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In bridge, can the "rule of 20" be used outside of opening bids (e.g for takeout doubles)?
Here's another example from today's New York Post. West opened 1 club. (He had a 19 point 1NT hand, and was planning to re-bid 2NT.) North made a (takeout) double with (s) KQxxx (h) Qxxxx (d) xx (c) x, which according to partnership agreement, showed 5-5 in the majors. East passed, and South was forced to bid 1 H with (s) xxx (h) xxx (d) Kxx (c) xxxx. They went down three doubled vulnerable. East-West could have made game, but not slam in 3 NT or one of the minors.
The "rule of 20" says that you can OPEN when the sum of your HCP plus the length of your two longest suits is at least 20. That is, 10 HCP plus a 5-5 or 6-4 distribution, 11 HCP with a 6-3 or 5-4, 12 HCP with 5-3, and you need 13 HCP for a 4-3-3-3 distribution.
Here, I WOULD have doubled with  (s) KQxxx (h) KQxxx (d) xx (c) x (ten high card points plus 5-5), but not with North's actual hand (only 17).
Would you find the "rule of 20" useful in this context (takeout double, or even "unusual" NT overcall showing two minor suits)? Would you refrain from doubling even with my "hypothetical" hand? Or would you have doubled like North with a tally of less than 20? Would vulnerability affect your application of this rule?

What North and South did is not a take out double, but a conventional response to a strong club opening.
One of the most important things to do facing a strong club is to intervene, making it more difficult for the opposing side to reach the optimum contract. You don't want you opponents to relay themselves into a hard to bid (grand)slam that no one else will make.
One of the simplest defenses to a strong club is Mathe, where Double shows the majors, and 1NT shows the minors. This is the easiest way to convoy shape, so your partner knows where to intervene, or where to sacrifice.
In this particular auction it would probably be better for South to bid 1D asking for North's better major as South has no real preference, and North would be 1S.

Welcome to the site. A good answer and an upvote to get you started. Suppose this isn't a "takeout double" but "a conventional response to a strong club." Even so, would the "Rule of 20" help deter a "double" with a too-weak hand? I wouldn't double with only 7 hcp unless my suits were 7-6 or 6-6-1.

The Rule of 20 is only an opening theory, it says nothing about hand evaluation in a competitive setting. If you had an opening hand strength there are many different bids you can do. For example your KQxxx, KQxxx xx x should bid 2C over a natrual 1C showing 5/5 in the majors. Likewise you have 1d/1h/1s/1n to show hands with strenght and 2dhs to show weaker distributional hands.

The modern use of a takout double is not an opening bid. The primary purpose is an inqiry about partners hand. It is the standard pratice to show 3 suiter hands (your classic 4441 shape), monster hands (X and then rebid over partner is very strong), and hands stuck that want to do something (for example, hands that need a club stopper for 3NT. Takeout double and if they bid clubs raise to game). It can also be used for balancing.

As for when to takeout double, that depends on the context. If we are assuming that 1C is natural, 1C - X should be a normal takeout double showing (11)/12+ and a need to know what partner has. While 1C - p - p - X (none vulnerable) could be strong, or it could even be 8 points perfect shape, just trying to push the auction up a little bit. It depends on partnership agreement. Is your partner okay if you double on AQxx xx KQxx AJX planning to move to NT if your partner has hearts? If not, 1C-X-p-4H would be a disaster

Sorry for saying this, but this is a very strange question! It looks like you don't really understand the purpose of takeout doubles as they currently are played by the majority of people.
As to the specific situation you mention, you seem to be forgetting that Grue-Cheek use a strong club system, in which 1C shows 16+ any (I believe), and thus a takeout double over that needs to have a specialized meaning, like Levin-Weinstein choosing to show 5-5 in majors.
The primary purpose of takeout double is to try and find a fit, and thus the shape requirements(shortness in opp suit, support for other suits) are given precedence over the strength requirements (especially for minimum hands).
For instance, if 1C was natural, the "typical" way to deal with 5-5 majors is to use a combination of Michaels (weak + strong) and natural overcalls (intermediate hands, overcall 1S then 2H etc), rather than making a takeout double. The situation you describe is different as 1C is not natural.
The purpose of rule of 20 is to help judge whether to open or not (in the first/second seat), by trying to give some weight to long suits and is another in a long line of rules which are probably better left untaught.
Trying to use this rule to decide whether to make a takeout double is very strange and shows a lack of understanding of takeout doubles (IMO). For e.g, with long suits of 5+, you tend to overcall with most hands, and would not make a takeout double if you didn't have the right shape/strength etc.
This seems to be a case of trying to apply the wrong tool.

You're certainly entitled to your opinion. But mine is that takeout doubles require both shape AND strength. The "Rule of 20" was originated to create a "sliding scale" of "more shape, less strength" for opening bids. THAT's what I want for take out doubles as well. The "expert" went "down 3 (instead of down 2) because he had too LITTLE strength. (Unless his shape was something like 6-6-1-0).

@TomAu: Levin-Weinstein are both experts (and not "experts" :-), they just narrowly lost the Spingold yesterday). You can try applying whatever rule you want to, but in the end it is a matter of risk vs reward. As Bob mentions in his answer, trying to disrupt opponents constructive bidding, especially when they open 1C is something one should strive to do, but you should also consider the risk. There is lesser risk in showing a 5-5 weak hand, than showing a 4-4 major "rule of 20 acceptable" hand. Good luck.

(the 1C in the comment above is about a strong club)


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In Bridge, should a defender "encourage" with a "stranded honor?
In the example in Today's New York Post, the bidding went: S 1 spade, N 2 clubs, S 2 NT, N3 spades, S 4 Spades (East and West passed throughout).
West led the 9 of hearts, which as between these defenders, meant "top of nothing" in a two or three card suit,  probably looking for a ruff. With A732 of hearts, East signaled with the 7, got a heart lead to the ace when West came in with a high spade trick, and led back a heart for a ruff.
North's hearts were KJxx. Suppose East had the QUEEN of hearts instead of the ace, but the ace of DIAMONDs instead. With a supposed "stranded" honor (assuming West's top of nothing lead denied the ace), should East have DISCOURAGED on hearts and have West lead a diamond?

It depends on the hand. This question cannot be answered without looking at the East/West hands.
In general, you tend to discourage when you either don't want the suit continued, or want a shift (even though you might have something there).
You tend to encourage if you want the the suit continued  (or can stand it to be continued),  or don't want a shift. In some situations, by implication you would have a honor in the suit.

