We’ve talked about Planning the Play where you count HCP and Tricks (winners & losers) in the 1st 90 seconds before you play to trick 1. Let’s focus on our counting skills and see what we can do on every hand, whether we declare or defend. As we learn, we need practice before the skill becomes 2nd nature. During our practice phase we might find erratic results and inaccuracy – keep going! Don’t stop. The better your counting skills, the better you will be at the table.
|What do we count?||Where’s our data?|
|1. High Card Points||1. Bidding|
|2. Declarer’s/Partner’s shape||2. Opening leads/New Suit|
|3. Losers||3. Information from Dummy|
|4. Tricks for Declarer||4. Defensive Signals|
|5. Tricks for Defense||5. The play of the hand (Discovery)|
Counting begins with a clear understanding of the bridge language (bidding and signals). We add judgment – inferences that stand the test of time – to build our estimates. Then we adjust our count as the hand progresses. This is the tough part – we have to stay focused and active for 11-12 tricks, even with a boring hand. Our goal is to help our side count what matters so we get our best result on every hand. Let’s look at some examples.
Warning – counting can be exact when we are able to discover facts during play, or approximate when we make assumptions about bids and signals. Either way we are building information based on inference and deduction to guide our play. We start with a sound estimate from the bidding, dummy and opening lead, then refine the count as the play proceeds.
Assume a 2/1 Game Force approach – the more common duplicate system. Use the bidding to create an approximate picture of the hands you don’t see.
We’ll start by counting HCP. There are several sources of information to help us form a HCP count of the unseen hands. When we are declarer we look to count the opponent’s hands. When we defend we are counting declarer and partner’s hands. While bidding is the most obvious source of HCP information, there are several others to consider.
We can locate Honors by:
|Bidding||What they bid and what they don’t bid|
|Leads||What they lead and what they don’t lead|
|Information from Dummy||HCP and Shape|
|Attitude or Suit Preference Signals||What partner signals and what partner doesn’t signal|
|Finesses and Discovery Plays||Find other honors safely to eliminate options|
During the bidding you should be thinking along the following monologue: “LHO opened so s/he has at least 12 HCP (some open on 11 or less), partner passed so s/he is unknown but I suspect less than 8 HCP. RHO responded at the 1 level so RHO has at least 6 HCP. I hold a balanced 10 HCP so partner has a most 12 HCP, but he would certainly bid with the right shape and most any 8 HCPs. My best bid is….” By keeping this monologue running throughout the auction you will create a view of what opponents and partner hold before partner makes the opening lead.
Here’s some basic bridge bidding language. Your agreements might be different. Note how invitations are then used to find top count (or superior losing trick count) within a known range.
|Openers||Range||Unbalanced hands bidding||Balanced hands bidding|
|12-14 HCP||Minimum||1 suit, simple rebids||1 suit then rebid 1NT|
|15-17||Sound||1 suit, Jump Rebid, Bid 3 times||1NT|
|18-21||Strong||1 Suit, Reverse or Jump Shift||1 Suit then jump to 2NT|
|22+||Very Strong||2 – game unless 2nd negative||2 then 2N rebid|
|Openers||Range||Unbalanced hands bidding||Balanced hands bidding|
|0-4 HCP||Ext. Weak||Pass. 2nd negative for 2 if no A/K||Pass. 2nd negative for 2 if no A/K|
|5-7||Weak||1 bid, unless forced by partner||1 bid only unless forced by partner|
|7-9||Constructive||1 or 2 bids, but not past 2 of partner’s 1st suit.||1 or 2 bids, but nothing new past 2 of partner’s 1st suit.|
|9-11||Invitational||Bids to the 2NT/3 level||Bids to the 2N/3 level|
|12-15 / 16-19 / 20+||GF / Slam Inv / Slam||2/1 GF, Forcing Raises, 4thSF Control Bids|
Some opening lead inferences you already know….
|Lead||Context||HCP shown in that suit…|
|A||Unbid suit||4 or 7-10 HCP. Leading an unsupported Ace from length is both bad and rare. Don’t count on it in the big game|
|Partner’s suit||4 HCP, likely shortness|
|Switch unbid suit trick 2 (Suit contract)||4 HCP, likely singleton.|
|K||Unbid suit||5-6 HCP|
|Partner’s suit||3-6 HCP, possible shortness|
|Switch unbid suit trick 2 (Suit contract)||If Q in dummy, want’s you to return suit (Bath Coup defense).If no Q then think singleton.|
|Q||Unbid suit||3 or 5-7 HCP. 5 or 7 w/ AQJ or KQ10|
|Partner’s suit||2-3 HCP|
|Switch unbid suit trick 2 (Suit contract)||3 HCP, suspects declarer will ruff 2nd round|
|J||All||1 or 4-5 HCP w/ KJ10 AJ10 (Ask J denies?)|
|10||All||0 or 4-6 HCP w/KJ10 or AQ10 (0 or 2 higher).|
|x||Unbid suit||2-4 HCP if low (A, K, Q likely); 0 if high (7,8,9)|
|Partner’s suit||1) Low from 3 or more. High then low means doubleton. No HCP promised2) Low implies honor 2-4 HCP. MUD with 3 and no honor. 2nd best w/4 and no honor.|
While we didn’t include trump leads, most trump leads are made to reduce declarer’s ruffing power or to avoid leading away from unprotected honors in the remaining suits. With no partnership bidding there is a strong inference partner holds HCP in all 3 suits when leading a trump. With partnership bidding, partner must fear a cross ruff or be void in your suit if they lead a trump.
