text:
Can you suspect false carding from the following situation?
You are playing this hand at 3NT having arrived there after you bid 1NT and North 3NT, East and West having passed throughout. Only you are vulnerable. (The hand is linked for reference; but you'd only actually get to see your hand and dummy as below, plus individual cards as they are played).  Dummy is North, the lead (by West) is the 5 of hearts 6, T, won by J in hand.
AK9
63
AT94
J985

QT8
KJ7
QJ82
AK3

You have two chances for your ninth trick; a diamond finesse is 50-50. You also have an extra chance (8% by my calculation) if East has Qx of clubs, since you can drop the Q, then finesse against Tx remaining in West.
Since clubs is a "key" suit, I begin by inventorying the opponents' combined holding: QT7642. I start by playing the A, and expect the two lowest cards, 4 and 2 to drop (which in fact is the case). Say one opponent drops the 6 instead; I would then expect his partner to have the 4.
I lead the K, and sure enough, East drops the Q. But here's the tricky part; West drops the 7, meaning that the 6 and T are outstanding. Put another way, they can't both be playing their lowest card and at least one of them must be falsecarding!
Should I now suspect "chicanery," and go back to my 50-50 diamond finesse because my a priori 8% chance of a successful drop is now too low? (The actual South player tried a finesse which lost to East's ten.)
But perhaps South could now capitalize on the 3-3 break (36% a priori) by putting up his Jack, since the queen has been sacrificed. I can understand why East falsecarded, but why would West do so? Because if he hadn't I would have taken the club finesse, thinking that West had four cards and the queen was an honest drop from East. But faced with evidence of chicanery, I would suspect that E-W were trying to hide the fact that the diamond finesse would work.

@PieterGeerkens: I changed the first two sentences so that the bidding and vulnerability information  matches the link. Reminder noted.

If the diamond hook loses you'll still make the hand when hearts are 4-4. That makes cashing a second club questionable, since you could be setting up the defenders' fifth winner.

@AdamWildavsky: After trick 1 there is only a 1110 / 2019 = 11/38 chance that Hearts are split 4-4. (ie that both unplaced Hearts are with East, with 9 and 11 cards unknown in West and East respectively.) Combined with the Diamond finesse that gives roughly a 64.5% chance to make the contract. Testing the Club Q first gives a 50% + 1/3 * 48% = 66% chance to make on a straight doubleton Q, plus the additional chance here of an expert defender attempting a subterfuge that fails on an endplay.

Dear Frank has omitted one additional possibility - there is a throw-in working against West when (a) it is actually possible to make the contract and (b) West holds T762 of Clubs. Once the Club Q falls on trick three this play should be visible to Declarer.
Cash three Spade tricks ending in Dummy to leave this for Declarer
S: -
H: 3
D: AT94
C: 5

S: -
H: K7
D: QJ82
C: -

and the possible West holding to be these:
S: -     or  J     or  J    or  J
H: AQ8       AQ8       AQ8      AQ
D: Kx        KX        K        Kx
C: 6         -         6        6

In all cases West has at most three cashing tricks, and no exit - just lead the last Club to West, pitching a diamond from hand, and wait for your last 2 tricks.
Update #2 - Play details:
Spades should be cashed in the order K; then Q; then A to maintain control if Spades break worse then 4-2. Then the Diamond Q should be pitched from hand on the 4th round of Clubs to unblock; there is no need for more than 2 Diamond tricks and we desire to win both in Dummy.
Update #3 - Odds of both lines of play:
After trick 1 there is only a 11*10 / 20*19 = 11/38 chance that Hearts are split 4-4 (ie that both unplaced Hearts are with East, with 9 and 11 cards unknown in West and East respectively). Combined with the Diamond finesse that gives roughly a 64.5% chance to make the contract.
Testing the Club Q first gives a 50% + 1/3 * 48% = 66% chance to make on a straight doubleton Q, plus the additional chance, as here, of an expert defender attempting a subterfuge that fails on an endplay.
Update:
Note that an expert West holding the Diamond K, and thus knowing that his partner has at most three HCP, will almost always false card in Clubs so that (a) a false card by his partner in the suit is believable; and (b) if East cannot false card in Clubs then Declarer won't know whom to believe because the signals are inconsistent. It is a mandatory play at that level, and cannot hurt because his partner (a) already knows what to return if he gets in and (b) has nothing to be fooled about.
The guideline here is that when the defensive values are split decidedly unevenly between the two hands, the weaker hand false cards only out of necessity while the stronger hand will false card frequently. This can sometimes assist Declarer in placing cards, but works to Defenders' advantage more frequently.

Note that after 3 rounds of Spades by Declarer any Spade remaining in West's hand cannot be an entry to East, as it is the 13th card of the suit.

Thanks for your help/guidance in improving my question. I'll grant you that this sequence "works to defenders' advantage more frequently." But the price seems awfully high, because declarer would benefit more from one 36% chance (3-3 split with Jack high because the Queen was dumped) than with four 8% chances (exactly Qx with East). And the first is what was created to produce the illusion of the second. Not to mention the other possibility you brought up.

@TomAu: I cannot follow what you are arguing. This hand has to be IMPS play because in matchpoints you test the diamonds first in order to set up a squeeze or throw-in for extras in Clubs and Hearts.

Coming from me, a question would be IMPS or rubber, because I am not familiar with Matchpoints. It's been 40 years since I've played that version of bridge.

@TomAu: Accurate defense is simply not possible without both communication, based on agreed signalling methods for attitude, count, and suit preference, and faith that partner's signals can be trusted absolutely whenever a decision actually needs to be made on the signal. That latter point is at the core of when and how to false card as a defender: Never lie to a partner who will have to make a decision based on your lie. This has the advantage of simultaneously showing mixed-signals to Declarer at occasional times when he is looking to make a critical decision.

Good defenders do not simply play the lowest card from their hands when following suit; they signal for partner. Intermediate players sometimes signal when they should not. Here, West was presumably signaling count -- initially playing their lowest card (showing that it was played from an odd number), then playing their highest (showing that it was played from an even number). This is consistent with the situation that West started with 762. Count signals are frequently played to declarer's leads.
If E played the Q from QT4, this was a very good play (assuming that they did not hold the DK as well) because it gives declarer a chance to go wrong. If West signaled count faithfully, they would have ruined partner's play. I would cash the CJ and try diamonds if clubs didn't start 3-3, congratulating West for deceptive signaling if they started with T762 and no DK.

Throw in of West is on if West has 4 Clubs - just lead the last Club around to him after cashing three Spades, pitching a diamond from hand.

@PieterGeerkens That's a good point.


text:
Should "100 or 150 honors" allow you to open light?
By "light," mean with something like (s) AKQJx (h)Jxx (d)xxx (c)xx, or (s) KQJTx (h)Jxx (d)Axx (c)xx, or even (s) AKQJT (h)xxx (d)xxx (c)xx?
I can think of two reasons. 1) I was taught that three or four honors in sequence is worth a point or so more than their nominal value, so e.g. AKQJx is worth 11, not 10, and KQJT is worth 7-8. Then AKQJT is worth about 12. If I make these adjustments, I have enough to open. And 2) the honors bonus will defray whatever penalty I incur.
Or am I "stretching" too far to open in most positions and vulnerabilities?

Experts only play Honours scoring in money games; against suckers. "If you don't know who the sucker in the games is; it's probably you." Don't twist your game around trying to adjust for this; collect it when you or partner hold it, concede it when the opponents hold it, and practice improving your defense and card-reading skills instead.

@PieterGeerkens: The point of the question (as revised), is "Do the honors (including 1 T) signal that the holding is stronger than its nominal value? (That is, "10" is really worth 11?)  In your other example, you convinced me that your "11 hcp" holding with tens and nines was actually worth 12.

Asking about Honours is just a red herring that obfuscates the real question on hand evaluation.

As for me, I do not think about hand strength here. There are only 3 reasons to bid, and if you have 2 of them- you can bid:
Constructive - to bid you best contract
Destructive - create a problem for opponents
Defense plan
Here you suggest very different hands. I'll answer about AKQJx -3-3-2, because KQJxx, Axx, Jxx xx is completely ok to open imho.
I don't like to open 1s with AKQJx. For several reasons.
 If you are going to win the bidding - you would probably choose NT or spades. So, if you finish in spades - you are definitely playing from the wrong side. May be it's impossible to reach spades from another, but who knows? If your partner supports spades, your J almost disappears. And you still have 8 losers.
If you find NT- how many HCP you need to win the game? Something like 14-16 , otherwise you will not find 4 tricks, or opps will hit their suit faster.
Of course, much less could be enough, with some lucky leads and distribution. But generally, your partner should hold strong NT.
For destruction I can open 2sp. This does not work very good, because of flat shape, but if I want to make a move...
For lead- you don't need to open. If opps bid 1nt-3nt - double. If they have lots of points- they will walk to 3nt if you pass.

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text:
Does the "Rule of 15" suggest that you should pass with 13 points (and short spades) in fourth seat?
Only you vulnerable, you have a  13- high card point hand like the following: (s)x (h) AJxx (d) KJxx (c) KJxx. (No x is higher than a 7). Three passes have preceded you.
The "Rule of 15" suggests that you open in fourth seat only if the sum of your high card points and spades add up to at least 15. It works most often for 11 point hands with four spades. Here, you have the full opening point count (13), but are weak in spades, the highest ranking suit.
On "average," your partner will have nine, or one third of the remaining 27 points, giving your side about 22 (out of forty). Balanced against this is the near-certainty that the opponents own the spade suit. (Partner would have opened with a "weak two" spades with six, unless they were very weak.)
Does this consideration suggest that you should pass in fourth seat, even though you might have opened, say one diamond, in first, second, or third seat?
Edit: I am now also assuming unfavorable vulnerability, that is "only you vulnerable" (the original version of the question said both vulnerable). Does vulnerability make a difference in this borderline case?