@Aryabhata disagree that you need to see West's hand, if you are actually playing as East then you wouldn't. seeing North and East's hands would be useful though, but I think we can assume that either there is a better suit or defense has no hope

@jk: Yes, the East hand, the bidding, the dummy, the scoring, the vulnerability are needed :-)

Yes I think hearts should be discouraged. Given West's lead is top of nothing then South must have the Ace and probably the ten too (if not its one of North's xs) so hearts are pretty disastrous, especially as West's lead has probably given declarer a free finesse.
Of course to really know we need to see the other suits in the visible hands (one would assume there either has to be a better suit to attack or defense has no chance)
It's also probably worth noting that top of nothing is usually a lead made when nothing better is available so we can probably infer that West has a poor hand to lead with.

If you had phrased your answer as, we really need to know the hands, but given the absence of that information, it is probably right to discourage, I would have upvoted it.

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In bridge, can "good" players get away with bidding "light"?
The conventional wisdom is that it takes 26 points to make a game. But authors such as Terence Reese have written compendiums of how they made games with 23-25 points by "outplaying" the defense; tricking a defender into a bad discard, or setting up a complicated squeeze/endplay pattern.
My understanding that the dynamics are something like the following: With 24 points, the chances of making game are about 50-50; with 26 points, 65%-70%; with 28 points, 80%-85% (mostly bad suit breaks, 5-0 or 4-0 will hurt you).
Do experts like Reese bid "light" because they can beat the above odds? Or did they blunder into contracts "light" and then find a way to pull them out.
Once I surprised a partner by making a game (3NT) when we had only 24 HCP points between us. But I had AJT9x in a key suit, opposite her Qx. After losing a trick to the king, we made four tricks in the suit with only 7 HCP, leaving 17 to make five more tricks.
I argued that the JT9 sequence was really "three jacks" and we had 26 HCP de facto, if not de jure. Could it be that experts have a better sense when "24 or "25" points are really more like 26?

"It takes 26 points to make a game" is clearly a rule of thumb, not a hard rule.  Anyone who has played more than a few hands of Bridge should be able to see that, sometimes, light hands combined with intelligent play make a contract; and, sometimes, a solid point count is brought down by a bad lie of cards or a clever defence.
I don't think any of this is at all controversial.  An expert is going to be able to read his/her hand for more than just a bare point count.  As you say, JT9 is worth more "points", in the right circumstances, than J32, though an absolute beginner may not yet understand why.  An expert is more likely to have the confidence to relish the challenge of trying to win out with a borderline hand.  An expert is more likely to have the arrogance to assume he/she can outplay the opponents, even from a seemingly unfavourable position.  If the expert bids correctly, the opponents may not even realise the cards and the points actually favour them, until it's too late!
I'd definitely worry slightly about a partner who is "surprised" by 24 HCP making a 3NT contract, I have to say!  It seems like they must still be missing something crucial in their understanding of what causes a Bridge round to be won or lost...

We play Chicago, so my partner on one set of hands is my opponent two times out of three.

also experts are more likely to have more advanced bidding systems and so will have more information in certain situations

Depending on scoring method and vulnerability, bidding games that are more likely to go down than to make may score better in the long run! At IMPs, if you have a 40% of making a game and a 60% chance of going down 1, it pays better to bid it! At rubber bridge that doesn't hold true because of the carryover from part scores.

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In Settlers of Catan (like Diplomacy), is the secret to winning avoiding "peaking too soon?"
In a two person game, one should try to make the "best moves." (If your opponent doesn't, you'll crush him unless the dice or other luck factors go very much against you.) That's not always true in a multiperson game.
In Diplomacy (which I know better), the player that goes from three to six cities in the first year becomes an obvious target. (Russia, which goes from four to six is the most frequent winner, but the second most frequent loser.) So in the beginning it's better to keep a low profile, do good but not great, let other players fight it out for half to two two-thirds of the game, and make a "run" toward the end.
Could a similar dynamic be at work in Settlers of Catan? That is, you want to do well enough in the beginning to "keep up with the pack," and yet not so well that other players see you as a threat and gang up on you? Is it even possible that bad play (or bad dice) in the beginning will generate a "sympathy" or "no threat" factor that will cause other players to treat you well later on?  And is one way is to get ahead quietly by accumulating good cards instead of good hexes?
It's impossible to pre-arrange this, but if I could, I'd arrange to have all my bad die rolls in the beginning and the good ones at the end so I could be "non-threatening in the beginning, and make a surge at the end. Are there other ways to accomplish this in the game?

I often write that it depends on the group, but I think that's especially applicable here. If you are playing against computer AIs for instance, of course you want to maximize your VPs at every step.
In general, though, I don't think it's wise to sandbag in Catan--or to inwardly cheer bad luck. In the worst case scenario, aggressive Robber usage and trade embargos will hold you back until someone catches up with you. At that point, you can earnestly point out that you are no longer winning. Even if you're the obvious leader, as long as you have no more than 6-7 VPs, you can often arrange a mutually beneficial trade with someone desperate enough for what you have to break the opponents' embargo.
Additionally, having a powerful position gives extra resources, which can help you forge ahead or expand a lead, even if the other players are trying to stop you. If you plan to take an early lead, I think it's definitely better to go for cities and settlements, not Longest Road. Definitely avoid going for the Longest Road early in the game, until you either actually need the road, or the 2 VP are close to mattering to decide the winner. Having the card paints a target on you as a leader, and distracts attention from other possible leaders, but doesn't help you generate any more resources. Another worry is getting two cities off the gate (maybe with an early ore/grain settlement placement) but being hemmed in without a decent third building site opportunity.
I've seen players try to stay at 7 VP and hoarding resources until they can make a big break by taking Longest Road and building 1 VP worth of stuff in the same turn. It's sometimes worked, but sometimes fallen flat as savvy opponents can look at the resources you've been gathering and guess what your opportunities are. And isn't the point of pondering strategy to prepare for savvy opponents?

+1 for Points on the board being better than theoretical points (Longest Road, Largest Army, Dev Cards)

I have also noticed that it sometimes hard to redirect players from the early leader in a Catan game.  I also agree that points on the board are more important then longest road but largest army is hard to steal once someone has claimed it and hard to know what people have in hidden dev cards

One thing to bear in mind is, even if you are in the lead, will an opponent want to place the robber on your hexes? One way to avoid this is to try to share hexes with other players. A city on an 8 ore is a good robber target, but if 2 other players are also on that ore they aren't going to want to place the robber there.
Cards like largest army/longest road can be counter-productive if they get you a large point lead, but you lack cities/settlements to keep up with the other player's production. Getting early settlements are never a bad idea though; better to have 2/3 hexes from a new settlement with 1 blocked from the robber than 0/3 from not having it and no robber!

