When to Invite Game after Partner's Limit Bid

Introduction

This article deals with the situation where your partner has made a limit bid that is two levels below a game contract and you need to decide whether (a) to bid game; (b) to invite game, (c) to settle for a part-score. The most common relevant situation is where your partner has bid 1NT and you need to decide whether to bid 3NT, invite game with 2NT (or whatever invitational method you use), or pass.

We will assume that your and your partner's hands are relatively balanced, so that the Milton Work high card point count will be an appropriate tool for valuing your hand.

Don't forget to adjust the basic point count according to the features you have. If you have a good 5-card suit (that you expect can be established without too much difficulty) then you should add one point. If you have a good 6-card suit (sometimes it is necessary, or tactically sound, to make a balanced hand bid with a semi-balanced hand) then you should add two points. If you have the dreaded 4-3-3-3 shape then subtract a point. Aces, and useful spot cards, are positive feature, while isolated queens and jacks are negative features. With a preponderance of positive features, then add a point, but if it all looks negative then subtract a point.

When Should We Bid Game?

It is well-known that you should bid game (in no trump or a major suit) when you know that your partnership has at least 25 hcp. Having 25 hcp does not guarantee that a game contract can be made, of course. All it means is that, with 25 hcp, you expect to make game about 50% of the time.

If we have 25 hcp and we bid a game contract then there is a 50% chance that we will make our contract and beat any pairs who stopped in a part score. On the other 50% of occasions, though, our game contract will fail and we will lose to any pairs who stopped in a part score.

If we have 25 hcp and stop in a part score then there is a 50% chance that we will beat any pairs who bid a non-making game, and a 50% chance that we will lose to any pairs who bid the game when it makes.

From this we can deduce an important fact, one that is not properly appreciated by the average bridge player: When our partnership has exactly 25 hcp we do not care very much whether we are in a game or a part-score contract.

When our partnership has 24 hcp or less then game is odds against, so we will settle for a part score. When our partnership has 26 hcp or more then game is odds on, so we will bid to game.

Deciding whether to Bid Game or Invite Game

There is a very simple rule that you can use to calculate whether you should bid game, invite game, or settle for a part score:

Note: Contrary to popular opinion, and widespread practice amongst club players, it is not correct to invite game if the maximum that your partnership may have is 25 hcp. Why is this? Because at best your partnership has 25 hcp, when game will be a 50% chance. While if your partnership has less than 25 hcp game will be odds against. It therefore pays you, with a maximum of 25 hcp, to settle for the safe part score.

In case you wish to quibble with this, let me re-emphasise that you must adjust the basic point count according to the features you have. If you and your partner would look at S 6 3, H Q 10 5, D A Q J 7 2, C Q 9 8 and call it 11 hcp then you will expect to make most of your 25 hcp games and a lot of your 24 hcp games. But this is because you are not properly valuing your hand. For me that hand has 12 hcp. Contrast that with a hand having negative features, such as S Q 6 3, H Q 5 4, D A J 7 2, C Q 6 4 If you can see 11 hcp here then ask yourself whether this hand is the equal to the previous hand. For me this hand has 10 hcp. Any valuation system that assigns the same value to both of these hands is clearly faulty. You and your partner should get into the habit of adjusting your high card point totals. Then you will find that the "at least 25 hcp for game" rule will work for you.

When Should an Invitation be Accepted?

This rule is even simpler. Accept a game invitation when your point count is in the top two points of the range you have shown.

For example, if your previous bid of 1NT showed 12-14 hcp and your partner invites you to bid game, accept the invitation if you have 13 or 14 hcp but reject the invitation with only 12 hcp.

Why is this method right?

Let us look at an example. Your partner opens the bidding with 1NT, which in your system shows 12-14 hcp. You have a balanced 11 hcp (after making any adjustments). Should you bid game, invite game, or settle for a part score?

You may have a total of 25 hcp, if partner has the maximum of 14 hcp, but our rule tells us that we shouldn't invite game, i.e. that we should pass 1NT. We should only invite game if we may have 26 hcp and we know that we cannot have that many points.

Failing to follow the rule

If this seems counter-intuitive, let's take a closer look at what would happen if you were to invite game with 11 hcp:

  1. If opener has 12 hcp he will refuse the invitation. You will play in 2NT when you could have been in 1NT.
  2. If opener has 13 hcp he will accept the invitation. You will play in 3NT with only 24 hcp, a poor bet.
  3. If opener has 14 hcp he will accept the invitation. You will play in happily 3NT, getting a good score half the time and a poor score half the time.

In cases A and B you will be worse off for having invited game. Only in case C does your invitation lead to a desirable outcome.

Following the rule

Our rule tells us that we should invite game only when we have exactly 12 hcp. Why does this work? Let's take a look:

  1. If opener has 12 hcp he will refuse the invitation. You will play in 2NT with 24 hcp, a sensible contract.
  2. If opener has 13 hcp he will accept the invitation. You will play in happily 3NT, getting a good score half the time and a poor score half the time.
  3. If opener has 14 hcp he will accept the invitation. You will play in 3NT with 26 hcp, a very good bet.

In case A you will be in the best possible contract, odds-on to make. In case B you are in a 25 hcp game, which is a 50% contract that you are happy to be in. In case C you are in a game contract that is odds-on to make. All three cases lead to a desirable outcome.

You will put yourself in more makeable contracts using this rule. Opposite a 12-14 hcp 1NT, you should only invite game with exactly 12 hcp. Opposite a 15-17 hcp 1NT, you should only invite game with exactly 9 hcp.

This "Invitation Rule" Allows 4 hcp Limit Ranges

It has long been a tradition that the range of a 1NT opening bid should be 3 hcp. For example, 15-17 hcp, 12-14 hcp, or even 10-12 hcp.

But our "Invitation Rule" works just as well with 4 hcp ranges.

As an example, let's say that your partnership's 1NT opening bid is now 12-15 hcp. Your partner has opened 1NT and you have a balanced hand. If you have 10 hcp or less your side cannot have as many as 26 hcp and so you should not invite game. If you have 13 hcp or more your side must have at least 25 hcp and so you should bid game. If you have 11 or 12 hcp your side may have as many as 26 hcp and so you should invite game. Your invitation will be accepted when opener has 14 or 15 hcp, so that your side's total will be 25, 26 or 27 hcp, all cases where you would want to be in 3NT. Your invitation will be rejected when opener has 12 or 13 hcp, so that your side's total will be 23, 24 or 25 hcp, all cases where you would either prefer to be in a part score or where 3NT is only a 50% bet, so you don't mind not being in game.

Having a wider 4 hcp range for your 1NT limit bids does have the drawback that more game invitations will be made, and more of the invitations that are made will be refused, so you will end up playing in 2NT more often than when you are using a standard 3 hcp range. Nevertheless, if a wider 4 hcp range for your 1NT bids helps the structure of your bidding system there is good reason for you to choose to use this wider range of limit bid.

Author: Chris Burton
Gravesend Bridge Club