 → 5 | A Q 7 4 3
K Q 3
J 8
A 10 2 |
| 579. | Q 7 4
A 9 7
10 9 7
A 10 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 6 5 3
K 3 2
A 3
J 9 6
|
5 → 4
10 → 2
8 → 2
2 → 2 | A J 8
Q 10
K J 8 6 5
K Q 5 |
| 592. | J 4 3
Q
K J 7 5
Q J 6 5 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 9 8 7
A 3 2
9 8
K 10 2
|
5 → 3
10 → 5
8 → 3
2 → 3 | A 6 5
K 10 9 7
A 10 6 3
A 9 |
| 620. | K 7
K 2
J 10 8 7 6 5
K Q J
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 9 8 4 3
9 3
A
A 10 9 5 4
|
5 → 3
10 → 3
8 → 4
2 → 3 | A Q 6 5
A Q 10 7
K 9 3
6 2 |
| 633. | A J 3
10 9 3
8 7
A Q J 6 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 8 4
7 2
A J 10 6
10 5 4
|
5 → 2
10 → 2
8 → 2
2 → 3 | Q 7 6 5
A K Q
K 9 5 3
K 9 |
| 643. | Q 9 8
A 9 7
J 6
A J 10 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K J 6 4
K 10 2
K 9 5 3
9 5
|
5 → 3
10 → 2
8 → 2
2 → 2 | A 7 5 3
Q 3
A 10 8 7
K Q 6 |
| 650. | J 4 3
A K
K 10 8 6 3
9 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 7 6 5
10
J 9 5
A J 5 2
|
5 → 3
10 → 4
8 → 3
2 → 3 | A 9 8
Q 9 7 3 2
A 7
K Q 10 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 651. | Q 8 3
A 2
8 7 3
K 9 6 5 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 9 6 5
9 7
K J 9 5
A Q J
|
5 → 4
10 → 5
8 → 6
2 → 5 | A K 7 4
K Q 10 3
A 10 6
10 2 |
| 669. | K J
K 7
J 6 5 3
K Q 10 9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A 9 7 6 5 4
9 2
A 10 9 7
2
|
5 → 2
10 → 2
8 → 2
2 → 4 | Q 8 3
A Q 10 3
K 8
A J 5 4 |
| 673. | J 5 3
10 2
K J 7 3
A J 9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 7 4
A Q 7 3
10 9
10 5 2
|
5 → 3
10 → 2
8 → 2
2 → 2 | A 9 8 6
K 9
A 8 6 5
K Q 4 |
| 698. | 3
A 9 7
A 10 6 3
Q J 10 5 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 9 7 6 5 4
—
J 8 5
A 9 2
|
5 → 1
10 → 2
8 → 1
2 → 1 | A J 8
K Q 10 3 2
K 9 7
K 6 |
| 706. | K 5
9 3 2
A 8 5 3
K Q 9 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 9 7 4 3
10
K 10 9
A J 5 4
|
5 → 3
10 → 3
8 → 4
2 → 3 | A Q 8 6
A K Q 7
J 7 6
10 6 |
| 708. | 8 3
K Q 10
J 9 5 3
A K 9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A Q 9 7 5
7
K 10 7 6
10 5 2
|
5 → 2
10 → 2
8 → 2
2 → 3 | K J 6 4
A 9 3 2
A 8
Q J 4 |
| 711. | A 5
Q 3
J 10 8 3
A Q 6 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 6 4 3
A 10 2
K 6 5
J 9 4
|
5 → 3
10 → 1
8 → 2
2 → 2 | K Q 9 8 7
K 9 7
A 9 7
K 10 |
| 726. | K 9
2
A K 7 6 3
K 10 9 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A Q 8 7 5 3
Q 10 3
J 10 8
5
|
5 → 2
10 → 3
8 → 2
2 → 2 | J 6 4
A K 9 7
9 5
A Q J 2 |
| 727. | K J 3
10 9 3
K 10 8 6 5
A 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 9 7 6 4
K
3
K Q 10 6 4 2
|
5 → 1
10 → 2
8 → 3
2 → 1 | A 8 5
A Q 7 2
A J 9 7
J 9 |
| 728. | 9 3
K 10 7
7 6 3
A K 10 6 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q J 8 5 4
Q 3
K J 10 8
Q 5
|
5 → 2
10 → 2
8 → 2
2 → 3 | A K 7 6
A 9 2
A 9 5
J 9 4 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 9981. | 6 3
A 7
K J 8 3
K J 10 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 8 7 5 4
K Q 10 2
10 7
Q 5
|
5 → 0
10 → 0
8 → 0
2 → 0 | A Q J 9
9 3
A 9 6 5
A 9 6 |
| 9982. | A Q 9
K 2
J 7 6 3
K 10 9 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K J 6 4
A 10 9 7
10 5
6 5 4
|
5 → 5
10 → 4
8 → 4
2 → 2 | 8 7 5 3
Q 3
A K 9 8
A Q J |
| 9983. | A 8 6 3
A K Q
J 8 3
10 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q J 9 5 4