Yes, this is very often the case.
In many instances, opponents will go after the player who has the most visible lead in victory points on the board, that is settlements, and cities, and longest road. In this case, the trick is to hide your strength by buying development cards instead of the more visible items.
Each development card is worth about a victory point (on average), but many players don't know this. Some development cards are exactly one victory point. Other development cards give you the equivalent: a road building or progress card is worth slightly less than one victory point, a monopoly card quite a bit more. Knights hard the hardest to judge; you need about four of them to get largest army and 2 development points, but they give you other advantages like saving you resources and helping you steal some from opponents.
Another possibility is to produce large quantities of a less strategic resource such as sheep or wood. "Everyone" knows that one sheep is worth less than the equivalent amount of any other resource--until you build a sheep port and trade sheep at a 2 to 1 ratio for what you need. At that point, "quantity becomes" quality but many opponents will not realize this.
Another issue is that bad hexes are so only ex ante. If you have been getting a disproportionate amount of a critical resource from 2, 3, 11, and 12 hexes, people may look at your "board" and say that you have a bad setup without realizing that you have already reaped the benefits of "lucky" dice.

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Is "Longest Road" an overrated strategy in Settlers of Catan?
At one level, "longest road," is an "obvious" way to win the game.
At another level, could it be too obvious? That is, a player clearly pursuing this strategy might stir too much fear in opponents, who will then try to break up the road, or hamper him in other ways?
Also it requires an abundance of certain materials, namely wood and brick. Could a single-minded focus these materials hurt a player's game in other ways?
Is there a "better" way to build the longest road, i.e. build settlements with "short" roads some optimal distances apart, then connect them "naturally" toward the end, when opponents' attentions are focused elsewhere?
Do people in your games use a "longest road" strategy too much, or conversely, "too little?"

This might be a little too open-ended...

It's definitely a strategy that is compelling to the novice.

Like many great games, Settlers of Catan rewards those players who are willing to be adaptable.
Doggedly centering your strategy, from the beginning, on obtaining wood and clay (to the exclusion of other goods) and building road after road with it, is likely to secure you a certain number of victory points.  That number is nowhere near enough to win you the game - you're going to have to do other things with your time and resources at some point to clinch first place.
Does the Longest Road bonus incentivise road building?  Of course it does, to some extent, just as the Largest Army bonus incentivises buying cards.  What it mostly does, though, is ensure that there is competition in various areas of the game.  If only one player cares about roads, the Longest Road bonus will fall to them without any effort on their part.  Likewise for Largest Army if only one player is bothering to buy cards.  However, gamer psychology is such that, given an obvious bonus to be obtained, players will not be able to bear letting it go easily, and at least some of them are likely to compete vigorously for it.
As such, I see the Longest Road bonus less as "a strategy" and more as a nice little, well, bonus... if you're brave enough to enter into a competition with other players over it.  Competition is necessary for a game to work, but it can, as you rightly point out, paint a general target on your forehead, or make enemies of specific other players.  If that's not the type of thing you like to get involved in, you might indeed want to adopt a more surreptitious strategy.
Certainly I would tend to prefer not aiming for the Longest Road early: let other people set themselves up as "the one to beat" by gaining an early lead.  Keeping an eye on the road situation, and perhaps setting yourself up to win with a late road-building spurt, is great though.  As I say though, adaptability is key: if everyone in your group fancies themselves as road-builders, it's a very risky strategy.  If no one else is doing it... you'd be a fool not to pile in there as quickly as possible, really!

It seems like the best strategy then, is "hit them where they ain't."

I think Longest Road gives a player who happens to have an abundance of wood and brick late-game a way to convert those resources into VPs, and deny those same VPs to others. It also rewards players who have built several settlements and built their opening settlements near each other, and slightly discourages shooting straight for cities--not that shooting straight for cities isn't still a great strategy if the appropriate resources are available.
Going for Longest Road before the player has at least 6 VPs from cities and settlements is probably a waste of resources in most cases. The opponents can make more valuable resource investments in the short term and fight for Longest Road later.

Longest Road, while usually important to victory, is not worth pursuing to the exclusion of other elements. It's only 2 of the 8 additional victory points needed (remembering that it's a race to 10, and you start with 2 already).
It is, at best, 1/4 of your victory. Largest Army and new cities are likewise equally important.
For my own play, I've found that it's best to simply concetrate on getting the resource base you need, and then use longest road as a means to snap up the last 2 VP, rather than worth direct strategizing about... quite unlike one's establishment of settlements and cities.

There are two main winning strategies. Longest road is one of them. The largest army is the other. It's possible, but difficult to win using an assortment of other benefits. Let's say the ratio is about one-third, one-third, one-third for road, army, and other.
"Road" and "army" also correspond to two basic playing styles: Expansion (using wood and brick) and development (using wheat, ore, and to a lesser extent, sheep). Basically, you go for longest road if you are wood and brick heavy, and largest army, if you dominate the other three resources. The downside of always playing for longest road is that you don't get to use the other, development, style of play.
There is a warning that "correlation does not equal causation." It's true that "longest road" often wins, but that is a reflection of the fact that the longest road builder is also dominant in the wood-brick activities. For instance, you should build settlements at the minimum distances apart from each other along the road so your opponents don't break it up. And you should build roads to "2 to 1" harbors for brick and/or wood so that you can trade these goods for the ones you are short on. If you don't do these other two things, "longest road" won't do you much good.


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In Settlers of Catan, what are ways to "hide" your strength until the end?
For instance, is accumulating cards less visible/threatening than accumulating resources, settlements or roads?
Conversely, is building "basic strength" (e.g. settlements and cities) less provocative than going after a single resource? Yet could this be more effective (because it allows you to pursue multiple resources) than obviously trying to "corner" one?

