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Gambling at Bridge
(Page of 4)

West
xx
AQxxx
Kxx
xxx
North
KQx
xx
A10xx
J10xx
East
xxxx
Kxx
xxx
Qxx
South
AJxx
Jxx
QJx
AKx
W
N
E
S
1NT
P
?
D

Your partner opens 1NT (15-17) and as North you must judge whether to bid game. You can count to ten, and since the book says bid game with 10 HCP,you raiseto 3NT. LHO leads a low heart. Before your partner can get started, the opponents have 5 tricks lined upin their direction and large smiles on their faces. "Sorry", you murmur. Ugh.3NT had no play, but 4 on the 4-3 fit would have made. Since partner's 1NT was a book bid, clearly you must have donesomething wrong.

Nothing could be further from the truth! Most bridge decisions are made under conditions of uncertainty. When you raised to 3NT, you could not know which cards your partner would hold, and those cards determined whether 3NT would or would not make. Any time your score depends on an unknown, like which specific cards your partner holds, judgment decisions become a form of gambling. So let's talk about that for a moment.

Suppose I offered you a bet at even money for $100 which you will win 99% of the time. How do you feel right now? Pretty good I expect. We roll our fair 100-sided die and, when the die settles, the number 1 appears, the only number that allows me to win the bet! Now how do you feel? Annoyed, I'd wager.How will you feel if I offer you the same bet tomorrow? Still happy? Regardless of how you feel, you should accept that second bet before I think to withdraw it. If you can adopt this attitude towards losses, you are well on the way to putting me in the poor house.

Returning to our decision to bid 3NT, when you raised 1NT to 3NT, you did not know which specific cards your partner held, and hence you were uncertain of the outcome. You were, in effect, placing a bet that your partner would take 9 or more tricks. As any gambler can tell you, bets sometimes lose. But losing does not necessarily meanyou made a bad bet.A bet is only bad if it will not win often enough to justify the risk it involves.

If you wonder whether your 3NT bet was justified, instead of looking at the result, ask how often did that 3NT bet rate to succeed? Suppose you were dealt the same balanced 10HCPhand 1000 times, and each time your partner was dealt a different 15-17 point balanced hand. How often do you think the 3NT contract will succeed? My guess is 60% of the time or more. This more than justifies your 3NT call,even though sometimes, the contract has no play at all. Your decision to bid 3NT was a good bet that happened to lose today.

People too often evaluate decisions based on the result, rather than by asking whether they made a good bet. It is natural to feel gun-shy after your game bid gets a bad result, but if you allow that shyness to make you invite the next time you hold 10 HCP, you just made a far worse bet. By inviting with 10, you will too frequently miss successful games that a bold 3NT call will find.

Good bidding means making good bets. Good bidding also means accepting with equanimity that good bets can fail, and failed bets don't necessarily indicate bad bets.

How can I tell when a particular bet is or is not a good one?

If your bet wins often enough that you show a profit by making the bet, it is a good bet. It doesn't have to win every time, just often enough. How often is that? If you know the amounts wagered, you can easily calculate the percentage chance of success needed to break even on a bet.

Your wager / (Your wager + opponent's wager) x 100% =break-evenpercentage

For example, suppose you are offered a bet where you will wager $12 and your opponent $3. What is thebreak-evenpoint?

12/(12 + 3) x 100% = 80%

Your bet must win 80% of the time before you will break even. Or put another way, the bet must win 4 times as often as it loses just to break even. Gamblers call that 4-to-1 odds, and many gamblers find it easier to think in terms of odds than percentages. If the4-to-1 odds against you sounds like this bet will be a waste of your money,you are probably right. Fewreal bets win four times as often as they lose.Is there a bridge equivalent?

South
x
AJ109xxx
xxx
xx
W
N
E
S
1
3
3
4
4
?

Playing IMPs at favorable vulnerability,your opponents have just bid a vulnerable 4 game. For the sake of argument, assume you and your partner have an agreement that his raise promises exactly 2 offensive tricks, so you feel certain a 5-X contract will be down 3, which would be less than-620 on defense if their game makes. On the other hand, everyone hates a phantom sacrifice -- maybe their game won't make. Tick-tock,tick-tock... your opponents are staring at you now as you struggle to make your choice.

How should we make this decision? Perhaps if we knew thebreak-evenpercentage, that would provide some guidance.In bridge, we don't bet dollars, we bet IMPs (ormatchpoints). How many IMPs are wagered in this bet?

By sacrificing in 5 we would wager:

11 IMPs (the IMPs we will lose when the -500 sacrifice is phantom)

against 3 IMPs (the IMPs we win when the 4 game makes)

Thebreak-evenpoint is 11/(11 + 3) x 100% = 78.5%.

If we are going down 3, our sacrifice must succeed almost 80% of the timejust to break even.In practice, before placing that bet, you better think the opponents are certain to make their contract. On the actual hand, if partner's two tricks were the AK,we could beat them with a ruff. If you miss a good sacrifice, the price is very cheap. If you take a phantom, the price is very high.

Calculating the odds offered by a betis usually more difficult than my simple example. For example, what if you believe your sacrifice could be -2, -3 or -4 depending what partner holds? It would be a lot of math to do in your head before every bid. Fortunately, it is largely unnecessary. If you have studied the odds on common bets, you can devise bidding guidelines that steer you right most of the time.