-1: To the question, sorry. Based on the article you linked, your question does not even apply!

Larry Cohen here explicitly provides, as an example of failing the Rule of Fifteen, this eleven point hand:
S: 3
H: K J 5 4
D: K J 8 7
C: K 9 8 7

However, he proposes the CRIFS variant - Cohen's Rule in Fourth Seat - Whenever the Pearson Points count (HCP + # of Spades) is between 14 and 16, instead assess your opponents. If they are amongst the better players of your club pass, and if they are amongst the weaker players of your club bid. To quote Cohen directly:

Who needs to open and have to do battle with an expert pair who will fight hard for the partscore and play or defend well?

Update
In regards *vulnerability, I see that as irrelevant at this decision point. The amount by which one goes plus or minus instead of taking a zero score is of much less significance than assessing the relative likelihood of each.

A very good reason to pass. You don't want to open a basically "borderline" or even hand against your strongest opponents.

@Aryabhata: You're right; not sure just what I was thinking when I wrote this.

Your answer does answer the question asked, IMHO. Granted, it answers a "figurative" as opposed to "literal" interpretation, but I'm all about "figurative," as you seem to know. I also ask about "edge" cases a lot, and this is one example.

@TomAu: No. This is a site for objective Q&A. If someone asks "how do I use a fly swatter to kill a mosquito", you don't respond with "use a cannon" :-) I suggest you re-read the FAQ (if there is any).

Rule of 13 trumps Rule of 15.
If you have 13 points you open.
If you read the first few sentences of the article you linked, it says clearly you only apply that when you have 9-12 points.

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Do most good pre-empters do so within "tight" point ranges?
I'll use "weak two" bids as a frame of reference.
My understanding of a "weak two" bid is that it is usually made with six cards of a suit, and at least five high card points (hcps). If that's all, they will be in the suit, that is KQxxxx or AJxxxx, and this would be done mainly at favorable vulnerability (not vulnerable vs. vulnerable). At equal vulnerability, you need either another honor in-suit (e.g. KQJxxx) or a side suit honor. At unfavorable vulnerability (vulnerable vs. not), you need both, for a maximum of about 10 hcps.
A "strong "pre-empt" at the three level would have the values for a "weak two" bid with a seventh card.  The theory is that the extra "trump" would compensate (on offense) for the higher level, so you would go down as much as for a "weak two" bid.
A weak "pre-empt" would have the seventh card, but be about a queen lighter (and less likely to have the side value) than a weak two bid. It might range in strength from QTxxxxx to AQJxxxx with little or nothing outside. The theory is that the extra suit card compensates for a king "lighter," and your weaker defense (by one trick) means that you can "afford" to go down an additional trick on offense.
Are most expert pre-empters at least consistent within these two philosophies (or any other)? That is, do they pre-empt "narrowly" either with something like 5-10 hcps if using strong pre-empts, or 3-7 if "weak?" Or are there systems or experts that will run the whole gamut of say, 3-11 high card points for pre-empts?

"most" bridge players are weak players, whose style should not be copied. Do you actually mean "Do most pre-empters do so ...?" or do you actually mean "Do most experts pre-empt ...?"

@PieterGeerkens: I amended the question to most "good" pre-empters in the title and "expert" pre=empters in the body. That rules out the weak ones. The last sentence also refers to "systems or experts."

In addition to the excellent answers already, I would note that there is a difference in seat for most expert players, also.

First seat preempts both opponent, so will be a bit wider.  Say 4-10.
Second seat preempts only one opponent (and one partner), so a bit narrower. Say 6-10.
Third seat is more complex as they often can open at the 1 level many 8-10 point hands, so they tend to the weak/narrow side.
Fourth seat is very narrow and higher, often something like 11-14, since you're not preempting any more.

On top of that of course is vulnerability concerns and other issues - this is very general.  Unfavorable, the range will be quite a bit narrower, 6-10 in first seat, say.
Better players also include other information in their decision to preempt.  A "weak" preempt will likely have most of the points in the trump suit, for example.  Open 2H with a T98543 suit and you're headed for heartbreak, so to speak.  They'll also be less likely to preempt with a hand that looks like a good defensive hand particularly in the other major, so something like

S QT9
H KT9875
D 5
C T95

Is perhaps something you don't preempt with, as it has a nice spade suit worth at least a trick most of the time, a stiff diamond to make that even more likely, and the heart K is somewhat likely to be worth a trick as well.  (In favorable vulnerability I probably preempt with that anyway, but in neutral I probably wouldn't, even though my neutral vul preempt range is 5-11.)

Equal vulnerability I probably want the heart suit headed by KJT, unfavourable vulnerability probably KQT, all else equal. Favourable vulnerability I see this as just right for an opening 2H call.

The choice a partnership makes in this regard will influence their relative strength at Matchpoints vs IMPS. Opening wide-range pre-empts facilitate more frequent interference with the opponent's auctions, but make finding game or slam yourself more difficult. This is a clear Matchpoint strategy (as emphasizing the frequency of a winning result on the hand).
However opening narrow-range pre-empts eases the task of finding a good slam or game, but reduces the frequency of being able to interfere with the opponents auctions. This is both more constructive, which eases partnership harmony, and a clear IMP strategy (which emphasizes weighted value of results).
Most published systems tend to emphasize IMP -oriented systems, because this is also appropriate strategy for Rubber Bridge. Consequently, in their published works most authors recommend narrow-range pre-empts.
It is worth noting that Barry Crane, arguably the ultimate Matchpoint player and an avid proponent of early-in, early-out bidding, recommended in 1st and 2nd seat wide-range pre-empts in the majors, but narrow-range in the minors.

"The rule of 1-2-3" means that you should be within one trick
  of making when vulnerable versus nonvulnerable, within two
  tricks at equal vulnerability, and within three tricks at
  favorable vulnerability. ....
Generally, for an opening bid at the three level, you should have a
  seven card suit.  To open 3C or 3D, you must also have the A and two
  of the next three honors in your suit.  This facilitates getting
  to 3NT (and makes an opening bid of 3 in a minor alertable).

The reason given is that this gives opener's partner the most detailed information on how high to raise the pre-empt. It does sacrifice some capability to pre-empt at the three level in the minors, but his is probably the least effective, and most informative for the opponents, pre-empt range. One could do much worse than to follow Crane's guidance.

Wide ranging weak 2s are so common that there is a well-known convention called Ogust for dealing with them.  After a bid of 2N by responder, opener's bids at the 3 level give no information other than whether his or her hand is stronger or weaker (usually 7 vs 8 losers) and whether his or her pre-empting suit is better or worse (usually how many of the top 3 honors).
This convention gives up the ability for opener to show features in particular suits (which can be important for responder to know how well the hands fit together), but partnerships playing wide-ranging weak 2s usually find they need it.  Obviously they think the wide-ranging weak 2 is worth it.
Higher preempts are usually not as wide ranging since you can preempt one level higher on a hand with more offensive power or one level lower (even bidding a weak 2 with a 7 card suit on occasion) on a hand with less offensive power.  (The exception is 3C, and I have heard of pairs adopting "3D Ogust" to cater to this problem.)


text:
What are the preconditions for a trump promotion in bridge?
My understanding is that there are two main conditions. The first is that the defense has a long suit with which they can set up a "ruffing finesse," usually against the declarer's trumps by leading through a newly created void (usually after a lead or two).
The second condition seems to be when the defense has a number of "intermediate" trumps, typically ranging from Q to 8. (If the defense had four trumps 5432, a promotion wouldn't work, and if the four defensive trumps were AKQJ, it wouldn't seem to matter.) With a promotion, a defender uses an intermediate trump to force out a higher trump to promote partner's intermediates.
Is this second precondition in fact the right one? And if so, how do you, a defender, detect the precondition either when making an opening lead (West) or responding to one (East)? Is it because you see a lot of low trumps in dummy and some intermediates in your own hand? And then do you infer that if partner has one or more trumps that they are likely to be intermediates?

This is far too broad Tom - as in any card-game coup, the essential precondition is an imposition of zugswang, the compulsion to move (first, and suffer consequential severe disadvantages). If you are talking about how one recognizes such a condition that is because one is skilled and counted the opponents' hand. If you are actually asking about when to suspect this when choosing an opening lead, ask that question instead of this one..

Expert bridge players don't think this way; there is no magic check-list of coups and strategems that they review in their head as they decide on a play. Rather they have studied these play sequences extensively, and at the table concentrate on counting the opponents' hands, simply recognizing patterns as they are spotted. The underlying principle is always about maneuvering the sequence to impose zugswang on the opponent before it is imposed on you - someone is always under compulsion to make a next play.

@PieterGeerkens: Amended the question per your suggestion.

The Bridge Encyclopedia identifies 4 situations in which trump promotions ("the creation of trump tricks by forcing the premature use of trump cards by the opposition").

Uppercuts - ruffing high to force opponent to overruff, thus promoting a trump trick in partner's hand.
Establishing long tricks in trumps by forcing opponent to ruff - as in a forcing defense.
Coup en passant to create a positional trump trick. Example:
      K
      -
      -
      2
A           Q
-           -
-           A
A           -

      J
      -
      2
      -

With spades as trumps and the lead in the south, if declarer (south) leads a trump, they lose both tricks. But if they lead a diamond, the spade King will be scored en passant - either west will trump and declarer will discard from dummy, or west will discard and declarer will ruff with the king.
A positional overruff threat. For example, if south holds KQx in trumps and west holds AJ, playing on trumps will lead to west taking a single trump trick. If instead east plays on a side suit in which south and west are both void, south must ruff high to prevent an overruff with the J, but this establishes the J as a second trump trick (as long as west does not overruff with the ace!).

The fourth case is even more interesting when West holds AJx in trumps, and must under-ruff South's ruff with the K or Q in order to preserve the extra trick.