Hoarding developments cards is a great way. Here's a few specifics on that, along with a few ways that don't involve development cards (note that you usually don't want to exploit your hidden strength until you think it will propel you to victory):

Hold off using a Monopoly card even if you get it very early in the
game. Wait for exactly that right moment when there are many of one
resource that you can monopolize and efficiently convert into several
settlements/cities/dev cards.
Hold off using a Road Building card until it results in you getting
longest road and a new settlement all on the same turn.
Hold off using a Year of Plenty card until you happen to have a card
combo in your hand where employing it results in a 3 victory point
turn.
Have a couple roads that go off to horribly unproductive locations -
but are nonetheless potential settlement sites. Many people
automatically assume you'll never build there - but you will on the
turn it vaults you to victory.
People often have no clue that you'll have longest road with
just 2-3 more road links closing 1 or 2 loops. Do this on purpose,
particularly if you have a hidden road building development card.
If playing with the Seafarers expansion, have extra ships available
that you will eventually use to build a surprise settlement, or
better yet a surprise settlement on a new island that gets you a
victory point bonus, or best of all combine with leaping to longest
road. But of course try not to make it obvious you're planning this.

Of course, if you have a hand of 7 unplayed development cards, you will be greatly feared so all the hidden strength tactics involving development cards work best when you have 2-3 unplayed cards.
Perhaps the most important hidden strength:
Gear your initial settlement placement and early building towards the end game. In other words - go for ore and grain, with a little sheep thrown in. You will fall behind in the beginning but so long as you get at least 1 additional settlement, you'll have no problems towards the end of the game while others stall out. Taken to extremes, it's possible to win with only 2 settlements, as I did here (nobody realized how strong I was until the game was just about over - those 15 development cards were all mine, though I didn't have enough turns to play them all!):

That's the only thing that (sort of) worries me about this answer - a big stack of development cards is all very well, but holding them all up until the "optimum" time may not leave you enough time to play them all!  In general though I endorse this answer, development cards are a strong way to conceal the true strength of your position.  You have to watch out though that you aren't playing with the sort of opponents who think "hmm, he has three development cards I don't know what they are - better count him as being 2VPs better off than he seems to be" and attack you :D

@thesunneversets I agree with you that sharp players will be wary of a good player holding 3 unplayed dev cards. That's why you need a big bag of tricks. Note that 3 of the items above don't involve dev cards (4 if you count the seafarers tip).

Hold a Monopoly card. Most opponents will assume it is a VP card, but played at the right time you can use it to create a huge turn.

One way to do this is to have a disproportionate number of rolls come from sheep hexes connected to your first two settlements. The reason is that sheep is the least valuable resource under most strategies, and therefore least likely to attract the robber (all other things being equal). This strategy works best if you you can build on the sheep port with your third settlement.
Because of the above, your early development will likely be slower than those of other players with more strategic resources. This disadvantage will disappear, once you build the port and trade sheep at 3 to 1, or better yet, at 2 to 1 for the sheep port. At that point, you will be in as good as, or better position than others to trade for scarce resources, but they may not realize this if you fell behind them in the early game. So this is a good "come from behind" strategy.


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In bridge,should a responder devalue her hand if short in opener's suit?
I opened a "strong two clubs." Partner bid 2 NT, which between us, meant "9-plus points, slam interest."
I bid my suit, 3 spades, with the following: (s) AKQxxx (h) AKx (d) Ax (c) xx. That's a 6-card suit with 22 points (20 in high cards, two more for the minor doubletons).
Responder bid 4NT, and we ended up in 6 Spades, which went down, because my left hand opponent had JTxxx of spades.
Partner had: (s) x (h) xxxx (d)Kxxx (c) AKxx.
She said, "I had 10 HCP, 12 counting the spade singleton. That, with your 22 should mean a small slam."
My response was, "Spade singleton" was the whole point. You should have downgraded your hand when you  heard 3 spades, because you didn't have normal trump support. If you had xxx or Jx, the contract would probably have been made."
Should partner had "downgraded her hand" and refrained from bidding the slam with shortness in my spade suit?

Seems like you just got hit by a bad trump split.  3-3 or even 4-2 probably would've made the contract even with partner's singleton.

"Bidding your suit" typically means 4 or 5 card length.  Because of that, I would expect the bidding to go more like this:
Partner sitting there with one card in that suit would then respond with their suit (4C in this case), which denies support for your spades and shows that clubs is their best suit.  The new suit bid is forcing, so it's now back to you to decide what to do.  Partner doesn't have your spades, but you can rebid them since you've got 6 of 'em.  If you really want to you can make a NT bid, since partner should have your one weak suit covered.  Whatever you reply with, partner has a chance to correct if they're significantly over the 9+ they've promised.  With the length you've got, a spade rebid is valid and 4S should be a solid contract.  After that you each have to decide if you're going to go to Blackwood and look for the slam possibility.
Sure there's interest in slam, but there's no 8-card fit.  And the bidding should show that.  Someone has to make the call as to whether or not to go there, and at what point the bidding stops.  That's whoever makes the Blackwood bid.  With an even split, you get it.  Without, you don't.  As long as the player making that bid understands the risk involved and wants to go for it, it's all good.
If both of you understood the danger you were getting into and the possibility of a bad split ruining it all, then I can't say you've got any problems in the bidding.  If on the other hand someone thought the slam was solid, then I'd say that your bidding needs to be a bit more descriptive.
In specific though, YES, there are two specific situations where shortness doesn't give ANY points:
1) In the trump suit
2) In a NT contract
And that's one of the more reliable rules in bridge.  8 )

I don't like 4C at all. Responder has a nice easy 3NT because 2NT showed all the values he had and he doesn't have his own suit nor spade support. However, I agree with @woodchips that responder's first bid should have been a waiting 2D.

@ruds: I don't have a problem with 2NT. But the narrative above was "modified." What REALLY happened was that partner heard "2 clubs" and bid 4NT (Blackwood) with "12" (ten plus two for the singleton), and we landed in six spades. I said, "I wish you had limited yourself to 2NT, let me bid 3 spades, and then made a decision between 3NT and 4 spades with your one spade." She said, "That's not the issue. I had 12, you had 22, we had 34, small slam." As Americans, we are both aggressive bidders, but one more than the other.

Well, there's the flaw in understanding right there.  34 is certainly enough for a small slam; in NT or with a trump fit.  You weren't in NT, and you didn't have an 8-card trump suit.  The primary concern is finding the fit, and going straight to 4NT takes away all the room you should be using to do so.  Applicable bridge rule: "When there's no fit, QUIT."

@Task: Actually, only (1) is a reliable rule of bridge. Reread boring old Goren again closely, and you will note that his 16-18 point notrump range includes +1 point for a doubleton if held, and -1 point for a 4333. Though few realize this, good old Goren actually invented the 15-17 HCP point notrump long before modern bidding theorists made it popular in the 60's and 70's. In traditional Goren, the points counted for shortness are actually measuring the power of the additional long-suit length, not ruffing power, for which he added additional points after finding a trump suit.

