Stratégia v impovom hodnotení

Na potulkách internetom, som našiel čosi o stratégii v impovom hodnotení. Text je v angličtine.

MP strategy is based on risk versus reward with risks and rewards measured in IMPs. Every contract can be viewed as a risk of X IMPs to earn a reward of Y IMPs should you succeed. Often times, you must compare two or more bets. For example, the decision to accept an invitation compares the odds on a partial to the odds on a game. The decision to defend 4S or bid 5H requires you to consider:
--the possible +/- score on defense
--the possible +/- on offense

Some principles:

1. Make bets that earn more IMPs when right than they lose when wrong.
*  Bid vulnerable games (which offer favorable odds) aggressively.
*  In a double game swing situation, bid one more.

2. Avoid bets that offer unfavorable IMP payoffs.
*  Take few sacrifices. 
*  Don't enter a competitive auction when your hand offers no chance for game and a lively chance of going for a number. 
*  Bid grand slams only when the contract rates to make 75% of the time or more.

3. When reward is (near) constant, minimize risk. 
*  Don't get to 5M if you can play in 4M which offers the same reward. 
*  Play the safest game with a choice of games
*  Play the safer slam with a choice of slams
*  Take a sure number rather than bidding a questionable game

4. When risk is (near) constant, maximize reward.
*  With fits in both diamonds and hearts, play 4H, not 4D
*  When there is little chance of an opposing double, prefer 3NT to 2NT (since risk is similar but reward is much larger for 3NT).

5. When passivity rates to surrender a large reward to the opponents, accept big risks for even a small chance of a plus score
*  If the opponents are likely to have a game or slam, intervene aggressively. There is little difference between -500 and -420. But if bidding gives you a smallish chance for +50 instead, then the risk is worthwhile.

6. Look for situations where you can trade unfavorable for favorable payoff.
*  If you have a choice of showing a major or a minor suit and you can only show one feature, bid the major. The bid will win when you catch a fit. If you catch a major suit fit, your chances for game and hence a reward are fairly high. When you catch a minor fit, your limit is usually a partscore. Thus bidding the major trades a bet that has low payoff for one that has high payoff.

Favorable Odds
Some contracts have favorable returns for your wager (better than 1-1) others don't. For example, a close vulnerable game will lose -6 IMPS when you go -1 and will win +10 IMPS when you make--almost 2-1 odds. Playing a partscore in that situation offers you only 6-10 odds, so when in doubt bid the game.

Break Even Odds
Some contracts are high risk/reward. For example, a slam contract risks losing a game bonus in exchange for a slam bonus--you will either win or lose 10 + IMPS with this decision. This decision offers about 1-1 odds. Don't risk a game bonus for even odds unless slam will make more than 50% of the time. Similarly, if the opponents have entered the auction and could penalize a 3NT contract if your suits break badly, you will want at least 50% odds to bid a vulnerable 3NT, rather than the usually wing-and-a-prayer. The chance of going -500 and losing 9- to 10- IMPs means you must temper your aggression.

Unfavorable Odds
Some contracts offer unfavorable odds. Your partner has opened 3H. You raised to 4H. The opponents have now bid 4S and you must decide whether to bid on to 5H. You estimate that 5H will be down 3 for -500 against a possible 
-620 if 4S makes. What is the reward to risk ratio? 
*  Your upside occurs when you indeed have a cheap sacrifice: + 4 IMPS 
*  your downside occurs when you can defeat the 4S game: - 11 IMPS

Even if the sacrifice is correct 3 times in 4, sacrificing is still only a break even bet in the long run because the reward is small. In practice, you should feel virtually certain that the opponents will make 4S before you consider a 5H sacrifice, and even then think twice because you may have overestimated your offensive potential.