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How would a "blocking" strategy play differently in Ticket to Ride than other strategies?
Most of what I've read about Ticket to Ride focuses on "constructive" strategies of getting long destination routes and building them out for their large bonuses, including the longest route bonus. This allows one or more players to get over 200 points, but presumes a minimum of "blocking" from one player to another.
On the other hand, if players are inclined to block each other, then long destination routes might be a liability (because they can't be completed, and earn a negative bonus). In such a game, it seems like the trick is to take the two shortest destinations, build them "fast," and then spend the rest of the game blocking other people's routes. In such a game, scores might be closer to 100 than 200.
If only one player is playing "blocking," this strategy might not work, but it seems that if four or five (out of five) are playing this way, the game would play very differently than as discussed in the first paragraph. Just how would it play differently? Have I gotten at least some of the changes right in the previous paragraph>

What do you want to ask? If all players are playing differently, will the game play differently? Well, yeah. I don't see a point of this question as it is now.

@Deo: Modified the question to how would it play differently.

The (revised) question is actually very simple. I laid out a bunch of hypotheses in the second paragraph. Are they right or wrong? Is there anything that I have missed?

I think you have it mostly right already, and certainly it will vary based on the people involved, but in my experience the jump from players focusing on their own agenda to being more interested in disrupting their opponents means shorter tickets are better, there is likely to be a lot of hoarding up cards until someone has enough to actually pursue a route, the longest train will be shorter than in the first scenario, etcetera. In my experience if one player pursues a blocking strategy while the other tries to do their own thing, the "do my own thing" player will win more often than not. That may change when you get into higher numbers of players.

This matches my experience as well generally.


text:
In bridge, how low an "unlucky" percentage would a good player guard against?
If a contract depended on say, a finesse, most good players would look for plays that would give a better than 50-50 chance of succeeding. (Unless the finesse was marked by the bidding or early play.)
Most good players would make, or consider making, a safety play to guard against a 4-1 split (except maybe in matchpoints). This occurs with a greater than 28% frequency (or 14%+ if it was relevant with the singleton on one side and not the other).
But I read of a situation in a tournament where a world class declarer took an inordinately long time to study the play of a hand, to the point where his opponents called the tournament director (TD). When the TD asked the player why, the player answered that he had just worked out a way to make the hand against a distribution with only a 2% chance of occurring (a 5-0 trump distribution with the 5 "offset" a finesse).
He looked like a genius when the relevant opponent admitted to having that hand.
Apparently, there was little time to play the game out, but the TD awarded the point to the player after the player described his game plan and the opponents conceded, showing down their hands. All the other declarers on that board went down.
Is that unusual? Do good players routinely study ways to guard against 2% chances over the board? Or do most players have a higher threshold, say in the 5%-10% range?

2%?  I don't think most would worry about 2% on most hands, because most hands you'd be losing a higher percentage of the time to protect against the lower.
But yes, in this kind of case it's not uncommon to protect against 5-0 splits.  While it's not common, 2% is 1 in 50 hands, meaning it might come up a few times in a weekend; the difference between a highly experienced player and a top-tier player might only be a few hands, and those would be some of them.
It really comes down to the hand.  If the hand is played at IMPs (where making the hand is paramount, rather than overtricks), and it's solid for 4-1 or 3-2, then there's no reason not to explore 5-0 split lines.  I've certainly done it a number of times before, and I'm hardly a world class player.
I suspect your story is a bit of an apocryphal one, given the description of the actions after the tournament director was called are inaccurate to what would really happen at a tournament (slow play involves slow play warnings, and eventually board penalties, but would not modify the results of a hand; the tournament director would not "award the point" either, it would be up to the opponents to accept the claim or not, if a claim was indeed what was made).  But the actual details - that a world class player considered his line of play for several minutes in order to find a safe line against a 5-0 split - are entirely reasonable, if a bit boring compared to the dramatic telling.

In an IMPs situation, you can calculate the IMP odds to determine what the right thing to do is. Let's work an example.
The declarer is in 4H vulnerable. Line of play 1 makes 5 most of the time, but x% of the time goes down 1. Line of play 2 always makes 4. Let us assume that your opponents are in the same contract will always take the safety play. Line 1 wins 1 IMP for the overtrick (100-x)% of the time, but loses 12 IMPs for going down x% of the time. 1 * (100 - x)% = 12 * x% when x = ~8%. So if that's the situation, you should only take line 1 if it has less than 8% chance of going down.
Most situations are a bit more complicated but the principle is the same.

I don't think that's what OP is asking.  OP is asking how often people bother to spend the time to figure out a line for a 2% likely play, not how people compare different lines of play with different probabilities.

You can judge whether thinking about a 5-0 break is worthwhile by figuring out the odds of the break and the likely number of tricks a safety line would take.

Yes, you certainly can, but OP is asking if people do, not if it is possible to.

A good player takes these things into account.

@Joe: I see this answer by ruds as an answer to the title of the question. The other question, "do good players do that", is a pointless question IMO. Answer is, yes depending on the situation. Now what does that get us? Anyway...

@Aryabhata The title of the question is "How low an unlucky percentage would a good player guard against".  This doesn't address that - it only shows how you would choose one line over another.  Very different question.

@Joe: If you are thinking of the question having an answer like 2%, then the question is completely nonsensical/subjective. The only sensible interpretation of the question IMO gives ruds' answer as a reasonable answer. Anyway, Tom has the knack of asking strangely worded questions :-), so I will drop out of trying to come up with a reasonable interpretation of his question this time.

I'm thinking of the question having the answer that I gave...  He's asking "Do expert players spend the time to find the best possible line when the odds are very low it will be needed", more or less.

Many, many years ago, in the 35th European Championships, played in Birmingham in 1981, Hungary and Britain played a hand which showed the extremes to which some players go to ensure the contract.
(I have since been able to find the hand in the EBU archives and have updated my answer accordingly.)
Dealer South, Game All.

North: SAK5     H6     DAQJ1075 CA82
South: SQ109875 HKJ987 DK       C3

In the closed room, after an initial pass by South, the bidding was as follows:
    West       North           East          South
   (Rose)   (Dumbovitch)     (Sheehan)    (M. Kovacs)
    Pass        1D             Pass           1S
    2H          3H             Pass           4S
    Pass        6S             All pass.

Kovacs took two rounds of trumps, leaving the King in dummy, played the King of diamonds from hand, with the high trump in dummy securing entry to the remaining diamonds and the slam against a 5-1 split in diamonds.
In the open room the Hungarian West doubled, rather than bidding 2H, at least hinting at a 2-suiter. Collings, sitting South for Britain, also found himself in 6S facing a club lead.
He won the Ace of clubs in dummy, followed by the Ace of spades and a low heart. When East played low, Collings could afford to lose the heart trick to West. He could then ruff a heart, draw trumps and take the diamond tricks in his own time.
The diamonds were 6-0. The safety play succeeded and 17 IMPs went to Great Britain. (From EBU Quarterly, August 1981, page 15)
In general, as ruds explains, you estimate the expected value of the safety play. As a rule of thumb, you play safely at rubber and IMPS. At match points you try for overtricks if you are in a contract that most of the room will be in. If you are in a slam that you think very few people have bid, then you would also play safely to ensure a top or near top.

That hand's a great find. I only wish I could upvote more than once.

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text:
What system is this expert using?
You are at favorable vulnerability. LHO deals and passes. Partner bids one heart, RHO opponent passes. An expert (Frank Stewart) "surely" recommends that you respond 1NT with the following: (s)J954 (h)3 (d)T (c) KQ97632. This is the case even though you have four spades. (Stewart has major issues with "Standard.")
If you had (s)J954 (h)3 (d)T8 (c) KQ9763, he would "consider" bidding 1NT.
I did the same thing (bid 1NT) with a (somewhat) similar hand (neither vulnerable) and got into trouble when partner bid two spades, "reversing" with two spades, and only 13(!) points.
Under what system would Stewart's recommendation be a reasonable one? Or is it because the circumstances are (somewhat) different from mine in the above hands, where Stewart recommends running out to a "weak" 3 club bid if partner responds at the two level? Put another way, what might be the context of Stewart's remarks?

Not forcing NT.

@Aryabhata: So could I have been right to do what I did if partner and I had agreed to use "not forcing NT?" I was not this person's regular partner but a "stand in."

Assuming some simple variant of standard american as played in the US, 1NT is 6-9 (or bad 10) and looks like your partner overbid with the 2S bid. Of course, it all boils down to what you agreed upon. In the US, sitting down first time and saying "standard", I would assume 1NT is not forcing (showing 6-9) and that 2S is a reverse like bid.

So the problem clearly is your partner reversing into 2S with a weak hand rather than you responding 1NT?

Stewart's recommendation is reasonable in any standard system, whether 1NT is forcing or not.
Unless your partner's hand was very unusually distributed, it sounds like your partner was at fault for reversing with only 13 points.
Reversing means bidding at a new level (here 2 spades over 1 NT) in a higher ranking suit (spades ranks higher than hearts) than your opening bid. In essentially any natural system this promises 16+ points.

Why is even a forcing 1NT not an issue?
The hand shown has a 7 card club suit and two singletons. Whether 1NT is forcing or not, this hand expects to play best in clubs. Two clubs directly shows too much strength. Bidding 1NT followed by Clubs (presumably 3 Clubs) typically shows this type of hand.
There is a decision whether to ignore the 4 card spade suit or not. Once the hand is this distributional it can make sense. You'll have a hard time getting to clubs after you bid 1 Spade because a second suit by responder usually shows extra strength (and is often artificial).
Notice that if you had had the same hand but with 3 spades and 2 diamonds, there would be no question that 1NT is the bid.