While the long-suit length is certainly valuable, and long-suit points are interchangeable with short-suit points, you'll note that it's actually the length and not the shortness that is valuable.  Shortness doesn't give any points in NT.  Length can, yes, but shortness is technically valueless in NT.

The Blackwood convention is often misused, or perhaps just misunderstood. The bidder needs (among other things) to be sure that there are twelve tricks available; normally this means the trump suit is 5-4 or better (my dog-eared Bridge manual says "4NT is not definitely Blackwood unless a trump suit has been agreed" but that is probably too extreme nowadays).  If your partner knew that the contract would be in spades, the singleton is a minus rather than a plus, so you don't have the points for slam.  There could be a slam elsewhere, of course. in which case the two 'phantom points' could reappear; but she has to bid a suit (probably 4C) before you can agree the level.


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Can a takeout doubler pass a redoubled contract?
South opened one diamond. West doubled for takeout with the following hand:
s) Axxx (H) Kxx (D) Kxx (C) Qxx
North redoubled. This took me (East) off the hook with something like s) xxx (H) xxx (D) xxx (C) xxxx. I could pass, because the redouble allowed West to bid again. She bid one spade, we were doubled, vulnerable, and went down four (-1100).
Could she have left in the redouble by passing? One diamond redoubled does not make game, although it makes a ton of overtricks. Even so, would the likely loss have been less than -1100 or even -800?
Or was the problem with the takeout double in the first place.

1D redoubled making 4 is 830 non-vul and 1430 vul according to this (excellent) calculator: http://www.rpbridge.net/xsc1.htm.
Redoubled overtricks count!
Partner should bid 1S. 1S double going down 4 with a probable 4-3 or better fit (LHO or RHO both didn't mention spades) and two Kings seems quite unlikely, and that is against opponents for whom double of 1S will be for penalties. It is probably more useful to play 1S double (by LHO) in this situation for something else (LHO cannot have a trump stack), in which case, you have even more reason to bid 1S.
In this case I would say the problem is with making the takeout double in the first place. (Of course it depends on partnership style and form of scoring, but the below can probably found in most textbooks).
There is a rule of thumb regarding takeout doubles: With a 12-14 hand balanced hand, you should avoid making a takeout double.
In this case you have a really flat hand, 4-3-3-3, with three cards in the takeout suit. Your hand is defensively oriented with likely 3 defensive tricks in your own hand.
If you make a takeout double and partner jumps to the three level in your 3 card suit you will likely go down.
Another reason to pass with 12-14 defensive oriented flat hands is that if you have a game, LHO will likely pass and partner will get a chance to reopen.
And to answer the question in the title, sure, a redoubled contract by the takeout doubler can be passed, but it is probably a bad bid.

Can't argue with this good analysis, +1!

Vulnerability affects overtricks as well as "going down?" I didn't know that. Or is it just overtricks when doubled and redoubled? Is this a relatively modern change? I didn't get any of that when learning bridge in the 1960s.

@TomAu: I believe it is one of those modern changes.

I think I "downvoted" you by mistake! (Clicked on the wrong button while accepting you). Could you edit your answer so I can correct and upvote you?

@TomAu: Coincidence! I was just editing the answer to mention that form of scoring might matter :-)

I "fixed" my vote.

@TomAu: I also fixed the link to the calculator.

I don't think there's anything wrong with attempting to bid one's "best" (least worst in this cae) suit after one's takeout double is redoubled.  It was unfortunate that this resulted in a terrible contract, but this is Bridge, bad breaks can and do happen.
I suppose the question is whether West was sensible to opt for a takeout double at unfavourable vulnerability. Again, I'd say that while the risks are obvious if East turns out to be holding nothing, 12 points including an ace is not obviously a terrible hand to try one's luck with.
As long as West was aware of the risks, just accept that things went tragically wrong and move on.  After all, the alternative is to risk an irate partner (in a parallel universe, holding much better cards) demanding in the autopsy "why on earth didn't you make a takeout double on that textbook hand?!"

If partner has a much better hand, and it gets passed out. West should be the irate one: "Why not reopen partner?". FWIW, it is a textbook hand alright, but as an example of when not to make a takeout double.

(Of course, we are probably reading different textbooks :-))

Yeah, it's a good point that this takeout double is not ideal. Having fewer than 3 diamonds would make it a lot better. Maybe I should have called it a "textbook highly marginal takeout double hand" ;)

The takeout double looks reasonable - enough points and support for the other 3 suits. It does of course depend on what you've agreed in your bidding system, some systems would require a shortage of the doubled suit (2 or less).
As far as leaving it in one diamond redoubled vs bidding one spade, with the information your partner has to go on it's impossible to say for certain which will lose you more points. I'd definitely go with one spade if your opponents are vulnerable and probably pass if they're not.


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How to identify when to try a "Merriamac Coup" in bridge?
A "Merrimac Coup" in bridge usually refers to the "suicidal" lead of a king, in order to force out an opposing ace before the opponent is ready to use the ace as an entry. If that hand (usually dummy) is short of entries, this might cause "transportation" problems in establishing and cashing a long suit.
Suppose I can see that dummy has a broken long suit, and a side ace. Would this be a good time to try the Merrimac Coup?
Suppose I am the opening leader, with a king. Are situations based on the bidding and my holding where I should try a Merrimac Coup before seeing dummy?
Are there situations where declarer was originally a responder, and might be short of entries, so that I should try a Merrimac Coup into the "closed" hand?
And can there be a Merrimac Coup with a card other than a king? Suppose I have A-Q of a suit as opening leader, lead the ace, and see a king  (plus a long suit) in dummy. Would the lead of the queen to dummy's king constitute a Merrimac Coup?

It really depends. If you think declarer hasn't got enough tricks after your sacrifice of the K, and would absolutely need to establish dummy's suit, then yes, you could try it.
It is theoretically possible to execute the Merrimac on the opening lead, but the situation would probably be very rare. I haven't seen any, but I suppose given some time, we can cook up an example.
Yes, Merrimac can also be done on the closed hand, if you have a good enough read of the hand (which you should strive to, in any case).
And yes, using the Q to knock out the K can also be termed as a Merrimac Coup.
Not sure if I answered your question.

Pretty good answers to the question. Looking forward to more advanced examples (e.g. on opening lead).