Let's do that now, for twocommon constructive bidding scenarios:

  • Game versus partscore
  • Choice of games


Game Versus Partscore

Vulnerable at IMPs, you open 1. Your partner raises to 2. You have the option to bid 4, or stop in a spadepartscore. How often must a 4 game make for your bet to break even?

The IMP odds for a vulnerable game are approximately 10-to-6 in favor of bidding game (because you win 10 IMPs when your game succeeds but lose only 6 IMPs when it fails by one trick). That gives abreak-evenpercentage of only 36%. In other words, you should be bidding more games than you make!

If you make 50% of your vulnerable games, you are doing well on your game bids, but you are still playing too many part-scores! Some of those part-scores should have been bid to game. Let me put this another way, if you make most of the games you bid, you are not bidding enough games.

This is one of the biggest differences between expert and near-expert players. Ironically, top expert players go down in game frequently while near experts go down a lot less often. Yet the top expert players are still winning more IMPs than their more conservative near-expert peers. That happens because they pick up plenty of 10-IMP swings when they make the games they bid so often.

How can you adapt your bidding tactics to exploit the favorable bidding odds offered by game contracts? One way is to invite less often.

Just overbidto game on all, or almost all hands, holding invitational values. This tactic puts your partnership into more frequent marginal games, exactly the ones where you stand to gain 10 IMPs if the contract makes! Defenders do make mistakes. If they guess the wrong lead, you'd much rather that it cost them 10 IMPs against your game, than 1 IMP against yourpartscore.

OK, I hear you say, but what if they KNOW I bid like a loony. Won't they learn to double every game I bid? When you overbid in a constructive auction holding invitational values,opponents have a tough time doubling. Think about these two auctions:

1 -- 2 -- 4

1NT -- 3NT

How is the enemy supposed to know that the game bidder has stretched? Game might be cold for an overtrick. They can't safely double unless they are certain of defeating the contract.

"Wow," some of you are thinking. "This sounds GREAT, I can go nuts bidding games. Whoopee!" Forthe red-blooded males among you, this observation does not give you carte blanche to overbid in all game auctions. In competitive auctions, the risk of a penalty double is often much morereal. When one opponent has shown values, his partner can and will double an overbid frequently. But when both opponents are passing and neither knows whether his partner holds cards, it usually takes an unlucky layout (such as a 5-0 trump break) before an opponent realizes he should double.

IMP odds on game = 10 to 6 when vulnerable; 6 to 5 when non-vulnerable

Preferred bidding tactic = Jump directly to game holding invitational values

Choice of Game

Occasionally, you may be called on to choose between playing 4M or 3NT, or between 3NT or 5m. For example, consider this hand:

North
QJx
K10x
xxx
KQ10x
W
N
E
S
1
P
1NT
P
2
P
?

3 is the normal call to show a 3-card limit raise. However, given your soft cards and plentiful losers, if partner has a little help in hearts, 3NT might be a better game contract.

If both 4 and 3NT make or fail, your decision is irrelevant, but if one goes down, the winning decision is extremely important. If, at the other table, your opponents play the wrong game, the decision is worth+10 or +12 IMPs.If your opponents stop in a partial, the right decision is even more important.You will gain either +11 or +16 IMPssince you will be winning a game swing instead of losing -5 or -6 IMPs to the makingpartscore.

Choice-of-game decisions are among the most important in bridge. In fact, they are far more important than invitational auctions. If you go wrong in an invitational sequence, it normally means you miss a marginally good game or you bid to a marginally bad one. In the long run, those decisions cost little. If you go wrong in a choice-of-game sequence, those decisions cost many more IMPs.

So what conclusion should we draw? When different games are realistically possible, bid scientifically. We cannot afford to bash to game if by doing so we risk bidding the wrong game. In our example above, I like a 2NT rebid. 2NT shows responder's values and leaves room for opener to continue describing his hand. If opener rebids 3, my next call will be 4. Having only one heart stopper, opposite a singleton heart, 4 looks like the safer game. If partner rebids 3, or raises to 3NT, I will play in 3NT. With soft cards, we may well have only 9 tricks in either NT or spades.

Here is another auction where we should pay attention to choice-of-game considerations.

1 -- 2

3 -- ?

4 could be the best game if responder holds 4+ hearts and only 3 spades. Regardless of what other game tries you use, 3 should be a natural game try, and responder's 4 call should be a natural raise, not acue-bidon the way to 4.

IMP odds = 1 to 1 when enemy bids game, 2.5 to 1 when they stop in a partscore

Preferred tactic = Bid as scientifically as possible to the best game

Conclusion

Players often call a speculative bid such as an aggressive jump to game a "gamble." They forget that virtually all bids at bridge are gambles. A pass of partner's game try is just as much of a gamble as a pushy bid of game. The question is not whether your bid is a gamble, but whether you have made a good gamble that succeeds enough to make a profit. Sometimes that conservative pass is a worse gamble than a wild jump to game.

In this article, we saw how IMP odds provide us with a tool for evaluating gambles (both wild and dull ones). We also used the IMPoddsto identify two guidelines to direct our constructive auctions:

1. Game versuspartscore:If you are certain of the right strain, bash to game often, holding invitational values, especially when vulnerable.

2. Game versus game:If multiple strains are still possible, bid scientifically to game to find the best strain.

Next week we will examine how IMP odds change in slam auctions, and we also look at the psychology of gambling.

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