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Gambling at Bridge Part 2
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My last article introduced a way to think about your bridge bids, particularly those that place the final contract. You can think of a bid as a bet on the final outcome. If the outcome is favorable, you will win some IMPs. If the outcome is unfavorable, you will lose some IMPs.

Frequently, the number of IMPs that you might win or lose by making a given bidcan be easily calculated. IMP odds is defined as the ratio of:

<IMPs you could win>

--------------------------

<IMPs you could lose>

Let's look at some examples to illustrate. Vulnerable at IMPs, suppose the auction has begun:

W
N
E
S
1
P
2
P
3
P
4
P
P
P

You bid 4 in preference to playing 3. What are the odds on your 4 bid?

Tricks Your Score Alternative score Net Score Your IMPs

10 +620 +170 +450 +10

9 -100 +140 -240 -6

If we ignore less-likely outcomes for the moment (like making only 8 tricks), the IMP odds on your vulnerable4 bet are 10-to-6. The 10 IMPS you win when game makes to the 6 IMPs lost when game fails one trick. Those odds are quite favorable, and consequently you will make this bet as often as your hand makes it vaguely reasonable, even though adopting this strategy means game will sometimes fail.

Imagine you could make this bet 100 times. Let's suppose that to make the game contract you would need:

  • a finesse onside
  • a 4-1 or better trump break
  • No unlucky ruff

Given these conditions, you estimate your chance of winning this bet as 45%. If events follow to form, you will lose 55 of your 100 bets. However, despite losing many bets, you would still show a profit at the end:

55 hands x -6 = -330 IMPs

45 hands x +10 = +450 IMPs

100 hands +120 IMPs

A wise gambler takes this bet, knowing it will often lose. Good IMP strategists do exactly the same thing. When a bid offers good odds, experts don't mind making the bid, even if it loses reasonably often. This is why you will never see Bob Hamman or Eric Rodwell berating his partner after he raises 1NT to 3NT, and the contract happens to fail. They understand that partner's aggressive call was a bet, and unless he feels it was a bad bet, he is happy that the bet was made, even though it lost today. They have given up the attitude of hoping that every bet they make will win. They simply try to make good bets, and hope that, over time, the bets return a net positive.

If we give up the model that all our bets should win, what do we replace it with? Instead of hoping to win all our bets, we have a more limited goal:

  • Make good bets
  • Avoid bad bets

Easy to understand, but harder to master in practice. It helps if we learn to recognize common good and bad bets.

IMP odds are a tool for evaluating our bets. We have already seen that IMP odds on a vulnerable game are 10-6, but is that completely accurate? No it isn't. Before we go further, we need to look more deeply at what IMP odds really mean.

More about IMP odds

When you calculate IMP odds, you must consider the score in both your own contract and at least one alternative contract. This notion is often foreign to newer players. To the newer player, the 4 bid is "good" if it makes and "bad" if it didn't. And if the 4 contracts happens to go down 2 instead of 1, that is clearly even worse, right? Not always. When you learn to analyze alternatives, you occasionally find score anomalies like this one.

W
N
E
S
1
P
2
P
3
P
4
P
P
P

Once again, your contract is 4, and your option was to pass in 3 and collect that score.

Tricks Your Score Alternative score Net Score Your IMPs

10 +620 +170 +450 +10

9 -100 +140 -240 -6

8 -200 -100 -100 -3!
The table says that when we make 10 tricks in 4 we do very well. If we make only 9 tricks, we score worse. With 8 tricks we will score even wor... wait a minute. What is that? Taking 8 tricks loses only 3 IMPs, not 6 or more IMPs??? What in the world?
Assumethenervous nelliesat the other table who held your cards stopped in 3. They may be nervous, but they play well, so they made the same 8 tricks you did. How will the scores compare?Your teammates will defeat them one trick and bring back +100. When compared to your -200, you lose only 100 points, or 3 IMPs. So ironically, even though you take a trick less in 4, your net score improves when compared to the 9-trick result. If I told you that your spade contract would take either 8 or 10 tricks and that your opponents would never double 4, the odds on your 4 contract would become 10-3 in favor of bidding 4, rather than 10-6! Let's contrast this scenario with a slightly different auction.

W
N
E
S
1
P
2
P
4
P
P
P

Your contract is 4, your alternative was 2.