Merrimac coup is not just for defenders. Declarer can do it too. Supposing one opponent has preempted at the three level and your partner doubled and you bid 3NT holding two covers in the preempt suit with say AKx. Naturally they lead the preempt suit. You have a suit race- do they set up their long suit or do you set up all your tricks. You hope that the preempter has a particular ace or something like that holding Kx versus J10xx, you lead the king hoping that preempter has either to cash his trick or just surrender and let you keep the trick so you can add others in other suits to make game.
You can guess to have to do the Merrimac Coup for closed hand say the bidding goes 3C,-,3H,-,3NT, all pass. You have one stopper in clubs (or else you hope partner has a stopper) and then you or your partner wins the lead (unlikely for there to be chances any later than the first trick. Dummy has two suits covered well and a third suit not well covered. The third suit is the one you lead as its likely the closed hand has the entry to knocked out.This assumes that the long suit (clubs) is not immediately run-able- e.g. missing an ace or a king offside.


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In bridge, are there some 13 point hands that should not be opened?
Suppose you have: (s) Jx (h)KQxx (d) KJxx (c) Kxx.
That's 13 points, by the usual count. But I can think of at least two things wrong with it.
First, there are no aces, meaning that the hand has fewer "quick tricks" than the usual 13-pointer. Second, the Jack of spades is "stranded," meaning that might not be worth a full point because it can be picked off by the opponents. And, of course, there is no five card suit, meaning that you need 13, not 12 to open.
Do the above negatives detract from your hand? Or must it be opened since you have 13?

Standard American?

@JoeGolton: I use mainly Standard American. But sometimes "bend" the rules.

While it doesn't make a huge difference, you having a stranded jack at least means the opponents don't have it. At the very least it means your opponents' hands will be slightly weaker.

Hands like this are why Barry Crane played 4-card Majors. Link: http://bridgewinners.com/article/view/barry-crane-bidding-system/

Assuming Standard American (5 card Majors), I'd open this with 1 diamond. If partner responds 1H you can raise to 2H to show how weak you are. With partner bidding 2D you can pass.
What's tough is when partner bids 1S. I personally would rebid 1NT because it best communicates the hand. It denies Spade support, communicates the point count, and truthfully expresses a stopper in every suit but spades. And it does not deny having a 4 card heart suit.
To your general point, yes there are 13 point hands that are better off passed. Two kinds:
1) 3-3-3-4 distribution. This is the worst possible shape for a hand - not just for trump contracts but also for no trump contracts, especially if the 4 card suit is weak.
2) 4-4-3-2 distribution where both 4 card suits are minor and the points are scattered around, with no solid suit anywhere (Note: if you swap the clubs and heart suits in your example, that would fit this template and I would pass).
I do this not because some book says so, but because I've gotten into trouble bidding such hands far too often. Both of these types of hands are better for defense then offense.
In the event your partner has 13+ there's no risk of being passed out of a game - and if you're partner has 12 or fewer than you'll more often then not find that the zero score you get after the hands are passed out is better than the down 1 or 2 you would have otherwise achieved.

Might be worth noting that, while 2D is passable in Standard American, it's fairly common to show 2d as the stronger bid (inverted minors) - so if you're playing with me, with my usual conventions, and pass 2d, expect some complaining afterwards!

Sure the JS is a fairly pointless HCP, but the spade shortness is worth something in a trump game.
It's the kind of hand that should definitely be opened, but only at the 1 level.  The point of opening the hand is to let partner know you've got something, at which point you're looking for a 4-4 heart fit.
So in my opinion the hand should be opened, a heart response from partner should be supported, and a 'pass' is the probable response to all non-forcing circumstances.  The biggest danger I can see in this hand is falling into the "use NT as an exit if nothing else works" trap instead of following the "when there's no fit, quit" rule.
Advertise what you've got, and let partner decide if there's any game here.
Well, that's how I read the hand at least.
Additional:
Now to carry on to the more general question, could there possibly be a hand that technically should be opened, but in fact really shouldn't be?  Sure there is, but it's important to note that it's all dependent on the situation, and not the hand.  The main point of opening a "weak opener" is to let your partner know that you've got the points; it follows that the time to NOT open it is when partner doesn't care.
When does partner not care what you've got?  When they don't have a hand good enough to do anything about it.  When can you know that's the case? When the situation makes it obvious!  For example, when you're in 4th seat and LHO and RHO have both bid.  LHO obviously has 13+, RHO has 6+, you've got 13, your partner can't have much to talk about; there just aren't enough points in the deck.  When the situation tells you something like that, then you know it's time to sit in the weeds and help the opponents dig themselves into a nice deep hole.
In general, yes, you should open a 13 point hand.  Because your partner might really want to know.  But there will be situations (not hands, situations!) where you shouldn't bid.
Like all good rules in bridge, you have to know when the rule doesn't apply.

I don't think there is such a thing as a hand that must be opened, of course if you deceive your partner too much they may stop playing with you.
In general I'd open 1nt (assuming weak nt) with this hand even without the J so certainly with. The only occasion I might consider passing is if I'm in the fourth seat and partner has already passed, even this is likely to depend on score/vulnerability at the time.

I'm more concerned about telling partner the "figurative" truth, rather than the literal truth. By passing, I'm saying this hand is basically weaker than (s) xx (h) xxx (d) AKJxx (c) Axx, even though the latter has only 12 HCP (but three quick tricks). I play a strong no trump.

I find this question amusingly old-fashioned.
I don't know any top player who wouldn't regularly open in 1st and 3rd seat
(s)xx (h)KQxx (d)KJxx (c)Kxx
or, looking at your comparison hand, I don't know any top player who wouldn't open in 1st and 3rd seat
(s)xx (h)xxx (d)AKxxx (c)Axx
It's simply way too valuable to get in first with a bid to disrupt the opponent's bidding and help partner figure out what to lead on defense.  Letting opponents have lots of uncontested auctions is a losing strategy unless their bidding is bad or your play is so superior to theirs that you have them beat anyway.  You can reasonably safely jump in with either hand, and your partner might not be able to.
(Both hands are passes in 4th seat because of the weak spades.  2nd seat depends on vulnerability and maybe a better read on the opponents' abilities.)

Have you not heard of the "trap pass." I was taught to "pass" with an opening valued hand containing, say KJxx in RHO's opening suit, and to "trap pass"  13 points as opener with "broken" values such as KQxx, KJxx,and Kxx, because one opponent may have AJxxx or AQxxx in those suits, and I want to find out which one before I bid. I would open with s)xx (h)xxx (d)AKxxx (c)Axx because the aces are really worth 4.5 (per my answer) and the hand is worth 12 hcps, not 11, In my other example, I would pass with (s) J6 but open with (s) JT because the latter  represents a "sequence".

