Vacant Places: How to Calculate Where Missing Cards Are

You’re in 3NT. You need to guess where the ♥K is. You have AQ in dummy, small cards in hand. Normal odds: 50-50.

But wait. LHO opened 1♠ and has shown 5 spades. RHO followed to 3 rounds of clubs, but LHO showed out on the third round.

Where’s the ♥K?

If you answered “probably with RHO,” you understand vacant places.

Here’s why: LHO started with 5 spades and 5 clubs. That’s 10 cards. They only have 3 vacant places in hearts and diamonds combined. RHO started with 2 spades and 3 clubs. That’s 5 cards. They have 8 vacant places in hearts and diamonds.

RHO has more room for the ♥K. Finesse through LHO (playing RHO for the king).

This is vacant places—one of the most powerful tools in declarer play. And most players don’t use it.

The Basic Principle

Every player starts with 13 cards. Once you know how many cards they hold in some suits, you know how many vacant places they have in the remaining suits.

A player with more vacant places is more likely to hold any specific missing card.

It’s not magic. It’s counting.

Example 1: The Opening Bid

LHO opens 1♠, showing 5+ spades. You need to locate the ♦Q.

You know LHO has at least 5 spades. RHO has at most 8 spades (13 total spades minus your 2 minus dummy’s 3).

But let’s say both opponents follow to 2 rounds of spades. Now you know:

  • LHO started with 5+ spades (let’s say exactly 5)
  • RHO started with 3 spades

RHO has 10 vacant places in the other suits. LHO has 8 vacant places.

RHO is 10:8 (or 5:4) more likely to hold the ♦Q.

That’s 55% vs 45%. Small edge, but it’s better than guessing.

Example 2: The Club Suit Tells You About Hearts

You’re in 4♥. Hearts split 2-2 (both opponents followed twice). Clubs split 4-1 (LHO has 4, RHO has 1).

You need to locate the ♠Q.

Count the vacant places:

  • LHO: 2 hearts + 4 clubs = 6 cards. Vacant places in spades and diamonds: 13 - 6 = 7
  • RHO: 2 hearts + 1 club = 3 cards. Vacant places in spades and diamonds: 13 - 3 = 10

RHO is 10:7 more likely to hold the ♠Q.

Finesse accordingly.

Example 3: The 5-0 Split

You’re in 6♠. Spades split 2-2. Clubs split 5-0 (LHO has all 5).

You need to locate the ♦K.

Count:

  • LHO: 2 spades + 5 clubs = 7 cards. Vacant places: 6
  • RHO: 2 spades + 0 clubs = 2 cards. Vacant places: 11

RHO is 11:6 (nearly 2:1) more likely to hold the ♦K.

This is a huge edge. Play accordingly.

The Math: A Priori vs A Posteriori

Before you see any cards, every missing card is equally likely to be with either opponent. This is called a priori probability.

But as you learn more—opponents follow to suits, show out, make bids—you update your probabilities. This is called a posteriori probability.

Vacant places is just formal a posteriori counting.

How to Count Vacant Places at the Table

You don’t need to be a math genius. Just follow these steps:

Step 1: Count the Suits You Know

Play a few rounds. See how suits split. Count how many cards each opponent has shown in each suit.

For example:

  • LHO: 3 spades, 4 clubs, 2 hearts
  • RHO: 2 spades, 1 club, 2 hearts

Step 2: Add Them Up

  • LHO: 3 + 4 + 2 = 9 cards known
  • RHO: 2 + 1 + 2 = 5 cards known

Step 3: Subtract From 13

  • LHO: 13 - 9 = 4 vacant places
  • RHO: 13 - 5 = 8 vacant places

Step 4: Use the Ratio

If you’re missing 1 card (say, the ♦K), the odds are 4:8 (or 1:2) that it’s with LHO vs RHO.

RHO is twice as likely to hold the ♦K.

If you’re missing 2 cards (say, the ♦KQ), the odds are a bit more complex, but RHO is still more likely to hold any specific one.

Example 4: The Slam Decision

You’re in 6NT. You have 11 top tricks. Dummy has ♠ KJ10 opposite your ♠ xxx. You need to finesse for the queen to make 12 tricks.

Both opponents have followed to 3 rounds of hearts. Both have followed to 2 rounds of diamonds. LHO showed out on the 3rd round of clubs (RHO has 5 clubs, LHO has 1).

Count:

  • LHO: 3 hearts + 2 diamonds + 1 club = 6 cards. Vacant places: 7
  • RHO: 3 hearts + 2 diamonds + 5 clubs = 10 cards. Vacant places: 3

LHO is 7:3 (more than 2:1) more likely to hold the ♠Q.

Finesse through RHO (lead low from dummy toward the king, hoping LHO has the queen).

When Vacant Places Doesn’t Help

Case 1: You Don’t Know Enough Yet

Early in the hand, you haven’t seen much. Both opponents have 12-13 vacant places. The ratio is close to 1:1. Vacant places doesn’t give you an edge.

Play a few rounds first. Gather information.

Case 2: The Distributions Are Balanced

Both opponents followed to 3 rounds of spades, 2 rounds of hearts, 2 rounds of diamonds. They’ve each shown 7 cards. They each have 6 vacant places.

