Gambling at Bridge Part 4 -- Slam Invitations
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My last article examined accepting a small slam invitation. Today we switch to the other side of the table. Can we invite when slam makes 50% of the time, or do we need better chances to justify an invite?

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Assuming that the final contract will make 10, 11, or12 tricks, what chance of success will the slam need tojustify making an invitation in this auction?

Small Slam Invitations

Let's start our investigation by thinking about the inviter's bidding alternatives. He can either

• pass 4
• invite slam, ending in either 5 or 6
What are the possible outcomes of a 5-level invitation? There are four:
• 6 makes, win 11 IMPs
• 5 makes, 0 IMPs
• 6 fails,lose 11 IMPs
• 5 fails, lose 10 IMPs

Notice that a slam try can win IMPs only if the partnership subsequently bids and makes a slam. A slam try can lose IMPs if 6 or 5 fail. Since the amounts won or lost are similar, a slam try needs approximately a 50% chance of success to break even. Therefore, after your slam try,you must make a slam as often as you fail in either 5 or 6. We can rewrite that statement as a formula:

(#handswhere 6 makes) >= (#hands where6 goes down) + (#hands where5 goes down)
This suggests we will need to make more slams than we lose (unless we never fail in 5). In other words, we need better than a 50-50 chance in our resultant slam contracts to justify a slam try. How much better?The answer is not set in stone. It depends on how often a 5 contract will fail and in turn failures in 5 depend largely on how often you play 5. For example, suppose you make 100 slam tries and:
• 80 times you end in 5
• 20 times you end in 6
• 5 makes 60 times
• 5 fails 20 times
What percentage of success will you need in 6, to break even on your slam try? Answer: 100%
• total losses in 5: 20
• victories needed in slamto break even: 20
• total slams bid: 20
• required success percentage in slam = 20/20 = 100%

Put another way, if there is not much chance of bidding on to 6 after a slam try, it probably wasn't worth making the try in the first place.

The Slam Invitation Process
The hand evaluation process for making a slam try usually requires visualization. We make slam tries in two situations:
1. The partnership might have 33+ HCP (i.e., a slam based on power)
2. We can envision hands consistent with partner's bidding that make slam cold (i.e., a slam based on fit)
In case 2 where slam will be based on fit, we try to visualize hands consistent with partner's bidding where slam is cold. If we can find them, and we think partner is quite likely to hold one, we can make a slam try.
The traditional (and excellent) slam evaluation guideline, invite slam if you can imagine a perfect minimum that makes slam cold,implicitly incorporates both questions. If slam could be cold facing a minimum, chances that partner holds the right cards for slam are high. Now let's look at a couple of slam invitation decisions.

Example 1

South
AQJxxx
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KQJxx
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Should South try for slam? North could hold the K and two outside aces, which would make slam excellent. But is that likely? Clearly not. Partner would have to hold the perfectmaximumlimit raise. My personal estimation is that even though slam will be cold if partner holds the right cards, he will only hold them one time in 10 or 20. Further, the 5-level will be in jeopardy. Partner might have zero key cards, or you might surrender a club ruff, causing 5 to go down. UsingRKC under these conditionswould be foolhardy, even thoughslam could be alaydown.

If you aren't ready to give up onslam chances just yet, perhaps you shouldcue-bid4 instead. If partner signs off in 4 you can pass with no risk of missing slam. If partner cooperates instead bycue-bidding4 or 4, he should have 1+ key cards. Perhaps we can bid RKC now?

Even though partner has cooperated, partner isstillunlikely to hold the 3 key cards that slam requires and the 5-level is still dangerous. Opposite 1KC we could be off 3 cashing aces. Perfect maximums are not dealt often enough to take that risk. Well that sucks--we still can't bidRKC!Does that mean we will never get to slam? Before giving up, let's askone more question:If I sign off in 4 over his cue-bid, and partner holds the magic 3 key cards, will he pass 4?

One of the messages of a slam try is,"Partner, slam is possible if you have perfectly working cards."Partner is entitled to drive to slam when he holds perfect cards after a slam invitation.If partner happens to hold two aces and the king of trump, he knows his hand could not be any better. He will certainly cue-bidagain over 4 or may just bid slam himself.

When considering a slam try, use this process:

1. Ask if you can envision hands consistent with partner's bidding thatmakesslam cold. If not, sign off.

2. Ask if, given the auction, partner is likely to hold thehigh cards needed to make slam cold. When he won't hold those cards often, the most you should do is make one below-game slam try.