Your choice (unless playing weak jump shifts, which are becoming popular) is between 1S and 1NT.  I personally would bid 1S:  If partner jump shifts I can rebid clubs again and again without showing extra strength, if he raises spades I don't mind ignoring the clubs, and if he rebids 1NT I have enough to give him a chance to make.  I will pass if his rebid is 2H, so the only problem is if he rebids 2D.  There, I will take a truly fals preference to 2H, and if they double run to 3C -- partner would be able to work out what happened.
The risk in responding 1NT is if partner has a 4=5 hand in spades/hearts and not enough to reverse, we will get a poor score in 1NT.  Unless we are playing Flannery, this is a much more common situation that a rebid of 2D.
If this probelm were presented in the Master Solvers Club, there would be votes for both responsesm and none for any other bid (which is why it would not be chosen for that forum).

The auction in bridge is not about describing your hand perfectly, but about reaching the optimal contract. This requires careful planning.
Here, it is tempting to bid 1s, but what will you do after the very likely 2d rebid? 3c is a huge and game-forcing bid, 2s promises a one-suited weak hand with spades (5-card, typically 6-card). 2nt? Worst of the evils and an overbid, so why not just bid 1nt straight? This also allows to naturally bid clubs later. And if partner has enough strength for reversing into 2s, you won't miss the spade game.
EDIT:
I dealt 100 hands restricted to N unable to reverse (5-7 hearts,0-6 diamonds, 0-6 clubs, 0-4 spades; 12-17 points). The available contracts for NS are (some are coming from the same deal):

3-4♣ - 45 times
5♣ - 15 times
6♣ - 3 times
2-3♠ - 20 times (12 times with spades 4-3: not unlikely if the response is 1s. In all but 3 cases, NS have at least 3♣)
4♠ - 8 times (twice with spades 4-3; only in one hand NS don't have 5♣)
1-2NT - 14 times
3-4NT - 6 times
2-3H - 6 times
4H - 2 times

I believe the statistics shouts for a 1NT response.

You forgot a preference to 2H in response to 2D: which some people might consider lesser of evils between 1NT and 1S followed by 2H. One reason to bid 1S is that with a hand like KQxx, Axxxx, xx, Ax with partner you have a good spade game. Partner does not need reverse values for spade game to make. You will miss out on the spade fit by bidding 1NT in those non-reverse cases.

I called 2nt "worst of the evils", not "lesser". However, 2nt (and even 3nt) has better chances than 2h: if partner is dealt non-singleton club ace, it will be often successful, while 2h is extremely unlikely to win.

Concerning the "hand like ..." - there are very few hands like that. And very few pairs will finish in 4s. And unless some of the defenders holds 6 diamonds (in which case the bidding is unlikely to end in 1nt), the 1nt contract is safe, so we are not going to lose.

So you are saying 2NT is the worst of evils (which was actually irrelevant to my point) and that 2H is even worse than 2NT? :-) I really suggest you deal out some hands. I am willing to bet (virtual money :P) that 2H will turn out to be better more often than not.

@Aryabhata, 2nt is a better contract than 2h, but the bidding is unlikely to end in 2nt; often it will be 3nt, sometimes doubled. I am not interested in your virtual money. I've dealt 100 hands for the bidding 1h-1s-2d-? (I've restricted N to 5-6 hearts, 4-5 diamonds, and 12-17 points). Despite there are more tricks in the heart contract on average than in no trump, 2h won 6 times, 3h once, 5h once. 2nt won 7 times, 3nt - 3 times, 4 nt - once. The vast majority of best results for NS - 3c to 6c, where one cannot finish (imo) after answering 1s.

Well. You won't always end up in hearts after giving a preference to hearts. So your simulation is flawed I would say. Anyway. No point discussing this further. We can do a (bigger) simulation ourselves and come to our own conclusions.

@Aryabhata Even on your example hand, 5 Clubs makes as well. (On a separate note, I suspect zhoraster's simulations are simply double-dummy results and make no assumptions regarding further bidding. That said if I happened to respond 1S I would also prefer 1H-1S;2D-2H to 1H-1S;2D-2N.)

@aes, I wouldn't have bid 2nt either in this situation, and I explained why. I can't imagine what "further bidding" you speak of. My main point was that I will  avoid this situation if I bid 1nt. All results are double-dummy, and the simulations are flawed, yes,  e.g. they don't take into account opponents' passes (the RHO's pass having very good chance to be trapping). But they give a rough idea of what can be an optimal contract here.

@zhoraster I think we're in agreement. I was explaining what type of simulations you were presumably running (double-dummy, as you confirm) and that they have nothing to do with any assumed further bidding! Your simulation results above in your post are quite nice and helpful in confirming that Clubs is the relevant suit to get across with this 4-1-1-7 hand!

Stewart's recommendation is reasonable in Standard American -- here, responder's 3C rebid cannot be natural and invitational because an initial bid of 2C would have included that hand.
It's also reasonable 2/1 Game Forcing base that includes the agreement that a 3C rebid after a 1NT response is natural and less than invitational. However, many players play that this shows an invitational hand with 6 or more clubs.


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If opener "pre-empts" in first or second position, can you reasonably assume a pretty strong suit?
Opener bids three of a suit. This particular opener always has seven cards when s/he does this. My a priori view of "average expectations" for opener's suit would be something like A-Q-T-8-6-4-2 (every other card for a total of seven). If I held, say, A-8-3, I would subtract the A and 8 from opener' hand, and replace it with a 7 and 5 (conservatively) or more likely, J-5 (a balanced high low), giving Q-T-7-6-5-4-2, or Q-J-T-6-5-4-2 respectively. If I held a K-J-9, I would mentally remove the opener's Q, and credit him/her with A-T-8-6-4-3-2.
Is this a reasonable way to estimate opener's suit holding? Could it actually be stronger (on average) if it is true that "no one" would open with Jxxxxxx or weaker? On the other hand, would I reduce my estimate if the opener would bid one of a suit with the above suit and say, a side ace?
For "guidance," consider the following questions.

Is it true that based on sheer numbers, hands as strong as AKQxxxx or as weak as Jxxxxxx are low probability events?
Do most conventions eliminate prempting with the above hands?
If yes, is the remaining range, (AKJxxxx to Qxxxxxx) reasonably well represented by my hypothesized "average expectations" or do you need further agreements for a narrower range to "bracket" A-Q-T-8-6-4-2?

This question is for first and second positions, third and fourth have their won peculiarities.

Seat, vulnerability, and partnership agreement all affect required strength for preemptive openings.
On seat:

In second seat, you are preempting 1 partner and 1 opponent; this seat has the narrowest range of suit quality and hand strength.
In third seat, you are preempting 0 partners and 1 opponent; this seat has the widest range of suit quality and hand strength.
In first seat, you are preempting 1 partner and 2 opponents. In this seat the hand might belong to your side or opponents'; it requires a narrower range than third seat but allows a wider range than second seat.

On vulnerability:

When you are vulnerable and opponents are not, missing your side's game imposes a higher cost and preventing opponents from reaching their side's game (or preventing them from finding their best strain) has a lesser benefit.
When you are not vulnerable and opponents are, missing your side's game imposes a lower cost while preventing opponents from finding their best contract has a greater benefit.
When vulnerability is equal, the cost/benefit ratio is in between. You should be slightly more conservative when both are vulnerable than when neither is vulnerable, because the penalty for undertricks is higher (though I take this as a lesser concern).

On partnership agreement:
Broadly speaking, preempts have two purposes. The first is constructive: you wish convey to partner your hand type. The second is destructive: you wish to prevent opponents from finding their best contract. Different partnerships will have different philosophies here as to which goal is more important, and this will vary by seat and vulnerability as laid out above.
The more constructive you wish to be, the narrower the range of hand strength and suit quality you should have. The narrowest common range is something like "my opening 3 bids show exactly 7 cards with 2 of the top 3 honors or 3 of the top 5, in a hand with 7-10 points and no void or side 4-card major." This is a very reasonable standard for nonfavorable second seat openings. This will help partner evaluate their hand for a raise to 3NT or 4 of your major.
The more destructive you want to be, the wider your range should be. This increases the frequency of the bid while decreasing the information given to your opponents. This will make it more difficult for them to determine whether 3NT is safe, for example, and make it more difficult for them to place cards in the defenders' hands during the play. The widest "reasonable" standard for 3-bids is something like "a good six-card suit or a bad seven-card suit in a hand with 2-10 points."
Edited to answer the sub-questions:

Given a 7-card suit (and no other information), it will have all 3 top honors 12% of the time, 2 top honors 44%, 1 top honor 37%, and 0 top honors 7% of the time.
With most of my partners, I would open e.g. a 7321 hand with AKQxxxx and no other honors at the one level in most seats, but at the three level in second seat. Other partnerships open it at the three level more often. With a 7321 hand with Jxxxxxx and no outside honors, I would open at the three level not vulnerable in third seat; other partnerships would never open such a hand. As mentioned above, this depends wholly on your partnership's philosophy of constructive vs destructive preemption. There's not a single right answer here.
I don't understand your "average expectations" rubric. Why do you care about the spots? If you have agreed to play sound preempts with your partner, and you hold Axxx AT Axxx Axxx across from your partner's 3H opening, you can be nearly certain that you'll take 10 tricks in a no trump or hearts contract. It's not reasonable to replace the AT in AQT8642 with the 3 and 5, because your partner has agreed to open only if holding two of the top three or three of the top five. They almost certainly hold KQxxxxx or KQJxxxx. If you agreed to play a wider range, you'll often have to lose a trick in hearts, but it's probably worth the gamble when vulnerable -- even if partner has a poor heart suit like Q9xxxxx, they'll generally have an outside king to make the tenth trick.

Upvoted for good philosophical discussion. But the other point of the question, is, do the "conventions" basically narrow the range of possible hands. For instance, if I have a 13 card suit, I would have exactly 10 hcp. With seven, I could have AKQJTxx or 8765432, but I would bid one of the suit with first hand, and pass with the second., basically ruling out those hands So is the actual range of hands ikely to be much narrower than the theoretical?I was thinking in terms of "permutations."