Yes it would be good to know if LHO has one of your suits, but not at the price of having to enter the auction one level higher.

Just for your education, Tom, you should try playing against one of those bidding systems designed around being able to open hands like (s)xx (h)AQxx (d)xx (c)QTxxx.  (Moscito is one example.)  Unless you learn an appropriate artificial defensive system to counter it, you'll find that you collect a few juicy penalties but lose far more in missed games and slams.  (In fact, such systems are banned from competitive play in the North America because the ACBL thinks players should not be forced to learn to play against them.)

These systems (e.g Moscito) allow opening with as little as 9-10 points (your example hand has 8.5, allowing 0.5 for the T), relative to your statistical average of 10. I was taught to open with an above average hand; 13 hcps with four of a suit, 12 hcps with with vie, 11 hcps with six (or 5-5-2-1 distribution), 10 hcps with 7 (or a good 5 with good distribution). Is the modern theory that the "first bid" is so valuable that it is worth opening with an inferior hand such as s)xx (h)AQxx (d)xx (c)QTxxx.

@TomAu: The jury is still out.  All I can say is that I wouldn't want to play against Moscito without a special system for distinguishing between weaker and stronger overcalls.  But what you were taught is generally considered close to a point too heavy these days even for Standard American.  I suspect you first learned at a time when people still said 26 points were necessary to bid game; simulations have firmly concluded that 25 is enough.

Points are sometimes misleading. You can "make" with 24 and e.g. a good five card suit, and you can "miss" with 27, flat distribution (e.g. 4-4-3-2 opposite 3-3-3-4) and all finesses wrong. Which is why I don't open with a highly "finessable "13. (I count 3 in the example hand.)

Finesses work half the time.  Games that make half the time ought to be bid.  (Games that make 40% of the time should be bid vulnerable at IMPs.)  Missing game/rubber bonuses is just as costly as getting set.

Most 12 point hands should be opened (one of a suit). The main exception is 12 hcps with a 4-3-3-3 distribution. Such a flat distribution reduces the value of the hand by one point to 11. Other exceptions would be where there are "quacks" (queens and jacks) "stranded" in a doubleton or singleton (also kings in the latter case), that are not pulling their full weight. Barring this, a hand as weak as KJxx KJxx KJx xx can be opened.
In the case of a 13 point hand, I would need either stranded honors or the flat 4-3-3-3 distribution plus another negative not to open. A hand like this might be QJx QJx KJxx QJx. Here, the second negative is that you have no aces and only one king. Even though the point count is nominally "13," it's more like 11 to 11.5 after the two above negatives. And even then, I would open one of a minor if the KJxx were in spades, because you have the "boss" suit under the rule of 15 (an adjusted 11-11.5 points plus 4 spades).
Make one or more of the x's a T, and I would open with 13 points and the 4-3-3-3 hand above. In your example hand, I would open with a 4-4-3-2 distribution and 13 point count. Reduce value of the Jack of Spades to 0, making the hand worth 12 points, and it would still be worth opening with a 4-4-3-2. Although you have no aces, you have three kings (more than your "fair share" of "two aces and kings"). Also, the Q and the second jack are well placed behind your kings.

Many players adjust the original high-card point count from Milton Work's 4-3-2-1 system. I, for example, discount singleton kings and doubleton queens and jacks.  I also add points for long suits, one point for each card beyond 4. I also discount unsupported honors known to be under an opponent's suit, and thus likely to be finnessable. (That would not apply at an opening when nothing is know of an opponent's holding). I also tend to somewhat discount a flat hand, and an aceless hand.
So given the example hand (s) Jx (h)KQxx (d) KJxx (c) Kxx.  I would rate this as a bad 12, discounting the Jx totslly, and noting the flatness and acelessness (if I found a fit with partner, i would add for the spade shortness, but only once I had a fit.) I would probably open this with 1D if not vulnerable, and might or might not when vulnerable, in 1st or 2nd set. (I would always open this in 3rd, and I would never open this in 4th seat.)
However, given a hand such as:
(s) Qx (h)KJxx (d) KJxx (c) Kxx.
I would be much less inclined to open. There are really only 11 working points here, and it is flat and aceless. There is no concentrated strength. This looks like a good supporting hand or a defensive hand, so passing and seeing what develops might pay off, especially vulnerable against not.


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In Puerto Rico, how do you tell whether it is better to trade or to ship a good?
How do you choose between "trading" a good (locally) and shipping it (abroad) when the two actions have rather different reward structures?
How do the relevant roles you might play (craftsman, captain, trader) affect these choices?
Of course, if you have a warehouse, that gives you a wider choice of whether to trade or ship, and whether to do so this turn or in the future. More to the point, how do you decide, "I need to buy a warehouse THIS turn, for 1-2 turns down the road?"

Don't forget that, when a shipping phase occurs, if a good can be shipped, it must be shipped.

@That's a good point. Is that why Player 1 should choose to Captain on turn 2, to force his opponent to ship for one VP instead of trading for two coins in this strategy piece?http://boardgamegeek.com/thread/13812/the-039best039-puerto-rico-strategy-startegy-amp

It depends on several factors that ultimately boil down to What is the roles overall value?

Is it the early game? - In the early game, it is usually more important to gain coins than VP. The reason for this, is that you can exchange coins for buildings that will gain you more coins/VP over the course of the game than you would earn this turn by shipping and taking the VP. Until you have your coin generating buildings setup, usually consisting of a high value trade good/large market/factory, coins are usually of greater value. Some of the expansion building make this distinction moot (Black Market).
Do your opponents make more Coins/VP because of your choice? - Usually, in Puerto Rico, you want to make decisions that benefit you more than your opponents. If choosing Trader will benefit your opponents more, you might want to Captain instead (or select some other role). The few times you might select a role that doesn't seem to immediately help you relative to your opponents, is when you are denying them access to the cash necessary to buy some building (Guild Hall pops up a lot here), or denying them shipping on a large boat (they have lots of corn and you take a large boat and possibly tie up all the boats from emptying).
Does the role have a coin on it - I will many times take a role card that has a coin, because all I need is that extra coin to buy a building I want during the next building phase.