More risk--no more reward
Some contracts increase risk without increasing reward. For example, a contract of 3 of a major has more risk of failing but no more reward than 2 of a major. Avoid getting to 3M unnecessarily. This is why game tries should be conservative and acceptances aggressive. If your game tries are conservative, then partner can safely accept most of them. This means that when you go beyond 2M, you will usually play 4M which compensates you with an extra reward for your extra risk instead of 3M which does not. For the same reason, slam tries above the game level must be conservative. A cardinal sin is getting to 5M and going down.

IMP principles in Constructive Auctions
Odds in constructive auctions reduce to simple principles:

1  Game try conservatively. Don't increase your risk without a good chance of earning a larger reward,

3  Accept game tries aggressively. Partner's tries should be sound and you might as well play a contract that gives you a reward for your added risk.

Raise directly to game aggressively especially when vulnerable--i.e., many hands that are only worth a game try in theory may be  better bid by just bidding game if the game try would reveal information that helps the defense. 

4  Slam try above the game level conservatively. 5M down one is a cardinal sin. Slam tries below game can be aggressive since they do not increase your risk.

5  Bid grand slams very conservatively. You risk your small slam bonus which is larger than the added bonus for the grand slam. 

IMP Principles in Competitive Auctions
Odds in competitive auctions produce a more complex set of principles.

1  Sacrifice infrequently. Before you intentionally accept a minus score, you should feel that:
--the opponents are certainly making a game or slam contract.
--your sacrifice has good chances to win 8+ IMPs (i.e., down 1 against a NV game or down 2 against a Vul game.)

2  Avoid double game swings. If two high level contracts (yours and theirs) both have some chances to make, play the contract, even if your chances of making are small. For the same reason, avoid double partscore swings.

3  Play for a plus score. When deciding whether to defend or bid one more, if you have a guaranteed minus by declaring, then defend even if you only have a small chance for a plus on defense (see 1. above). If on the other hand, you have a guaranteed large minus by defending, bid on even if you have only a small chance of making something (see 2. above).

4  Raise to a level that will offer the opponents an option that may cost them big. Sometimes this means overbidding to provoke them into bidding into a failing contract. Other times, it may mean underbidding. For example: 
(P)-P-(2D)-X-?. You hold: Axx, Jxx, Axxxx, xx. 
--5D will cost you -300 or -500 so won't win much even when right. 
--4D will drive the opponents into 4M, which you can not beat. 
--3D gives the opponents the chance to stop in 3M when they will make 4M. 
Therefore the underbid of 3D gives you your best chance to pick up a big swing.

5  Take a sure number instead of a questionable game. A sure +300 or better is a better bet than a game contract which will fail half the time.

6  Get the defend/declare decisions right. E.g., when when it is right to declare, it is more important that you declare than play the right strain. And when it is right to defend, it is more important that you defend than defend doubled. 

7   Declare with a high ratio of offense to defense (ODR). Your ratio of offense to defense is high when:
--your side has a big trump fit
--your high cards are in partner's suits
--your offensive tricks will come from ruffs more than from high cards.

You have a low ratio when:
--you have little fit for partner
--you have honors in the opponent's suit.
--your offensive tricks will come from high cards rather than ruffs.

This is the real justification for the law of total tricks. LOTT drives you to bid a lot with high ODR since having a big trump fit is one of the most important components of ODR. 

Defend or bid NT with a high ratio of defense to offense. For example, QJTxx, Kxx, xx, xxx. Auction: 1H-(1S)-? Although you have good 3-card support, this hand is clearly worth much more defending 1S than if declaring in hearts. Do not raise. Similarly, With KQTx, QTx, Qxx, xxx bid 1NT, not 2H. With 5-points wasted in spades, the last thing you want to do is encourage partner to bid game with a stiff spade, which raising will do.

9  Avoid 4m in competition. 4m is tough to make (10 tricks), and can push the opponents into a successful 4M. for 4m to earn a significant reward all the following must be true:
*  4m must make
*  3M must make
*  4M must not make

In all other situations, 4m will at best break even and may lose significantly.



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