I don't really understand your question, but maybe this answers it: If you've agreed that opening 3 diamonds shows 2 of the top three honors in a 7 card suit, and your partner opens 3D when you hold KJx in diamonds, you know partner has AQxxxxx. You can't answer the question without knowing your agreements.


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How does one evaluate a hand responding to a "strong" two clubs?
When opener bids a "strong" two club, responder bids two diamonds (waiting), and the opener rebids his suit, e.g. two spades, the responder is now the "captain" of the partnership. That's because s/he knows that opener has 8-9 tricks in hand, and what partner's suit is. In most cases, it's now the responder's job to evaluate his own hand at 0, 1, 2 or more tricks for the final contract. Nevertheless, some cards in responders' hands are more valuable than others.
Where would these (responder) tricks come from if s/he's relatively weak. An ace is a sure trick, but opener might have most of these. Can a king be counted as a trick on the theory that opener has the ace, or maybe the queen for "synergy?" How about other assets such as the queen of "trumps" (the opener's named suit), small "trumps," or "distribution?" I don't give as much weight to random queens and jacks (outside the named suit), even if they add up to 5-6 high card points or should I?
How do various systems or experts formulate their responses to two clubs, two diamonds, followed by a rebid of two of a suit or 2NT?

Trumps are still unknown by responder to a 2C opening - how could a key-card system showing the queen of trumps possibly work?

In your answer below, you said that I (the responder) would become "captain" after the opener's second bid. This means that after opener rebids, e.g. "two spades," it's my prerogative to decide whether or not spades are trump. Why can't I use a "key card system to make that decision."

Because key card tells nothing about fit, which is far more important to determine than defensive strength (key cards in unknown suits) at this early stage of the auction.

Sorry - your edit is making the question worse not better in terms of removing my down-vote. The single most important fact about every auction is who is currently the captain and thus it can never be ignored because no auction makes proper sense without that information. The failure to appreciate that in your question is the key reason for the down-vote. If you can phrase your question in terms that respect the importance of captaincy I will up-vote it.

@PieterGeerkens: I have rephrased the question to the best of my ability regarding "captaincy."

@TomAu I remember from your previous discussions that your definition of 2C is somewhat different from what is now common in systems based on Standard American (essentially all hands with 22+ HCP or any hand with 8.5+ top tricks). With that agreement, neither partner is captain after 2C-2D-2S since 2S does not set trumps and neither player is narrowly limited in strength. After 2C-2D-2NT, responder is captain since opener is limited to 22-24 HCP balanced.

The system I have played for many years is as following:
1. Opener rebids NT to show a balanced hand with a well defined point range:
Responder evaluates his hand as balanced unless making a transfer bid into his own suit. These auctions are very similar to 2NT openings except with greater strength having been shown by Opener.
1a. Opener rebids 2NT with a semi-balanced hand of appropriate strength (usually a range of 22-23 HCP) and a 5-card major (not longer) with an agreement enabling Puppet Stayman. Advantage is that Responder's second negative doesn't place Notrump contracts in his hand with the strong hand exposed and led through.

Responder will almost always rebid 3C (Puppet Stayman) to allow Opener to reveal a hidden 5-card major (or 6-car minor).
2. Opener makes a simple rebid in his Major suit:
Responder bids 2NT as a second negative with either less than 3-card
support or 3 cards only and a bust hand.
Responder raises to 4 of Opener's major with 3 or 4 card support and a few scattered points.
Responder raises to 3 of Opener's major with 3+ card support and slam interest, but no outside control.
Responder bids a new suit to show a control (either A or K) in the suit bid, 3+ card support for Opener's major, and no reason to deny slam interest.
Responder jumps in a new suit to show 4+ card support and shortness in the bid suit with no reason to deny slam interest. Generally this call is preferred to the simple cue-bid, as controls can be asked for later.
3. Opener makes a simple rebid of his minor suit:
Responder rebids as above, but with the change that all bids above 3NT emphatically deny interest in 3NT (obviously).
Responder rebids 3NT with a balanced 7 or 8 count well scattered and lack of interest in slam. The inference is that responder believes 9 or 10 tricks are available through sheer power, but that the fit is insufficient to make slam realistic. Opener continues only if a) his hand is completely unsuitable for notrump; or b) his hand requires only 2-card support to play well in his minor.

Miscellaneous comments on the situation:
It is vital to remember that will not be Captain for the auction will not be the 2C opener but rather responder. The key descriptive features of a 2C opener are that it is a strong hand, and can be described adequately in 2 calls so that partner can be captain. More complex hands should not be opened 2C, and both members of the partnership needs to be aware of that.
As such, all attempts at step and control responses to the 2C opener have been abandoned by serious players (with the possible exception of pure relay systems, which you cannot play in most tournament events).
For instance, the hand xxxxx-xxxx-x-xxx can be golden if opener's suit is spades with three worthless diamonds, and garbage if opener's suit is diamonds with three worthless  hearts. No bidding system can hope to describe the range of partner's hands adequately to opener, especially  when that conversation has to start at the three level, which is why responder is the captain as soon as the 2C opener is made, until and unless the opener can glean enough information to bid Blackwood.
Update
One of the ways in which opener becomes captain if he has support for a quality 5-card suit (or longer) shown by responder as a positive response. When this happens opener sometimes is in a better position to judge the combined playing capability of the hand by bidding Key-Card Blackwood in responder's suit.
Update #2:
Only the captain can ask for key-cards, because the premise is that the key-card responses will allow the asker to place the contract, both denomination and level, and only the captain can make that call (or make the requisite invitation).
Opener can take over as captain only when responder leads opener to believe that his (responder's) hand is fully described - there are circumstances where it may be appropriate for responder to have a stronger hand and/or a different fit in mind than he has lead opener to believe, but that is an advanced bidding technique that intermediate players have difficulty handling.
Also, it is critical that all responder's calls while opener believes himself captain be in sente rather than in gote, so that responder will have the guaranteed opportunity to make the final correction.  This can require responder to have considerable foresight in planning the auction.

I'm sorry if I confused you by "implying" that under the "key card system, the opener is usually the captain. That was not my intent. To that extent, the analogy with Blackwood does not completely hold.

Only the captain can ask for keycards, because the premise is that the keycard responses will allow the asker to place the contract, both denomination and level, and only the captain can make that call (or make the requisite invitation).

Accepted for your improved answer, and for helping me to improve the question.

Your question depends strongly on partnership agreements about 2C openings and followups. Evaluation as the weaker hand in the auction depends strongly on the types of hands partner might have. A reasonably common 2C agreement in the US follows these lines:
2C shows most hands with 22+ HCP, and shapely hands with 8.5+ top tricks (though e.g. AKQJxxxxx x x xx, lacking any honors outside the primary suit, is not appropriate for this call). Whether this includes strong, shapely two-suiters that do not have game in hand (e.g. QJxxx A AKQxxx A) depends on your responding style -- since I do not pass 1D holding Kxx xxxx xx xxxx, my partner can safely open that hand 1D with little fear of missing a game.
Responder bids 2D (waiting) with nearly all hands, reserving positive responses for very limited situations (e.g. bid 2M with a six-card suit holding exactly two of the top three honors and no outside A, K, or Q, or bid at the three level with similar honor holdings and a 7-card suit).
With balanced hands (including those with 5-card majors), opener bids NT at some level (though strongly consider adding the Kokish relay to your repertoire) to limit their hand strength and make responder the captain.
With hands unsuitable for NT rebids, opener rebids a suit. A typical agreement is that a jump in a suit sets that suit as trump. Here opener typically has a shapely hand and is looking for specific cards to bid slam, so opener is captain. With one partner I play that after 2C-2D-3M, responder should cue-bid an ace or bid 3NT to show no aces but one or more kings in hand, or 4M otherwise.
After opener's non-jump rebid, neither partner is captain -- neither partner has enough information to make decisions about strain or level. Bidding must proceed naturally, and partnership understandings are necessary to determine whether and how it is possible to stop short of game.

So how do you evaluate your hand as responder?
After opener's NT rebid, evaluate using standard methods.
After opener's jump-rebid of a suit, opener has captaincy -- you're there to tell partner about the key cards in your hand.
After opener's simple rebid, opener is unlikely to be very shapely, so you'll evaluate as in a normal auction, just starting a level higher. Things to look for: sources of tricks (long suits headed by multiple honors), cards that fit with partner's suit(s), aces and kings. Queens and jacks in unbid suits are unlikely to be terribly helpful.

Recognize that your partner has a powerhouse hand and needs relatively little from you to go far.
9+ points: Slam zone. Partner should have at least 22-23, the two of you have at least 31-32. If you have a suitable fit, your main worry is that the opponents will take two tricks off the top with two aces or AK of the same suit. With no more than eight or nine points between them, it's unlikely (though possible) that they will have such holdings that bump up against their point limit.
6-8 high card points: Game plus. With a reasonable fit, a ten trick contract is all but assured, eleven are probable, and a slam is possible with the right fit and controls.
3-5 high card points. Game zone. You should drive to game with a hand that might not merit a response opposite any other opening.
0-2 high card points. You discourage game if your system allows a sign off after say, a 2NT bid. For instance, after two clubs, two diamonds, two of a major, you bid 2NT, which allows partner to sign off at three of his suit. If partner bids 2NT, limiting his hand to 22-23, you should pass there, under such a system.
As for partner's bid of three of a minor (to play), let's just say that opener needs more than 22-23 to try for an 11 trick game. Plus the additional disadvantage of exposing the strong hand as dummy if the suit is diamonds.
If you have good shape and/or more than three cards in your partner's main suit, you need fewer high card points than listed above. You will need more points in the event of a misfit.