Tricks Your Score Alternative score Net Score Your IMPs

10 +620 +170 +450 +10

9 -100 +140 -240 -6

8 -200 +110 -310 -7

When the alternative is a 2 partial, down 2 in 4 costs 7 IMPs. Why the difference? In scenario 1, taking only 8 tricks greatly affected the score in the alternative contract (3), reducing its score by 240 points (from +140 to -100). In this scenario, taking only 8 tricks didn't impact the score in the alternative contract much (it went from +140 to +110) and that is why the IMP scores for the two scenarios differ so much.
What can we learn? When calculating odds think carefully about scores in alternative contracts! More importantly, we must remember that IMP odds are the odds on a decision (the choice between two contracts), and not on one contract. Change the choice and the odds will change.
"OK," I hear you say, "that is interesting academically, but really the difference is so small I don't care. I can ignore the different decisions and just treat all vulnerable game bids as offering me 10-6 odds can't I?" No, you most certainly cannot. Consider this auction:
W
N
E
S
1
P
2
3
X
4
?
After partner's maximal overcall double showing a game invite, let's assume that you knew4 would fail 2 tricks. Your alternatives are to play 4-Xor4. What are the IMP odds given these alternatives?

Tricks Your Score Alternative Score Net Score Your IMPs

10 +620 +500 +120 +3

9 -100 +500 -600 -12

The IMP odds on your game bid have declined enormously! In this hypothetical situation, the odds on your vulnerablegame are 4-to-1against you, so you'd have to be utterly confident that 4 is making before bidding on. At the table, you rarely know you are guaranteed +500 on defense but this shows the importance of "taking the money" at IMPs. If you know you're likely getting a big plus on defense, it is rarely worth chasing a largerplus in an uncertain game.

Poor odds
W
N
E
S
1
P
3
P
5
P
P
P
Which bidding decisions offer us the worst odds at IMPs and why? Suppose your alternatives are to play 4 or 5, and you bid 5 as in the above auction. Partner then rejects.

Tricks Your Score Alternative Score Net Score Your IMPs

11 +650 +650 +0 +0

10 -100 +620 -720 -12

IMP odds = 0 / 12

Wow. Those are some ugly odds! Whenever you raise the level without achieving a higher bonus, you increase your risk of going down without reward.

In practice you would only bid 5 to invite a slam or because you were pushed. When you are pushed into 5, the IMP odds on the call will look very different, since your alternative was to defend an enemy contract, not to play in 4. We will look at that complicated question another day. For today, let's focus on the simpler issue: how should these awful IMP odds impact our slam bidding approach?

We can afford aggressive slam tries below the 4 level, since if the slam search stalls we have not raised the level of the final contract. However, we surely must minimize occurrences of taking the terrible odds we receive when a slam search stalls at the 5-level. If we make slam invitations above the game level conservative, three results emerge:

1. We put ourselves in position to accept these bad odds less often

2. When partner refuses our invite, we have protection against losing a bet and paying off at those terrible odds

3. Most importantly, since our invite has full values, partner can accept most 5-level invitations, therebytrading a 0-to-12 bet in 5M for 1-to-1 bet in 6M.

Slam tries at the 5-level generally ask a specific question suchas:

  • "How many key cards do you have?"
  • "Do you have control of some specific suit?"

My general rule is this: I only make a try at the 5-level if I feel comfortable in slam any time partner answers YES to the specific question I ask. If I need him to hold a club control AND a good hand for his previous auction, then I sign off in game.


More Poor Odds

Similar terrible odds apply in invitationalpart-score auctions. When your possible contracts are 2 or 3, and partner rejects your invite, bidding 3 will earn 0 IMPs when it makes, and lose 4 or 5 IMPs when 3 goes down 1. The IMP odds are 0-to-4 or 0-to-5 and those odds aren'tgood.
Once again, since 3 is an undesirable contract, we do not want to play there if we can avoid it. One way to avoid playing 3 is to invite conservatively.
  • It reduces the number of times you are in position to face bad odds (as compared to aggressive invites)
  • When you do invite, partner can accept most of the time
I call this tactic ICAAfor invite cautiously, accept aggressively.I recommend it as your baseline for invitations to game or slam that endanger your game or part-score bonus. The ICAA notion is useful for addressing a common question, when we are vulnerable, and we want to get to more games, who should bid more aggressively, the inviter, the accepter or both? ICAA suggests increased aggression should be in the hands of the accepter. If inviter invites more often, we get to more games but we also get to more unnecessarily high partscores. If accepter takes on that role, we still get to more games, but we play fewer high partials.
Conclusion

Winning at IMPs is a matter of placing favorable bets and avoiding unfavorable ones. A vulnerable game is often, but not always, a favorable bet. Whether the bet is favorable will depend on the alternative scores available in other contracts. When youralternative is +500, a vulnerablegame is not a good bet. When your alternative is only +140, bid!
The worst odds in bridge occur when a contract offers no reward for success. Two common examples are speculative slam searches that stall in 5 of a major, and game-try auctions that stall in 3 of a major. When opponents are not there to push us around, we try to avoid these contracts. We can often apply the ICAA philosophy: Invite cautiously, and accept aggressively, to keep the frequency of these bad contracts low.
Next week we'll look at odds on small- and grand-slam auctions.
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