No edge. You’re back to 50-50.

Case 3: You’re Missing Many Cards

Vacant places works best when you’re locating 1 specific card (the king, the queen). When you’re missing 4-5 cards and need to know how they split, vacant places is less useful.

For splits, you rely on straight probability (3-2 is 68%, etc.), then adjust for vacant places if one opponent is much shorter.

Combining Vacant Places with Other Clues

Vacant places is just one tool. Combine it with:

The Bidding

If LHO opened 1NT showing 15-17, they have 15-17 HCP. If you can account for 12 of those points, the missing king is probably with RHO.

Defensive Signals

If RHO gave count in spades (playing high-low to show an even number), you know they started with 2 or 4 spades. That narrows their vacant places.

Opening Leads

If LHO led the ♥K from KQ, you know where those cards are. That’s information.

Restricted Choice

If RHO played the ♦Q from possible KQ, Restricted Choice says they’re more likely to have Q alone. Combine that with vacant places: if RHO also has fewer vacant places, the Q alone becomes even more likely.

Stack your edges.

Advanced: Partial Vacant Places

Sometimes you know an opponent has “at least X cards” in a suit, but not exactly how many.

LHO opened 1♠. That’s 5+ spades. They could have 5, 6, 7, or even 8.

You can still use vacant places, but you have to estimate. If LHO has 5 spades, they have 8 vacant places. If they have 6 spades, they have 7 vacant places.

Assume the most likely case (5 spades for a 1♠ opener) and go with it. You won’t be perfect, but you’ll be better than ignoring the information.

Example 5: The Crossruff

You’re in 4♠, planning a crossruff. You need to know if it’s safe to ruff out dummy’s hearts or if someone will overruff.

LHO has shown 1 spade, 5 hearts, 4 diamonds. RHO has shown 3 spades, 2 hearts, 2 diamonds.

Count:

  • LHO: 1 + 5 + 4 = 10 cards. Vacant places (clubs): 3
  • RHO: 3 + 2 + 2 = 7 cards. Vacant places (clubs): 6

RHO is twice as likely to hold any given club. If you’re missing the ♣A and need to know who has it, play RHO for it.

But more importantly: LHO is very short in clubs. If you ruff clubs in dummy, LHO might overruff (they only have 3 clubs). RHO is less likely to overruff (they have 6 clubs and will follow longer).

Plan accordingly.

The Human Element: Opponent Behavior

Vacant places assumes opponents are dealt cards randomly. But bridge players aren’t random.

If LHO is a weak player and opened 1♠ on a weak 5-card suit, they might not have the points for a missing king elsewhere. Adjust.

If RHO hesitated before playing to a trick, they might have a problem. That’s information too.

Vacant places is mathematical. But bridge is human. Use both.

Common Mistakes

Mistake 1: Not Counting

Most players don’t count at all. They finesse randomly and hope for the best.

Count. Even rough counting (LHO has “a lot” of clubs, RHO has “a few”) is better than nothing.

Mistake 2: Counting Only Trumps

You count trumps (because you have to) but ignore the other suits.

Count everything. Every suit gives you information.

Mistake 3: Forgetting to Update

You counted early in the hand, but didn’t update as you learned more.

Keep counting. Every card played is new information.

Mistake 4: Overcomplicating It

You try to track every card in every suit and lose track.

Start simple. Count one or two suits well. As you get better, add more.

The Practical Method

Here’s a simple system:

  1. Pick one opponent to track (usually the one who bid). Count their cards.
  2. After each trick, update. “LHO has shown 7 cards so far. 6 vacant places left.”
  3. Before a key decision, ask: who has more vacant places? Finesse accordingly.

That’s it. You don’t need to be perfect. You just need to be better than guessing.

Vacant Places in Defense

This works on defense too.

Partner leads the ♠K. Declarer wins the ace. Later, declarer leads a heart toward dummy’s KQ.

You’re missing the ♥A. Do you assume declarer has it, or partner?

Count declarer’s shape. If declarer has shown 5 spades and 4 diamonds, they have 4 vacant places in hearts and clubs. If partner has shown 2 spades and 2 diamonds, they have 9 vacant places.

Partner is more likely to hold the ♥A. Play accordingly (maybe duck, expecting partner to win).

The Deep Principle

Bridge isn’t random. Every card you see, every bid your opponents make, every signal they give—it all narrows the range of possibilities.

Vacant places is just formalized counting. It’s the math behind “this opponent is more likely to have that card.”

Good players do this instinctively. They don’t say “vacant places,” they just feel it. But when you’re learning, formalize it. Count the cards. Calculate the ratio. Make the right play.

Over time, it becomes second nature.

The Takeaway

Before you finesse, ask yourself:

  1. What do I know about the opponents’ distribution?
  2. Who has more vacant places?
  3. Does that change my play?

If you’re missing the king and one opponent has 8 vacant places while the other has 4, that’s a 2:1 edge. Take it.

Vacant places won’t make you perfect. But it’ll make you right more often than guessing.

And in bridge, that’s how you win.

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