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How does one evaluate the "strength" of a hand in Magic the Gathering?
In MTG (or other games), if one player is dealt a strong hand, and the other a weak one, the first player is likely to win. Unless, of course, the first player plays much worse or is unlucky during the course of the game.
How does one evaluate the strength of a hand in MTG? This is NOT a question about when to take a mulligan (which applies only to the weaker hands), but is a general question about all hands, weak, average, strong, and even "come" hands. (An example of a "come" hand, from poker is four to a straight or a flush, that is weaker than one pair, but will be a very strong hand if it "fills.")
I'm using some examples from bridge, which I know better:

One has a disproportionate number of the most powerful cards (three or all four of the aces in the deck).
One has a large number of moderately powerful cards (e.g. face cards, not all aces).
One has a hand with only average "raw" strength, but that is highly co-ordinated (e.g. seven or eight cards of a single suit for trumps). This can be combined with having few low cards, and hence few weaknesses, in other suits.
One has "position", e.g. by playing after an opponent with a slightly weaker hand, so it is easy to "cancel" or "one-up" him.

What are similar, or analogous advantages in MTG? Are there "standard" evaluation methods, as there are in bridge (with its high card point count), or is it more of a situational thing?

Short answer while working towards a long one: the most applicable skill from bridge is sequencing — being able to look at your hand and see how it will "play out" as a series of turns.

And in game 2+ of a match, you can also take into account the deck your opponent is playing, and the cards that would be useful for dealing with it.

@murgatroid99 Or game 1 if you know what they're playing (via "scouting," or hearsay, or draft signals, or because Bob always brings aggro decks to FNM).

Of course. I was using "game 2" as a catch-all for "after you know what deck your opponent is playing". I would also like to mention that in Magic, evaluating the strength of an opening hand may be more complicated than necessary. It all evaluates to one decision: do I mulligan?

I should also mention that Magic is fundamentally unlike bridge, so using bridge as a starting point may not be the most helpful. In bridge, everyone's playing the same game, evaluating hands composed of the same cards. In Magic, different decks with different cards have different gameplans and don't really have the same notion of strong hands, so anything that applies in general is going to be very vague.

There are a few articles in the Level One series about mulligans, i.e. evaluating whether a hand is strong enough to keep or weak enough to mulligan and try again. You might also be interested in reading some of these Keep or Mulligan articles. It's a little indirect; they're discussing what hands have and what they're missing, rather than explicit "strength", but that's pretty much the way you have to think about hands, and you'll see actual hands.

In response to your edit, when would knowing the strength of a hand be useful outside of choosing whether to take a mulligan? I may retract my close vote if you can identify another purpose.

@Rainbolt: I would want to know whether i am "strong" and therefore a favorite against a random, average hand, so I might "play not to lose" rather than "play to win." I would also want to know whether I have a "come" hand with "potential," and therefore NOT take a mulligan even if I have hand that's nominally "weak" (like four to a flush or straight in poker, that's nominally weaker than a pair of twos).

@TomAu That's not necessarily a bad question, but you know it has very little practical value, right? By the time you draw the hand, you're in the game, and you have to just play it - you're better off forgetting about precise hand strength and spending your time thinking about how to play in order to maximize your chances of winning.

Also, I hate to ask, but how much Magic have you played? It seems that answering your question (and explaining why it's hard to answer and doesn't matter too much in practice) requires explaining some fundamental notions of how Magic works, and I'm wondering just how much of that is necessary, and if you might be better served by some more basic knowledge of the game (whether reading, watching, or playing) before coming back to this question.

@Jefromi: That's what I learned from asking the question. As Alex P. wrote, "A good hand is a good plan," meaning that it offers a good story line. I would guess that a bad hand is one from which you can't easily fashion a coherent strategy. But I might retain a nominally "weak" hand with a good plan rather than take a mulligan. I'm learning the game to play with my nephew, and am a rank beginner.

I see - in that case I would definitely suggest just playing more games, even just goldfish games (your deck against no one, seeing how fast you can deal 20 damage); that'll give you much more practical knowledge than we really can in a general question like this.

I'm convinced that this is a duplicate. Playing to win and playing not to lose are the same thing to me. A "weak hand with a good plan" is an oxymoron in my opinion.

@TomAu "Play to win" vs. "play not to lose" is... a complicated proposition. See "beatdown vs. control" theory (linked below; you may also find the explanation in the first part of this answer helpful and "playing to your outs" (linked below). Basically, sometimes the best way to play a bad hand is to go all-in on a risky plan rather than playing conservatively.

While I agree that the question is similar to the linked possible duplicate, I feel that the two questions are posed and answered in very different ways, and this question draws on experience from another game for clarity. As such, I feel that this question is valuable to keep open even if there's a topical overlap.

@AlexP: That's exactly the point. If you have a "trailing" hand or position, you play "all out" and hope to "get lucky." If you're ahead, you try to control the variation and win by "attrition."

I also agree that this is not a duplicate, because the OP has made it clear that he needs more explanation than "when do I mulligan" - he also needed some general ideas of the game explained that are taken for granted in the "when do I mulligan" question. Unfortunately that also means it's bordering on too broad (look how long our answers are!), but I think it's probably on the okay side of the border.

@TomAu But that's more about how you play when you find yourself in that situation, more often because you didn't draw well, or because you had to mulligan a couple times and keep a mediocre five. That's not usually how you think about an initial seven-card hand; if it's really that bad you don't keep it.

@Jefromi I think this is one of those "too broad" questions where a non-exhaustive answer with some added reference is useful, though. Because you don't necessary know it's so vast unless you can already answer it.

A Good Hand is a Good Plan
Magic plays rather differently from a traditional card game:

Most cards in Magic require other cards as resources (e.g. land to generate mana). They can only be played once you've sufficiently developed your board. An effective deck has a mixture of early-, mid-, and late-game cards; what exactly that means varies greatly depending on your strategy.
Many cards are situationally useful — they're good because of synergy with other cards, or because they're reactive cards that answer an opponent's plays.
You get to tailor the deck to a particular strategy (outside of a few very special game modes like Momir Basic and Rainbow Stairwell).

So, most of the individual evaluative tricks don't work the same way at all. But that's fine.
Because, as you probably know, all of the evaluation tricks from bridge are cognitive shortcuts for figuring out the fundamental question: "How will this hand play out?" That's what you need to figure out in Magic as well.
Look at your hand and imagine what you're going to do in the next few turns. Imagine what your opponent is going to do, too, based on whatever information you have about them.
"I'm going to run my opponents out of trumps and then all these low cards will be tricks."
"I'm going to play some cheap creatures and use burn spells to clear the way while they apply repeated pressure."
"I'm going to use counterspells to survive long enough to cast my Wrath of God, then stick my planeswalker to control the board."
A good hand is, typically, one that presents some kind of coherent "story" or "gameplan" — ideally one that's powerful, fast, and resilient to disruption.
As a starting point:

What are you going to be doing on turn 1, turn 2, turn 3, et cetera?
Do you have enough lands to develop your board?
Do you have cards you can play early to help you stall or put pressure on your opponent? (Which do you actually need to do: stall or apply pressure? a.k.a. "Who's the beatdown?")
What's your opponent likely to do to disrupt you? What can you do to do to disrupt them?
What's missing? What cards do you need to draw to shore up your weaknesses or make your strongest play? (A bit of poker experience may help here. It also helps to understand "playing to your outs.")

Note that, beyond basics like "Make sure you will be able to actually cast something," what actually constitutes a good or bad hand is highly situational. Familiarity with your deck, with the metagame, and with general archetypes and strategies will all help immensely here.

"What actually constitutes a good or bad hand is highly situational." Then it would NOT seem that the question is a duplicate of "when do I take a mulligan," because THAT doesn't seem highly situational. Nor is the question unanswerable since you answered it.

@TomAu Mulligan decisions are situational, too. Consider that this is one of the best hands you could hope for against a control or combo deck but an absolute death sentence against burn.

If you want to see how this works in practice, probably the best way is to read what people have written about taking mulligans. That's really the only decision you can make after evaluating the strength of a hand: is this hand strong enough to keep, or is it weak enough that I'd expect an average hand with one less card to be better?
I know you've said you don't just care about mulligans, but this is really the only kind of real-world resource to point you at, and this is definitely a question where you'll benefit from looking at real examples. When you ask "how does one evaluate the 'strength' of a hand?" as a broader question, the answer in practice is "you don't." All you care about is mulliganing. If it's an obvious mulligan, you don't waste any time deciding precisely how bad, you just shuffle it back. If it's an obvious keep, you might be a little excited if it's really good, but you're not going to try to pin it down. The potential range of power is more like awful to reasonably good, not weak to incredibly strong. Generally, the best possible hand just means you have decent odds and you'll get to play a "real" game.
The Level One series has several articles about mulligans, trying to give some generally helpful advice. If you haven't played a lot of Magic, you might want to read some of the rest too, since that background will help give you the context you need to understand what you're really looking for when you draw your seven cards.
There's also the Keep or Mulligan articles on Channel Fireball, which are all about looking at specific hands for specific decks. That might be a little less meaningful if you don't grok the decks, but it'll give you an idea of the kinds of things people consider.

So this is clearly a pretty complex thing; people are writing whole articles not just about hand strength in general but about specific hands for specific decks! Let's come back to your comparison to bridge, and see why it's so different. For several reasons, Magic isn't as easy to generalize about as bridge:

In bridge, your opening hand is all the cards you'll have for the whole game. In Magic, your opening hand is just the first seven cards - even in a very fast game you'll see at least a few more, but you can easily see another seven, or in longer games, another twenty or thirty. So you have to think about your hand in the context of average subsequent draws. You're far from perfect information, and there's an element of chance.
In bridge, every hand is drawn from the same deck of cards, so you can analyze all hands in the same way. In Magic, every deck is different, so the main considerations for one deck in evaluating hands may be completely different from those in another deck.
In bridge, the cards all come with numbers printed on them indicating their precise "power", and there's not many possibilities. In Magic, not only are there not numbers like that on the cards, there couldn't be. Everything's contextual; it's more like a radically expanded version of nontransitive dice, where it's not "A beats B beats C beats A" but rather a large number of cards each of which are better than some others in some contexts, and worse than some others in other contexts.
In bridge, your opponents are also drawing every hand from the same deck of cards. In Magic, each opponent you play can be playing a different deck, which in turn changes the value of the cards in your deck. Something that's amazing against one opponent's deck might do absolutely nothing against another's.
In bridge, there are actually hands that can guarantee victory. In Magic, there's no such thing. Your opponent will always have at least some opportunity to interfere with your plans, and most often there's a lot of interaction and dependence on subsequent draws. So the power level ceiling is much lower - there's no such thing as a "come" hand. (Even in vintage, where you can play some pretty degenerate combo decks, your opponent can be playing free counterspells to mess you up on your first turn of the game.)

