Gambling at Bridge Part 3 -- Slam Bidding
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My last articles looked at IMP odds in game auctions. This time we will set our sights higher and focus on slam auctions. We will start with a simple question: What percentage chance of success in slam do we need tojustify bidding it? We will use a hypothetical (but unrealistic) auction to examine this question.

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Small Slam Versus Game

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What are the IMP odds offered by bidding 6 when a handwill make either 11 or 12 tricks?

Nonvulnerable Small Slam

Tricks 6 Score 5 Score IMPs

12 980 480 +10

11 -50 450 -10

IMP odds are 1-to-1

Vulnerable Small Slam

Tricks 6 Score 5 Score IMPs

12 1430 680 +13

11 -100 650 -13

IMP odds are 1-to-1

The odds on both a non-vulnerable and vulnerable small slam are 1-to-1. 1-to-1 odds means that the break-even percentage for a slam is 50%. In the long run, you will earn IMPs if you consistently bid 51% slams, and you will lose IMPs if you consistently bid 49% slams. In practice, we can not make such fine distinctions and there is not much point in trying to calculate whether your slam will be 49.6 or 50.4 percent. A good rule of thumb is to bid a slam that is at worst on a finesseand to avoid a slam that is at best on a finesse.

At worst on a finesse means you can anticipate slam will offer two lines of play that can be combined. For example, if your slam needs either a 3-3 break in a side suit OR a finesse. Even if you don't know the actual chance ofa 3-3 break, you can bid this slam. Whatever that chance is, it will be in addition to the chance of a winning finesse. You can be sure that slam will be good. (In actuality, your slam will be approximately 68%)

At best on a finesse means you can anticipateslam will require a finesse and may need other things to go right as well. For example suppose you know the partnership is missing one ace and the king of trumps. Ifslam is to succeed, it will need the trump finesse for sure. However usually that is not all. If any suit breaks badly, you could suffer an unlucky ruff. Your slam will need a trump finesse AND no ruff. Now this hypothetical ruff is probably unlikely. But whatever the chance is, even if it is 1%, it will drag your slam below 50% and hence make it not worth bidding in the long run.

The important notion to grasp is the correct slam bidding attitude. Games, particularly vulnerable ones, can be bid on a wing and a prayer. Many successful players take a cavalier attitude towards game bidding. They happily bid games which will fail a couple of tricks when they catch a poor dummy and think nothing of it. They intentionally wear rose-colored glasses, hoping to make their bad games on fortunate layouts or bad defense (or both). There are nosuccessful players who are that cavalier about slam bidding. The top experts do sometimes overbid to slam but only when they misjudge the auction. You can rest assured they will be discussing any bad slams they reach after the session.

IMPs is a game of aggressive game bidding and steady slam bidding.

Ten Tricks

What happens to our IMP odds if there is some chance of going down 2 tricks instead of 1 in 6? Presumablywe will need to make slam more often than 50% to compensate for the occasional -2 in a slam which loses extra IMPs right? Believe it or not, the answer is sometimes "no". In fact, if we knew in advance that a contract would frequently make only 10 tricks, we might need to bid lower percentage slams!

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Let's use a hypothetical simulation to see what happens when

• the contract may take 10, 11 or 12 tricks
• partner drives to the 5-level
• the enemy stops in 4

Suppose we face the decision to pass 5 or bid slam 100 times. Now on those 100 hands:

• 12 tricks makes 42 times
• 11 tricks makes 38 times
• 10 tricks makes 20 times
Slam makes on only 42% of hands which is less than the 50% we need to show a profit by bidding slam so bidding slam will lose IMPs overall. But what will happen to 5? On the 20 hands where 10 tricks is the limit, 5 will lose IMPs too.

Tricks 6 Score 5 Score 4 Score

12 980 480 480

11 -50 450 450

10 -100 -50 420

5 to 4
12 42 x +0 IMPs
11 38 x +0 IMPs
10 20 x -10 IMPs
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100 hands: -200 IMPs
When the contract makes either 11 or12 tricks, 5 and 4 score the same so no IMPs change hands. When the contract makes 10 tricks, 4 makes and 5 goes down and hence bidding 5 loses a game swing. If we stopped in 5 on all 100 hands, we would finish with a net loss of 200 IMPs.
6 to 4
12 42 x +10 IMPs = +420 IMPs
11 38 x -10 IMPs = -380 IMPs
10 20 x -11 IMPs = -220 IMPs
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100 hands: -180 IMPs
When the contract makes 12 tricks we win a game swing. When it makes only 10 or 11 tricks we will lose a game swing. Since we won only 42% of hands, unsurprisingly, we lost IMPs by bidding slam. But look at how manyIMPs we lost; we lost fewer IMPs than we would by stopping in 5!
Why did the 6 lose contract less fewer IMPs than 5? When 10 tricks is the limit, partner's decision to bid 5 has already lost us a game swing--regardless of whether we pass 5 or bid on to 6. In effect, we can ignore the 10-trick deals. If we look only at the hands where the contract makes 11 or 12 tricks, we see that:
• 12 tricks made 42 times
• 11 tricks made 38 times
12 tricks made more often than 11 tricks. Consequently, by bidding 6, we won a game swing 4 more times than we lost one. Whenever that happens, bidding slam will be less costly than stopping in 5. If we had made 12 tricks 38 times and 11 tricks 42 times then passing 5 would be the winner.
When all options lose IMPs, we prefer the option that loses the least so in this simulationwe would prefer to bid 6even though the chance of success in slam is only 42%!What can we learn fromthis confusing math? Three lessons:
1. A slam is only an IMP winner when it succeeds 50% of the time or more. Our primary goal is to bid only those slams that make 50% or more.

2. If the contract might take 10, 11 or 12 tricks and slam rates to be less than 50%, it is much better to stop in 4 than to push on to the 5 level where we will have only losing bets.For this reason, wemuchprefer to make our first slam try below game. If a below-game slam try is rejected, we can still play a nicesafe 4 rather than driving to a risky 5.
3. When the contract is already at the 5-level and 10-12 tricks are possible, bidding slam may lose fewer IMPs than stopping in 5 would. This occurs when 12 tricks makes more often than 11 tricks does.
The scenarios where you know in the auction to bid on to a poorishslam (because it loses less than 5)come up infrequently. You would have to strongly suspect that this is a 10-or-12 trick hand. But occasionally in competitive auctions you may wish to employ the strategy of intentionally bidding on to a mediocre slam. For example, if the opponents have bid 5 pushing you into a dubious 5 contract, a poor 6 contract confidently bid may offer surprisingly good odds. Not only might 6 be cheaper than 5, but it may also inspire an opponent to take a bad sacrifice.

Conclusion

The decision to bid a slam in constructive auctions is simple: regardless of vulnerabilitybid slam only when it is a favorite to make. Onesimple guideline to use at the table is theat best, at worst on a finessecriteria.
• Bid slam when slam will beat worston a finesse, i.e., when you will need a finesse OR some other favorable layout to be present.
• Stop below slam when slam will beat beston a finesse, i.e., when you will need a finesse AND some other nice layout to be present.

Finally, when 10 tricks is a possibility it does not pay to look for marginal slams. And on those rare occasions when you can recognize that 10 tricks are likely and the partnership has already gone to the 5-level, you may lose less in the long run by bidding a mediocre slam than by playing 5M.