7 3
10 7
A J 6 5
|
5 → 2
10 → 3
8 → 2
2 → 1 | K 7
10 9 2
A K 9 6 5
K Q 9 |
| 9984. | 8 4 3
K 2
A 9 3
A J 9 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 7 6
Q 10 7
J 8 5
Q 10 4
|
5 → 3
10 → 2
8 → 2
2 → 2 | A J 9 5
A 9 3
K 10 7 6
K 6 |
| 9985. | K 7 5
A 10
10 9 8 6
K Q 6 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | J 9 6 4 3
9 7
K J 5
A 4 2
|
5 → 2
10 → 2
8 → 2
2 → 3 | A Q 8
K Q 3 2
A 7 3
J 10 9 |
| 9986. | Q 7 5
A 9 2
9 7 6 3
K Q 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A 9 6 3
K Q 10
J 10 5
10 9 5
|
5 → 3
10 → 3
8 → 3
2 → 3 | K J 8 4
7 3
A K 8
A J 6 4 |
| 9987. | J 9 7 5
A 9 2
J 10 6
A 10 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 6 4 3
—
A 9 8 7
Q J 5 4
|
5 → 3
10 → 4
8 → 5
2 → 4 | A 8
K Q 10 7 3
K 5 3
K 9 2 |
| 9988. | J 6 3
K Q
K J 9 7
K J 10 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 5 4
10 9 7 3
8 6
A 9 6
|
5 → 2
10 → 1
8 → 2
2 → 2 | A Q 8 7
A 2
A 10 5 3
Q 5 4 |
| 9989. | J 3
K 10 3
9 6 3
A J 10 5 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 7 6 5
A 9 7
A 10 8 7
6
|
5 → 3
10 → 2
8 → 3
2 → 3 | A Q 8 4
Q 2
K J 5
K Q 9 2 |
| 9990. | K J 4 3
K 9 3
8 5 3
K Q J
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 8 7
10 2
K 10 7 6
A 10 9 2
|
5 → 2
10 → 2
8 → 2
2 → 2 | A 9 6 5
A Q 7
A J 9
6 5 4 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
| 9991. | J 5 3
Q 10 7
7 3
A Q 10 9 6
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K 9 8
A 3
K J 9 8 5
J 5 2
|
5 → 3
10 → 3
8 → 3
2 → 4 | A Q 7 6 4
K 9 2
A 10 6
K 4 |
| 9992. | 8 7 5 4
A 3 2
A 9 3
K J 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q J 9 6 3
—
K J 7 6
Q 10 9 6
|
5 → 2
10 → 3
8 → 4
2 → 3 | A K
K Q 10 9 7
10 8 5
A 4 2 |
| 9993. | K
K Q 10
10 7 6 3
K J 9 5 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | A J 9 7 6 4
9 3 2
J 8
A 6
|
5 → 3
10 → 3
8 → 3
2 → 3 | Q 8 5 3
A 7
A K 9 5
Q 10 4 |
| 9994. | 8 3
A 10 3
K 10 6
A Q 9 6 4
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K J 7 5 4
9 2
J 9 8 7
K J
|
5 → 2
10 → 2
8 → 2
2 → 2 | A Q 9 6
K Q 7
A 5 3
10 5 2 |
| 9995. | J 9 6
A 10
A 7 6 3
K Q 4 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | 8 7 5 4
K 2
K 10 8 5
J 9 5
|
5 → 2
10 → 2
8 → 2
2 → 2 | A K Q 3
Q 9 7 3
J 9
A 10 6 |
| 9996. | A J 6
Q 10 9
J 9 3
Q 9 6 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 8 5 4 3
A
10 6 5
K 4 2
|
5 → 3
10 → 6
8 → 3
2 → 1 | 9 7
K 7 3 2
A K 8 7
A J 10 |
| 9997. | J 5
10 7
A 10 9 8 7 6
K J 5
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | K Q 4 3
K 9 2
J 3
Q 9 6 2
|
5 → 2
10 → 2
8 → 2
2 → 1 | A 9 8 7 6
A Q 3
K 5
A 10 4 |
| 9998. | K J 6
K 9 3
10 7 3
K 10 6 2
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 8 3
A 10 2
A J 6 5
J 5 4
|
5 → 2
10 → 2
8 → 2
2 → 3 | A 9 7 5 4
Q 7
K 9 8
A Q 9 |
| 9999. | 9 3
A 9 7
A 10 8 5 3
A 10 9
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q J 7 6 5 4
K 10 3
9
Q 6 2
|
5 → 0
10 → 0
8 → 0
2 → 0 | A K 8
Q 2
K J 7 6
K J 5 4 |
| 10000. | K J 5
9 7 2
J 10 8 7 6
A Q
|
10 2
J 8 6 5 4
Q 4 2
8 7 3 | | Q 8 7 6
K Q
K 9
J 10 6 5 4
|
5 → 2
10 → 2
8 → 2
2 → 2 | A 9 4 3
A 10 3
A 5 3
K 9 2 |
| Simulation 8Z31 Main | | Top Long or Short Major? |
Acknowledgments to Sir Arthur Conan Doyle (1859-1930)
Photo is Basil Rathbone and Nigel Bruce as Holmes and Watson
© 2025 Richard Pavlicek