3. After partner cooperates with your slam try, sign off if slam requires a full working minimum. Take over and drive the auction further only when slam requires significantly less.

Example 2

South
AJxx
Axx
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Axx
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Partner has 18-19HCP,and we have 13HCPplus an 8-card trump fit. However, our shape is poor, and it's difficult to know exactly how likely slam is to make. Though we are clearly in the slam zone, I don't expect slam to be cold. Let's call it a 60% slam for the sake of argument. Should we risk the 5-level in pursuit of this marginally good slam?

Once again this depends on how often we expect to play in 5M. Given that slam rates to be only marginally good, we only want to try for slam at the 5-level if slam will frequently be biddable. Our major problem is the lack of a diamond control. Is partner likely to hold that control?

Given that he showed 18-19HCPand lacksthree aces, the chance that he controls diamonds is very high. I would expect we will get to slam 80 or 90% of the time (assuming wecue-bid5 and drive to slam after his 5 returncue-bid). Given that we do not play 5 often, we can afford to make a slam try, even though we think the slam may be only marginally good.

Experienced players have been drilled never to go down in 5M unnecessarily, and most have taken this lesson deeply to heart. Stopping too low on a hand like this one is a far more common problem among experts than is getting too high on hands like the first example. When slam is under consideration, 5M is generally a high-percentage contract. If, in addition, you will bid slam often after the slam try, then take the plunge. You will be going down in 5 only infrequently so you won't need much more than 50% chances in slam to justify your slam try. If you don't try on hands like this one, you are probably losing more IMPs by stopping too low in 4M than you are by overbidding to 5M and going down.

4-level invitations

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When we invite slam below game, we can afford to invite on hands where slam is not all that likely. Assuming no bidding slip-ups, we can still get out in a cheap game contract, so some bids that cater to catching an excellent, but unlikely, hand from partner can be tolerated. The key phrase is: "assuming no slip-ups." If your slam invite might encourage partner to overbid when he does not hold the specific excellent hand you need, thensign offin game instead of trying to cater to a miracle slam.

Leaps to Slam

What about jumps to slam? How often does a slam have to make to justify bypassing an invite and leaping to slam?

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In theory, leaping offers no upside when compared with inviting. Suppose you have 100 hands where you must decide whether to leap to slam or invite, and further suppose that slam will be good 90 times and bad only 10 times. By inviting, you can bid to the good slams and avoid the bad ones, which will win more IMPs in the long run than jumping to slam would. Furthermore, maybe partner has the miracle hand that makes 7 cold. Leaping to slam generally cuts off further exploration. As a general rule, when you see someone leap to slam it means one of two things:

1. The information communicated by an honest slam-try sequence would help the defense.

A typical example of this is when you hold an undisclosed void. Frequently, an opening lead in that suit will gain the declarer either a trick or the tempo needed to make slam. Leaping to slam and forcing the opponents to guess the right lead could be a winner. Unfortunately, an expert defender probably understands this too. He can often infer the location of your void and find the winning defense.

2. (more often)The leaper doesn't understand his own slam methods well enough to use them.

KitWoolseyholds an extreme opinion on this topic. He believes it isnevercorrect to leap to a slam in a constructive auction. He suggests that if youfeellike leaping to slam, bidRKCinstead, even holding a side void. TheRKCsequence ismore likelyto encourage a lead of the void than a leap to slam, which might warn the enemy to expect an undisclosed void.

Conclusion

Five-level tries generally require simple common sense.Don't make a slam try if the subsequentauction won't finish in slam often. Otherwise, make five-level slam tries whenever slam seems likely to be good anddon'tworry overly about going down in 5M. It can happen, but you are probably losing more IMPs than you win being excessively cautious avoiding 5M.

Leaps to slamshould be rare or non-existent.If you would like to jump to slam, considerbiddingRKCinstead. It may help you find a magic grand slam if partner holds a card you didn't expect, and if it does not, it will conceal your hand type from the defenders better than a jump to slam would.

Consider signing off after partner cues in response to your four-level slam try.Four-level tries imply you are looking for a perfect minimum from partner. If partner holds that perfect minimum, he will bid on over yoursign-off. You don't need to bid on over the game level yourself unless you can make slam opposite less.