Safety Plays and Probability

Expert declarers don’t guess. They know the odds, and they choose the line that gives them the best chance of making the contract, even when that means giving up an overtrick.

By the end of this module you’ll be able to:

Use the suit-split table to judge your chances.
Combine chances by trying them in the right order.
Apply “eight ever, nine never” and restricted choice.
Make safety plays that protect your contract.
Use avoidance to keep the dangerous opponent off lead.

1. How suits split

When you and dummy hold most of a suit, the cards you’re missing are divided between the two opponents. These are the approximate chances, at the start of play, with no information from the bidding:

Cards missing	Split	Chance
2	1–1	52%
	2–0	48%
3	2–1	78%
	3–0	22%
4	3–1	50%
	2–2	41%
	4–0	10%
5	3–2	68%
	4–1	28%
	5–0	4%
6	4–2	48%
	3–3	36%
	5–1	15%
	6–0	1%
7	4–3	62%
	5–2	31%
	6–1	7%

The pattern to remember:

An odd number of missing cards tends to split as evenly as possible (five missing: 3–2 is 68%).
An even number of missing cards tends to split unevenly (four missing: 3–1 is more likely than 2–2; six missing: 4–2 is more likely than 3–3).

Information changes the odds

These numbers apply before any information. The bidding and the play change them. If an opponent has pre-empted in hearts with seven cards, they have only six cards in the other three suits, so your missing spades are much more likely to be with their partner. Module 6 shows you how to use this.

2. Finesses and combined chances

A simple finesse works 50% of the time.
With two finesses to try, the chance that at least one works is 75%. The chance that both work is 25%.

Combining chances

Often you have two possible ways to make your contract. Try first the chance that doesn’t lose the lead, then fall back on the other.

You need one more trick. You can try:

A club suit of A K Q 4 opposite 7 6 2: a fourth trick if clubs split 3–3 (36%).
A diamond finesse: 50%.

If you take the diamond finesse first and it loses, you go down: 50%. Instead, cash the top clubs first. If they split 3–3, you’ve made it (36%). If they don’t, you still have the diamond finesse. That gives you 36% plus 50% of the remaining 64%, a total of about 68%.

Combine your chances: try the option that keeps the lead first.

3. “Eight ever, nine never”

You’re missing the queen of a suit and hold the ace and king.

With eight cards between your hands, finesse for the queen.
With nine cards, cash the ace and king and play for the queen to drop.

With nine cards the opponents hold four, including the queen. The drop works when the queen is singleton or doubleton, slightly more often than the 50% finesse.

This is only a guide. If the bidding tells you who holds the queen, play for it.

4. Restricted choice

You hold this suit and need four tricks:

            North
            A 10 9 4
West                     East
?                        ?
            South
            K 8 7 6 5

The missing cards are Q, J, 3 and 2. You lead small from South to the ace. West plays the 2, and East plays the queen.

Now you lead small from South again and West plays the 3. Should you play North’s 10 (finessing West for the jack), or play for the drop?

Finesse. If East started with Q J doubleton, East could have played either honour, and would play the queen only half the time. If East started with a singleton queen, East had no choice. So a singleton is about twice as likely as Q J doubleton.

This is the principle of restricted choice:

When an opponent plays one of two equal cards, assume they had no choice.

5. Safety plays

A safety play gives up a small chance of an overtrick, or a small chance of a better result, to make sure of the contract. Safety plays matter most at teams (IMPs), where making the contract counts much more than an overtrick. At matchpoints, each one needs more thought (Module 10).

Ducking to keep communication

You’re in 3NT. Dummy has a long club suit and no outside entry:

            North
            ♣ A K 6 5 4 3
            (no other entry)

            South
            ♣ 7 2

You need five club tricks. If clubs split 3–2 and you cash the ace and king and then give up a club, the suit is good, but you have no way back to dummy to enjoy it.

Safety play: duck the first round of clubs. Play low from both hands. When you regain the lead, play your remaining club to the ace and king: if clubs split 3–2, all the rest of dummy’s clubs are winners and you can reach them.

Protect against a bad break when you can afford a loser

In 4♠ with plenty of tricks elsewhere, you can afford one trump loser but not two. Instead of the play that makes the most tricks when trumps break well, choose the play that never loses two tricks, even if it sometimes loses an overtrick.

Before you play trumps, ask: “What could go wrong, and can I protect against it?”

Avoidance: keep the danger hand off lead

You’re in 3NT. West leads a spade, and you hold up your ace until the third round. Now West has the remaining spades, so West is the danger hand. East can’t hurt you, because East has no spades left.

When you need to develop an extra trick, choose the finesse or the suit that only East can win. If you must lose the lead, lose it to East.

Rules worth remembering

Odd numbers split evenly; even numbers split unevenly.
Two finesses: at least one works 75% of the time.
Combine your chances: try the option that doesn’t lose the lead first.
Missing the queen: eight ever, nine never, unless the bidding says otherwise.
Restricted choice: when an opponent drops one of two equal honours, play them for a singleton.
A safety play protects the contract at the cost of an overtrick. Use it at IMPs; think twice at matchpoints.
Identify the danger hand and keep it off lead.

Try these

1. You’re missing five cards in your trump suit. What’s the chance they split 3–2?

2. You need one extra trick. You can try a heart finesse or hope spades (A K 5 3 opposite Q 7 2) split 3–3. In what order should you play?

3. You hold A K J 7 6 opposite 5 4 3 2 in trumps and need no losers. Do you finesse the jack or play for the drop?

4. You hold A K J 7 6 opposite 5 4 3 in trumps and need no losers. Do you finesse or play for the drop?

5. In 3NT you have held up the ♠A until the third round, and West has two winning spades left. You can develop your ninth trick either by a diamond finesse into the West hand or a club finesse into the East hand. Which do you choose?

Answers

1. About 68%.

2. Cash the top spades first (play the A, K and Q). If they split 3–3, your fourth spade is a winner. If not, take the heart finesse. You combine 36% with half of the rest: about 68%.

3. Play for the drop. You have nine trumps and are missing the queen: “nine never”. Cash the ace and king.

4. Finesse. You have eight trumps and are missing the queen: “eight ever”. Cash one top honour first (in case the queen is singleton), then lead towards the jack.

5. The club finesse into East. If it loses, East has no spades to return. If the diamond finesse lost, West would cash the spades and beat you.

Words to know

Term	Meaning
Split	How the missing cards in a suit are divided between the opponents
Combining chances	Trying more than one way to make your contract, in the best order
Eight ever, nine never	With eight cards finesse for a missing queen; with nine, play for the drop
Restricted choice	The principle that an opponent who plays one of two equal cards probably had no choice
Safety play	A play that guards the contract against a bad break, at the cost of a possible overtrick
Danger hand	The opponent who can hurt you if they win a trick
Avoidance	Keeping the danger hand off lead
Ducking	Deliberately losing a trick, often to keep communication between your hands

What next?

Learn the split table for five and six missing cards. They come up on almost every hand.
Before every contract, say to yourself: “What could go wrong?” and look for a safety play.
Move on to Module 6: Counting the hand, which shows you how to replace the table’s odds with real information from the bidding and play.