How can counting come in handy? Let’s try 1 hand 5 different ways. Notice how the bidding changes the context for what we choose to count and how we use the information we find…
Give LHO 12 HCP and the most RHO can have is 3. Therefore RHO has at most one K or Q, nothing else. LHO’s red suit lead would imply an honor. LHO cannot be balanced 15.
Can’t know HCP initially. If LHO holds 11 HCP (Discovery) then the remaining 4 HCP are with RHO. Defer s until other suits counted. Take finesse through longer s unless Q gives that hand a biddable count.
If not a , LHO’s opening lead hints at an honor. LHO has 8 ± 3 HCP. & ~ AQ. If only 1 honor then expect 2 honors outsides. RHO has 0/1 . Finesse to RHO after removed (Avoidance/end play).
When RHO shows up with the A, they cannot have any Q. 6 HCP ensures a response to LHO’s opening bid.
RHO’s negative double suggests LHO’s bad Rule of 20 hand (55 in red suits). s should be 2=3=5=3. If LHO holds the A, all Q’s are with RHO. If not then RHO holds A and a Q.
Auction 1 we know the HCPs.
Auction 2 we discover shape and HCP through play. If they don’t open, then don’t have 12.
Auction 3 we know s and need to avoid losing tricks to LHO.
Auction 4 says RHO is limited to 4 HCP. When the A shows, nothing else fits in their hand. Play accordingly.
Auction 5 says too much bidding for the points missing – expect distribution (55 qualifies). Sometimes you can find more than 1 possibility and have to determine which is true from the play (discovery).
When partner leads a suit, the first signal is usually attitude. Positive attitude means holding A, K, or Q (J if obvious). Negative attitude denies one of these honors (and no HCPs to count). Remember opponents do not have to tell the truth to themselves or declarer. However if opponents are known to be strong and weak (bidding) then the weak hand will often tell the truth so the strong hand knows what to do.
Discovery is the purposeful play of a suit to determine what cards the opponents hold (HCP or length). This is a very important counting tool that can be used by declarer and by defenders (infrequently). Because count facts are confirmed through the play, we have to continually refine our estimates as we play each of the 13 tricks. This is why counting is dynamic. Concentration and decision-making pays great rewards. That’s why we develop our counting skills.
If declarer avoids playing a long suit in NT but works to develop side suit tricks, you can be sure declarer holds the missing honors from that suit in the closed hand. If declarer discards a small card from a long suit missing the K or Q, you can be sure partner holds that card. Declarer will look to develop length tricks where there is a 75% chance double finesse (e.g. AJ10xx opposite xxx) or a 50% chance missing 1 top honor. You know that the 1st suit you try to develop is the 1 that keeps all your chances alive – when you defend, keep in mind declarer is doing just that too!
1) Counting is a full time job that starts with the bidding, continues with the opening lead and opponent’s signals, and yields to discovery plays. Counting is important even when holding uninteresting 0 HCP hands.
2) What you count depends on what you need to know. HCP, shape or tricks. Counting losers is a special case that’s helps when you have a trump fit and want to decide contract level.
3) Counting requires a sound understanding of the possible dialects used by opponents. This is their bidding system, how they rebid, how they lead, and how they signal. Know the common bridge understandings that transcend bidding systems.
4) Bridge judgment uses opponent’s action or inaction to define their likely strength. We know the least when opponent’s are silent. Some passes are very revealing and limit responder’s or advancer’s hand.
5) Negative inferences are important. If an opponent holds a 6 card major and fails to open a weak 2, they are too weak or they have a side void or 4-card major. If they’re too strong they will open or overcall. Likewise if opponents open a 1 suit bid and we reach game with a combined 25 HCP, the opening bidder will never hold all 15 HCP in a balanced hand – they would open 1NT.
6) Counting is dynamic. Refine your estimate every time you confirm new information. New information comes from each round of bidding, the opening lead, declarer’s attack, partner’s signals, and the fall of the cards.
7) Why guess when you can count.