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Gambling at Bridge Part 5 -- Grand Slams
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My last article looked at inviting a small slam. I reviewed ideas for slam evaluation and examined how often to risk the 5-level in search of the elusive slam bonus. If slam bidding was like hunting, I would say bidding a small slam is like hunting for deer: exciting but commonplace. Grand slam bidding is like hunting bear: unusual and dangerous. Some days you eat the bear; other days, the bear eats you.

What are the odds on bidding a grand slam? How often should we bid one? What chances of success in the grand do we need to show a profit?

Grand Slam vs Small Slam

Assuming that the other table will reach a small slam, what are the IMP odds and break-even percentages for bidding a grand in a major?


Grand vs small slam (NV)

Tricks     Score     Alt Score     Net Score     IMPs

13          1510        1010            500              +11

12          -50          980            -1030             -14

IMP odds 14-to-11 against bidding a grand

Break-even percentage: 56%

 

Grand vs small slam (Vul)

Tricks     Score     Alt Score     Net Score     IMPs

13          2210        1460            750              +13

12          -100          1430          -1530            -17

IMP odds 17-to-13 against bidding a grand

Break-even percetnage: 57%

A grand slam produces an attractive slam bonus when it makes: depending on vulnerability, 500 points (11 IMPs) or 750 points (13 IMPs). But notice how many IMPs a grand slam loses when it fails.  Again, depending on vulnerability, a grand slam loses 1000 points (14 IMPs) or 1500 points (17 IMPS) when it fails. Since the losses are bigger than the gains, the break-even percentage is greater than 50%: 56 or 57%.

If we compare the IMP odds on grand-slam bidding to those in game-invitational auctions, we see IMP odds similar to those offered by stopping in a part-score after partner invites a game. 

Part score odds                          Grand slam odds

Vul part score                             Vul grand slam

10-6 against = 20-12 against         17-13 against

A vulnerable grand slam is slightly more favorable than stopping in a vulnerable partial after a game invitation.

NV part score                                NV grand slam

6-5 against = 12-10 against          14-11 against

An NV grand slam is more unfavorable than stopping in an NV partial after a game invitation.

The odds on a grand-slam decision are similar to the odds offered by stopping in a partial after an invite. Of course we would prefer to avoid the lower-odds contract on close decisions. However, there is an important difference between these two auction types: twice as many IMPs ride on your choice to bid a grand as on your choice to stop in part score. That means grand slam decisions are far more important to get right. Game invites are small bets. If you get some wrong, at the end of the day it isn't a big deal. Grand slams are big bets. You really don't want to get any wrong.

From this we derive a useful general principle: Bidding methods must cater to success on big bets even if it costs us a little accuracy on small bets.

Comparing a big bet like a grand slam to a small one like a part score feels a little strange. Maybe we should be contrasting a grand slam to another larger bet, a small-slam decision. The grand slam needs to be a slightly better chance than a small slam 56% percent versus 50%, so perhaps the bidding approach should not be all that different. When bidding a small slam, if you have confidence that slam will be at least 50%, you can bid it. Getting to 55% and 60% slams which fail quite often is a winning proposition, and if you get to an occasional 48% slam along the way, that is no big deal. So perhaps grand slam bidding should be a slightly more conservative version of small slam bidding. That seems like an attractive argument, but it ignores a crucial proviso to the IMP odds on a grand slam. 

If the pair holding your cards at the other table stops in game, IMP odds on a grand slam are terrible.


Grand Slam vs Game

The tables below illustrate the IMPs won and lost by bidding slams when the enemy stops in game. The final column shows how many IMPs are swung by bidding a grand versus stopping in a small slam.

Tricks     Grand       Small       Game          IMPs for slam            IMPs for Grand         Change in IMPs

13           1510          1010         510             +11                           +14                            +3

13           2210          1470        710             +13                           +17                             +4

When the enemy stops in game, bidding a small slam will be a large pickup, either 11 or 13 IMPs. Bidding to a grand slam scores an extra 500 or 750 points, but those extra points convert to only 3-4 additional IMPs so bidding a grand shows only little upside. What happens when a grand goes down?

Tricks     Grand      Small       Game        IMPs for slam          IMPs for Grand         Change in  IMPs

12           -50           980            480             +11                           -11                        -22

12           -100         1430          680             +13                           -13                        -26

YIKES! Trading a making small slam for a failing grand slam costs either 22 or 26 IMPs! How is that possible? Instead of winning a big bonus for making a small slam, you lose one by going down in your grand. Costing your side 26 IMPs on one board is a fine way to lose a match you otherwise had in the bag.

But how often will the enemy play a grand slam in game? Surely if we are considering a grand slam, the opponents will bid 6.  You'd be surprised. Even excellent pairs sometimes miss slams; some are just overly conservative, and others don't have good slam bidding methods. You may be aware the deal will make 6 or 7 because your methods provided information they did not have. Even if their bidding judgment is good, slam chances may not be as clear to them. And if your opponents are ordinary flight A players or below, chances that they play a cold slam in game get much better.

Consequently, whenever you are considering bidding a grand, explicitly consider whether the enemy is likely to stop in game. They won't miss small slam often in quantitative auctions, but if slam depends on finding fits and performing a careful evaluation, the chance is significant. When a game contract at the other table is realistic, you better feel certain there are 13 tricks off the top before you bid the grand, because seven may offer terrible odds.


Conclusion

Grand slams offer poorish IMP odds when the enemy also bids a slam. If you are certain the enemy will be in small slam, then you can bid a grand slam that is approximately 56% or better. However, you better feel truly certain your opponents won't miss slam, because grand slams offer hideous odds when the enemy stops in game. If there is some chance the enemy will stop in game, don't bid any grand unless you can count 13 tricks.

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