Card Combo Fun

I recently came across an article by Fred Gitelman on suit combinations. Fred is a great player and shares my love for complex suit combos. One from this article really caught my attention as I had never seen it before.

T543 opposite
AQ82

I set out on a quest to find both the best theoretical and practical plays. The best method to do this is figure out all the possible combinations a certain play caters to, and the probability of each one happening. At the table the latter is not possible past an approximation, but here we can figure it out more precisely.

Before doing this we must consider what possible plays we have.

1. Cash the ace and then lead towards the queen trying to guess the suit.
2. Lead small towards the queen like everyone would do at the local bridge club.
3. Lead small towards the 8 planning on leading small towards the queen next.
4. Lead the ten planning to run it.

Line 1, cashing the ace first caters to these holdings with left hand opponent:

• K
• J
• 9
• Jx(2)
• xx
• K9
• KJ
• 9xx
• Jxx
• J9x(2)
• Kxx
• K9x(2)
• KJx(2)
• J9xx

You may wonder why I left out J9. The reason is, if you cash the ace and the 9 drops on your left you will cross to dummy and the ten planning to let it run. This will cater to stiff 9 or K9 on your left, while leading low to the queen would cater only to J9. Also, if there is a (2) by a combination that means there are 2 of those combinations possible. For instance, J9x can be J97 or J96.

Line 2, low to the queen, caters to these holdings with LHO:

• J
• 9
• Jx(2)
• xx
• J9
• KJ
• 9xx
• Jxx
• J9x(2)
• Kxx
• K9x(2)
• KJx(2)
• J9xx

Line 3, small to the 8, caters to these holdings:

• void
• x(2)
• Jx(2)
• J9
• xx
• Kx(2)
• 9xx
• Jxx
• J9x(2)
• Kxx
• KJx(2)
• J9xx

Line 4, leading the ten from dummy caters to the same holdings as line 3 except instead of winning against J9xx on the left, it wins against stiff 9. Some interesting things happen if you lead the ten from dummy. Assume with J9x they will always cover, otherwise they give up the suit. So when you play the queen and it loses to the king, you will next lead small to the 8. That means you cannot pickup K9 on your right since with Jxx they can also cover. Again you will hook the 8 on the next round, but this time it loses to the 9. Now, let's say they had J976. If they did not cover the ten, you would know they must have J976 because with Jxx or J9x they must cover, so you could take a deep finesse of the 8 on the next round! To stop this, they need to cover with the jack again. If you play the queen you must lose 2 tricks. You may be thinking that once they play the jack you should play the ace next and then cross to dummy and lead small to the 8. However if you do THAT, you lose to KJx onside. This means, theoretically, it can never go ten low low king.

Summary: ok, ok you have no interest in the raw data. You want some numbers. Fine.

1. Line 1 wins against 14 3-2 splits and 4 4-1 splits
2. Line 2 wins against 14 3-2 splits and 3 4-1 splits
3. Lines 3 and 4 win against 13 3-2 splits but pick up 3 4-1 splits and a 5-0 split.

This makes line one close to 58.78 %, line two 55.95 %, lines three and four 54.52 %. So the theoretical best play is cashing the ace first, planning to lead small to the queen next if nothing eventful happens, or running the ten on the next round if LHO drops the 9.

This leaves one question unsolved; the best practical play. Well in practice if your opponent led the ten from dummy with Txxx, would you cover with Jxx? I would guess no expert would ever cover. Declarer could have KQ98 for instance, and you solve his guess. He could also have A98x and be trying to crash some honors (which you would let him do by covering). He may even have K98x and you again solve a guess for him. If you accept that Jxx would never cover, that can now be picked up by leading the ten first. This brings the percentage up to 57.91, within one percent of line 1. This means that if the opponents would ever fail to cover with either Jx or J9x, playing the ten from dummy is probably the best practical line. Jx is a clear cover, but some weaker opponents may fail to do it. J9x is also a good cover, though it could lose if declarer has AK8xx and figures out the position. Given that, some players may not cover. This suggests that the best practical line is actually the worst theoretical one.

Knowing your basic suit combinations is not essential to becoming a winning player as it has limited practical use. At the table you usually have some clues or information that changes the percentages. It is important to remember that these isolated combinations are all in a vacuum. That being said, I think all serious players should know how to work combinations out at the table, and have studied basic ones that come up fairly frequently. Even though it isn't essential to know them it certainly can't hurt.