All that said, we can certainly try to come up with some very general ideas.
The most important thing is mana. To first approximation, you're looking for the right number of lands. But as soon as your deck has multiple colors (which it most often does), you're also thinking about whether you have the colors you need to cast the spells in your hand and the spells you're hoping to draw. And since nothing is ever perfect, you're also often thinking about how likely it is you'll find the additional lands you need and the colors you're missing in time.
Next, you're looking for cards that will let you do what your deck wants to do, which varies wildly depending on the deck. In a very simple aggro deck, that might just be a selection of the cards that will let you deal damage as quickly as possible. In a more synergistic aggro deck, you'll want cards that work well together, not just all of one thing. In a midrange, you're probably looking for cards that will help you deal with your opponent's early threats as well as cards to help turn the tables on your opponent in the later game. In a control deck, you probably want cards to deal with threats and some spells to create card advantage (e.g. card draw), but you don't want the cards you'll actually use to win, which you can wait to find later. So even within a single deck, there's likely no simple notion of power, and across all types of decks, it's impossible to generalize. You're just looking for a set of cards that you think will play out favorably, in combination with the cards you'll draw over subsequent turns.
On top of all that, as soon as you have some idea what your opponent is doing (i.e. in the second or third game of the match) you'll re-evaluate all your cards based on how well they fare against your opponent's game plan. Are your threats ones that are easy or hard for your opponent to deal with? Are your answers ones that answer your opponent's biggest threats?
The only real things in common across all of this are that you want "enough" mana and cards that give you a good game plan. What that actually means in practice, though, can't really be said in the same way you can about bridge. In some sense, whenever you build a new deck, you create a game, and then within that game you have to figure out all these things about power and synergy that you'll then use to evaluate hands.

For what it's worth, one could try to force the analogy with your points, and come up with ideas that are certainly part of how one evaluates opening hands.

In decks that have a few "favorite" cards, rather than a more even power level across the whole deck, it can indeed be great to see one of those in your opening hand, like your point (1). This is more common in limited, where you might pick up a single copy of a rare bomb, and not draw it in every game. (In constructed formats, anything that amazing you're probably playing four of, so it's not as much of a surprise to see it.)
Similarly, like your point (2), even if your deck doesn't have a giant range of power, it may have some range, and so some hands may include better cards than others. Again this is more common in limited, where your 23rd best card is often not one you're terribly excited about.
In decks that care more about synergy (how cards interact with each other), rather than just individually powerful cards, the synergy of your opening hand is a consideration, analogous to your point (3). It's a lot more complex to evaluate than simply looking for a long suit, though.
It sounds like the closest analogy to positional strength (4) is simply hands that are awful on their own but if you draw the right card will be great. That certainly happens, but those hands can be anywhere from a regretful "it was so close" mulligan to a hopeful keep (you might do nothing the whole game, you might have a blowout win), So it doesn't really tell you much about actual strength.

But as we've seen, none of those are actually simple rules; the power of a card is by no means straightforward to determine, and there's an awful lot of context to take into account that can completely change things from hand to hand and from game to game. Trying to think of it in terms like this is likely not to actually help you much in practice.

It's hard to know what is needed in a "good" hand without knowing your deck and the deck(s) of the opponent(s).  There are some really obvious bad hands (like having 0 lands), but beyond that it's down to what your deck is trying to accomplish.
In bridge it's a lot more easy to assign values to high cards because you know exactly how much trick-taking power it's worth.  Aces only lose to trumps.  Between two kings, you can expect to get at least one trick.  You never draw more cards than your starting hand, so you know right at the beginning of the game exactly what is and isn't possible.
A better analogy for evaluating Magic hands is evaluating a poker hand like in 7-card stud.  Obviously, your opening cards are very important and go a long way in establishing your play.  But future cards (for both you and your opponent) can swing the game in either player's favor.  You have to take into account how many remaining cards in your deck will help you while doing the same for your opponent's board.
As far as "positional" advantages, deferring decisions as long as possible keeps your plan more hidden and reserves your spells for when they're really needed.  Waiting until the second main phase to summon creatures can be very helpful.  It's much like leading from dummy to declarer's hidden hand.  Hiding that information (when possible) can get your opponent's to waste their better cards on your average ones.  It's the same in Magic, where you might try to bait a kill spell for your lesser creatures before playing your bomb.


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Do "flat" hands devalue a 4-4 trump fit?
The advantage of a 4-4 trump fit is that you can ruff in either hand, and use the other one as the master hand. But if one or both partners have little ruffing value, then might that advantage be minimal?
Neither vulnerable, South dealt and bid 1NT. West passed, and you, North, hold:
(s) AJ4 (h) KJ32 (d) J63 (c) 953.
The columnist wrote that: "North could have judged to bid 3NT with his flat hand instead of using Stayman; South probably would have made nine tricks." I concur.
But North bid 2 clubs, South 2 spades North 3NT and South bid 4 hearts, inferring that North had four hearts.
North knows that his hand has a 4-3-3-3 shape, and can infer that South's hand is likely 4-4-3-2 or 4-3-3-3, with 5-3-3-2 being the other main possibility. Does it make sense under the circumstances for North to avoid Stayman since the likely ruffing gains are minimal? Or should South have left North in 3NT inferring that North had 3-4 in the majors, and 3-3, or possibly 2-4/or 4-2 in the minors?

Yes, this is appropriate evaluation. @hunter gives a reasonable explanation of why.

Assuming you are playing 15-17 NT, this is a difficult question, any action could be right.
That said, the typical suggestion to bid 3NT on 4-3-3-3 hands is when you have slightly more than what is needed for the 3NT game. Something like 27-28 points. With a max 27 points, it is possible 4H is better. (Not saying it is, though).

@Aryabhata: I'd feel the other way. With 25-27, I'm hoping that my holding is good for nine at 3NT. It's with 28 or more that I'd try a ten trick trump contract on "brute force," without hoping for ruffing help.

@TomAu - form of scoring is important here.  At matchpoints, the extra 10 points for a NT contract when you make the same number of tricks is valuable.  With combined 27-29, it's likely that you make 10 tricks at either contract.  Even at IMPs or rubber scoring, with extra strength, there may be a squeeze in NT that is not available at the suit contract in the case where trumps break badly.  With 25-26 points, the probability that opponents could break a suit at NT, or that you need and can get two ruffs at a suit contract, is a little bigger.

@TomAu: If you don't need ruffing help, it is safer to play in NT, isn't it? Your statement seems to contradict itself :-)

I have been taught that with a 4333 you never ever Stayman!

Two separate questions:

Should N have bid 3NT straight off the bat? In my opinion, yes, at any form of scoring, for the reasons you mentioned, and also to conceal information about N and S's shape from West (think about how much easier the lead is after a Stayman auction than after 1NT - 3NT).
Given that N initiated a Stayman sequence, should S have developed a sufficient picture of N's hand to figure out that 3NT was the best spot anyway? No. From the auction, as far as S knows, N could have any number of spades between 0 and 3. (Experienced partnerships will probably have a way to show spade shortness here, by way of showing long minors, but doing this on middling hands that are likely to wind up in 3NT anyway is again a mistake, giving too much information to West.) Even if S could know that N has 3 spades, he still knows that N chose to initiate a Stayman sequence and should respect N's opinion that N's hand has ruffing values. (S has no information about shape that N doesn't have.)

When you hold a hand like this you should not think, WHAT game you should play, it's better to discover SHOULD you play a game or not!
Theory gives us some clues: if your partner whispers you that he has 4 hearts - you can count losers in your hand - a bit less than 10 losers (counting by Klinger). That means, that 4hearts will never (never!!!) be reasonable.
So - plan your bidding. I suggest to bid 2clubs and...

(2di) - 2 or 3 nt (as you feel in this moment), personally I prefer 2nt.
(2he) - pass !!!
(2sp) - 2nt

As you can see, in my plan it does not matter if my partner bids hearts or spades with 4-4 in majors. But if he bids 2spades with 44maj(and i know it), i'd better pass 2 spades.
4333 is the worst shape and jumping to 3nt is a gambling - you'll need some good cards, nice lead and some good distribution.
May be you feel lucky today?

I'd argue that the preponderance of low spots is just as debilitating for this hand as the flat distribution - seven cards 6-spot and below is very unfortunate. Look how much better this hand plays in either denomination if it gets the S9 and D10 in place of a couple of exes.

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Can someone be "one trick" better at bridge against "club level" competition?
There is a player on the site who claims to be able to play bridge "one trick" better than some opponents. I don't doubt this if the opponents are say, advanced beginners.
But beyond a certain level of play, such odds become too steep even for a world class player. I'll use examples from other games where I'm sure of my premises to illustrate my question.
In chess, "queen odds" is a heavy handicap. So much so that while a beginner can be beaten by many people at those odds, even an intermediate player would be a favorite against a world champion given those odds. In golf, if an "intermediate" player has say, a +8 handicap (over 18 holes), even a world champion might be hard pressed to beat him by one stroke a hole, or a score of -10, on most days. Put another way, my definition of a solid "club" player is someone who would be a favorite with queen odds against a world class chess player or one stroke per hole odds against a world class golf player.
When I refer to "club level" competition in bridge, I mean people who play bridge regularly take lessons, and practice, and occasionally participate in tournaments against people of comparable ability, but do not play professionally.
In bridge, my understanding is that contracts are geared to a fight for the last trick. That is, when four of a major is bid, the declaring side usually has nine tricks in hand, the defending side three, and the fight is over the last trick. If partnership A is "one trick" better on average than partnership B, it would imply that the weaker partnership would lose essentially every contract that the stronger partnership A was (barely) capable of making.
Here's my alternate theory of levels: My feeling is that a club player is someone who can usually make contracts when the breaks are "normal;" e.g. there is an opposing distributions of one's trump or other key eight card suit of 3-2, (this occurs 68% of the time), or an equivalent high card distribution. An expert is someone who can often prevail against a 4-1 suit distribution, which occurs 28% of the time, or equivalent high card distribution. A world class player can beat even a 5-0 distribution the few times it comes up. So relative to the the club "68%-er," the expert player will prevail at least 20% more often (out of a possible 28%), and the world class player will win an additional 3%-5% more often. That's "less" than one trick.
So when someone claims to play bridge one trick better than others, could that possibly mean "club level" competition, or only at most against advanced beginners?

Absolutely. And the best in the world are that much better again, or more, than those players.
The year before his premature death I had the pleasure of kibitzing Mark Molson in a late KO round of the Toronto Easter Regional. I arrived at the break, and Molson's team was down a couple of IMPS. Receiving permission to kibitz, I parked myself behind him. Across the table was the client.
Not knowing me from a hole in the wall, Molson wouldn't even let me see his cards for the first hour. Gradually, as I demonstrated good behaviour, he loosened up and I was able to settle in to enjoy the game. After 15 boards no more than a couple of likely 1-IMP swings each way had occurred. On the final board Molson picked up a balanced 12 count and drove to a 3NT game opposite his partner's balanced 9. Two 4432 hands with a combined 21 HCP - but the opponents didn't know Mark was light, opening a deceptive opportunity that allowed him to steal a tempo. Mark also had all four 10's and three of the 9's amongst the combined holdings.
I saw a couple of opportunities for the seventh trick, but had no idea where to even begin for an eighth or ninth. After a couple of minutes (only) thought on the opening lead, Molson saw that if one finesse was on (for trick 8) he had a chance of combining two possibilities, either a squeeze on one hand or a throw-in to the other, for trick nine. The gods were smiling and he chalked up 9 tricks, a 10 IMP swing, and the match.
In the absence of a Deep Finesse analysis, or the pleasure of watching Mark play it, I'd have played this hand for +120 and likely have never even realized that I had missed a 30% Vulnerable game opportunity.
The best players in the world, the Bob Hamman's, Jeff Mechstroth's and Eric Rodwell's, are nearly as far above Mark Molson in ability as Mark was above me.
You have phrased the question with a hidden assumption that all tricks are equal. The scoring, especially in IMP play, makes that far from the case. A full game swing (made at one table, set at the other) scores the same as 7 or 9 overtricks depending on vulnerability. In a 64 board IMP match with well dealt cards a double slam swing for 20 or so IMPs is not impossible. Hands are won or lost in the bidding as often as in the play and defence, and a double part-score swing is the same 7 IMPs as a non-vulnerable full game swing.

What does "a trick better" really mean in the context of Contract Bridge?
An (undoubled) overtrick is worth either 20 or 30 points depending on denomination. An (undoubled) undertrick is worth either 50 or 100 points depending on vulnerability. Any calculation of the worth of a trick needs to weight these; but assuming contracts are made twice as often as set and denominations equally likely, as a ballpark estimate, one gets an estimate
of about:
V = ( 2 * (30 + 30 + 30 + 20 + 20) + 5 * (50 + 100) / 2 ) / 15
  = ( 2 * 130 + 5 * 75 ) / 15
  = ( 260 + 375 ) / 15  = 635 / 15 ~ 42

This is right on the cusp of the 1 to 2 IMP transition of the IMP scale, so let's say that our one trick better standard is also about 1.5 IMPs.
Here is the complete Round Robin record of France in the 2017 Bermuda Bowl:

Over the 336 Boards (16 * 21 rds.) of the Round Robin France accumulated a total net IMP score of +283, or 0.84 IMPs / board; against national champions that have placed well in Zonal championships to earn the right to compete at this level. By our estimate above that represents about 0.6 trick better than opponents who, on average, might well be 2-3 tricks better than typical club players. And France finished second to USA2 in the 144-board final by a score of 278-276.


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In Matchpoints, is it worth risking a ruff to try for an overtrick in the following situation?
You are in a four spade contract, (West and East passed throughout), and the two suits of interest are spades, and a side suit (call it hearts). These are the North and South hands, as given in a bridge column.

          S AQJ
            H A65
            D Q64
            C QJ74

            S T9876
            H K3
            D 32
            C AK32

The opening lead (7 of hearts,covered by East's 9) goes to your K of hearts. You lead a low spade to the Q in dummy for a finesse, and it holds (West and East play 3 and 2). If you now play A and J of spades, you will probably lose a spade to the king, but make your contract, because your natural losers are one spade and two diamonds. On the other hand, you can repeat the finesse by cashing the A of hearts and coming to your hand with a heart ruff. Your fear is that East will ruff with the K, and then go to West via a high diamond for a ruff. In rubber, the right thing to do is to draw opposing trumps as fast as possible by playing A, then "low" (J), in spades, conceding a trick to the opposing king.
But suppose this is Matchpoints (duplicate). Given East's and West's silence, is it reasonable to assume that hearts are split  4-4 or 5-3, and that you can return safely to your hand for a second finesse? If we can earn an overtrick half the time by finessing spades again, will that "make up" for the few times that East can ruff and defeat the contract?
(The column reported that the actual declarer went to his king of clubs, the second spade finesse lost to East's king, and East reached a high diamond honor in West for a club ruff, down one, since clubs were 4-1. This, to me, is a greater risk than the heart ruff.)
The bidding was North (opener) 1NT, South 2 clubs North 2 diamonds South 4 spades. Neither side vulnerable.

You say this is from a bridge column - if so, give the entire hand just as presented in the column. Without that information I cannot give an informed pinion.  It is impossible to make an informed whole hand opinion on only half a hand.

@PieterGeerkens: Hand was added.

Now, please specify the heart spots played to the first trick, and the spade spots played to the second and third. Defenders are trying to communicate, and I really want, and know how, to eavesdrop. There is a world of difference whether West led the heart deuce or four, along with whether they play fourth best or third and fifth. I also want to know whether the defenders play coded 9's and 10's leads.

A key observation from the totally inadequate description of the hand given so far - if you are not observing and interpreting the defensive carding you are presented with you shouldn't even be asking this question. Make your contract before you allow the defenders to do something subtle to set you unbeknownst.

Also are the Defenders playing standard or inverted signals; is their primary defensive signal attitude, count or suit preference; and what are their Notrump honour leading practices?

@PieterGeerkens: West played fourth best and East encouraged on the first trick. Both opponents played low trumps on the second. The problem started on the third: At rubber, I play A, then low in spades from dummy to ensure the contract. At Matchpoints, I play A, then low in hearts to try for an overtrick. Is that right?

You don't get it. I actually read the spot cards played by the defenders; and I read partner's and declarer's spots when defending. That is what makes me a superior card player. You say the lead was fourth best, but if it was the 4 how do you know if it was fourth best from four or from five? That is critical information for how fast I am getting a count on the hand, which will e essential for any endplays I might consider.

Now what is the vulnerability, who dealt, and what was the bidding? I want to know what the defenders know or can infer.

@PieterGeerkens: I added those details to the question.

Was this hand posted on July 5, the thirtieth anniversary of Barry Crane's death. Fifth of his eleven commandments is

Sevens are singletons.

I lead low to the Club Ace at trick three and repeat the Spade finesse at trick four. Assuming it wins I then cash the Spade Ace at trick 5 and if all have followed to the second round of Spades claim making 5, conceding two diamonds only.
The heart trick is a red herring, as even if the play wins it doesn't provide any additional tricks or any additional entries.
Many partnerships will be playing Jacoby transfers to make North declarer, so we may be facing an unusual defence. I must protect that by playing to take the eleventh trick. No-one will be missing game, so making is at best average.

In the problem, declarer went to his hand in clubs (an eight card suit), and  lost a club ruff after taking, and losing the second finesse. (East went to West in diamonds.) My solution is to have declarer go to his hand via a ruff in hearts (a five card suit), on the theory that the chances of opponents' "trumping in" are smaller. And I'd take this chance only in duplicate, not rubber.

@TomAu: S**t happens. The difference in a prioiri odds is very small: 3.9% for a 5-0 break in Clubs and 2.8% for a 7-1 break in Hearts, but the actual odds are now different in hard-to-calculate ways because of the information received, and the lead made. The Heart lead still smells, and you still haven't given me the Spade spots played by defenders on the first lead of the suit. The question is a trick because you refuse to provide full information.

From the question: "You lead a low spade to the Q in dummy for a finesse, and it holds (West and East play 3 and 2)." Actually, I'm worried about a 4-1 break in clubs, where East can "trump in." But the point is, with those "slim" odds against you, you should try the second finesse in Matchpoints (but not rubber)? Or am I missing something?

Actually, you answered my question with your comment. That is, if I use hearts, not clubs, for "transportation," to my hand,  I have to worry about a 7-1, but not 6-2 heart split (I can overuff anything but the king in my hand). The chances of a 7-1 break is < 3%, so in Matchpoints, I take that 3% chance for the 50-50 chance of a successful finesse, and an overtrick. Accepted for your enlightening comment.

@Tim Lymington: I deleted my answer since your (and Pieter's) comments taught me what I wanted to learn from asking the question. But the point of the question was that a lot more risks are permissible, even ex post, in Matchpoints, than in rubber.