To answer your specific question "Do I need to buy a warehouse THIS turn, for 1-2 turns down the road?" here are my informal steps for evaluating.
How many and how many types of goods are you producing?  How many and how many types of goods are being produced by others?  How many Warehouses are left?  What is the opportunity cost to buying the Warehouse?
If you are producing few goods and think you will be able to ship and hold onto what doesn't ship in the next round you can hold off.  You can begin planning for a Warehouse purchase and minimizing the hit to your doubloons (i.e., pick up a Quarry, select Builder, Trade what you fear might not ship).
If everyone (including yourself) is producing only enough different types of goods to fill the available ships you need to look at quantities and decide if you will be able to fit your goods onto one of the ships.  If you are producing a different good than everyone else and can get it on a ship so that you have guaranteed space for a round or two you don't need a Warehouse immediately.
Small Warehouses are a scarce resource, in the sense that there are not enough for everyone to get one.  Large Warehouses cost significant Doubloons and in games I have played I don't ever recall them all being built.  Do you think other players will build the Small Warehouses so that you will not be able to?  If so build now.  Also, there is an opportunity cost in terms of denying or not denying another player the opportunity to build a Warehouse and store their goods.
I have noticed (and we've talked about it in my PR group with mild consensus) that it is easier to make a decision to buy a Warehouse earlier in the game than later.  It seems tied to the opportunity cost.  Early in the game choices are limited by what can be afforded so it seems less a sacrifice to buy the Small Warehouse.  Later in the game it seems as if that higher priced building is more desirable because I've been working toward it so putting off building it to build a Small Warehouse is tough.  I tend to try to buy a Small Warehouse early in the game.  Sometimes I never need it, sometimes it saves me a lot of otherwise lost goods.  The upside of the situation where it is built but never needed is that you get the points at the end of the game.  If you build City Hall the Warehouses are violet buildings and will add points that way too.

In the beginning, you need money to invest, so the emphasis is on trading, which generates money. Here, you would want to use the trader and craftsman, all other things being equal.
Later in the game, as it gets closer to the endgame, you are after victory points, so unless you are a builder, the emphasis is on shipping, which generates victory points. Here, the captain is your friend.
There are some other considerations. All goods earn an equal number of victory points when shipped, but some goods are more lucrative than others when traded. In descending order, they are coffee, tobacco, sugar, indigo, and corn. "Comparative advantage" dictates that you want to ship corn more, and trade more coffee.

"derail your opponents' strategies by forcing [them to] trade when they would rather ship" How exactly do you force a trade? I am not sure I agree with your analysis of the beginning and endgames. While it is true that the beginning is focused on money, I don't find that craftsman/trader have a higher selection rate than other roles (many times, the coins on the role cards is where you will get early money). Similarly, I don't think the endgame focuses on shipping. Certain players (building strategy) would prefer if no shipping was happening.

@user1873: "How do I force a trade/" Maybe I was confused buy reading this strategy guide (the passage about "o captain, my captain"). http://boardgamegeek.com/thread/13812/the-039best039-puerto-rico-strategy-startegy-amp I deleted that passage. I also edited paragraph 2 to say, "unless you are a builder, the emphasis is on shipping, which generates victory points. Here, the captain is your friend." Also, the OP was trying to draw a contrast between trading and shipping, leaving building out of the equation.Between the two, shipping becomes more important than trading toward the game's end.


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In bridge, does it make sense to "tighten" or 'loosen" up on bidding depending on vulnerability?
For instance, the minimum standard seems to be about 12 points to open with a five card suit, or 13 points with a four card minor. That makes sense with equal vulnerability (both vulnerable or both not).
Suppose you're vulnerable and they're not. Are there players that would pass 12-13 point hands, needing 13-14 points (depending on suit length), because of the greater penalties for going down.
Conversely, at favorable vulnerability, (they are, you're) not, would you shade your opening requirements down to about 11 points to try to catch up?

Yes, totally it does.
Let's think about the game of Bridge clearly: what is vulnerability?  Why is it part of the game?  It can't just be that at some arbitrary times you score n points for pulling off a tricky contract, and at other times, for no particular reason, you score n*3 instead.  That would seem a pretty random feature.
All vulnerability is, to my mind, is a way of stipulating that there are designated times during every game of Bridge where taking risks is penalized less heavily than at other times.  A good player will know that it's worth pushing your luck to its limit while non-vulnerable, and playing it safe while vulnerable.
Bidding all your auctions "straight down the line" without any variation based on vulnerable or non-vulnerable status just doesn't make any sense to me.  If you think that way, then the scoring becomes a matter of random factors that sometimes really benefit you and sometimes come down on you much harder than you deserve.  Whereas the truth of the matter, at least as I see things, is that it's just another interesting tool to allow the skilled player to press advantages over a less skilled one.  But to do that you have to be prepared to adapt your bidding strategy to the specific circumstances of every single hand.

Because the mathematics of whether vulnerability favours aggression or caution varies with level, it is absolutely imperative that hand opening 1 of a suit not make this decision. It is appropriate and widely accepted as winning bridge, when vulnerable, to be more aggressive toward game, and less aggressive toward Small and Grand Slam. Likewise when Not Vulnerable it is appropriate to be less aggressive toward game yet more aggressive toward Small and Grand Slam. These decisions cannot be made by the hand opening 1 of a suit, ony by the hand making an invitation to the mentioned level.

For opening suit bids no, emphatically not. The reason is simple mathematics in that when you open (in 1st or 2nd seat) you have no idea whether your side is looking at part score, game, or slam; and the appropriate aggressiveness towards each of these levels varies differently with vulnerability.
The relative worth of game to part-score goes up with vulnerability so it is appropriate to bid slightly more aggressively towards vulnerable games at IMP (and Rubber, both Four-Deal/Chicago and standard) scoring.  For example, it is appropriate to bid a non-vulnerable game with a 50% chance to make (ie requiring only a finesse) and appropriate to bid a vulnerable game with a 35% chance to make (requiring a finesse and a 3-2 break).
However the relative worth of slam to game goes down when vulnerable, so one should be slightly more cautious bidding vulnerable slams at IMPS. It is now appropriate to bid a non-vulnerable small slam with a 50% chance to make but only appropriate to bid a vulnerable small slam with a 65% chance to make (roughly requiring only a 3-2 break).
Empirically, these percentage differences are often estimated as representing about a 1 or 1.5 point difference in partnership combined strength, when better information is not available.
Third seat openings however can probably discount the possibility of slam when holding minimum values, so here the logic is that one should open slightly more aggressively, not less, when vulnerable, because of the increased relative value of game.
This is all nearly the complete opposite of your suggestion. Only when making a competitive part-score decision or a preemptive opening does the logic of the question hold true.
Therefore, until you know which levels your partnership is aiming for, it is inappropriate to adjust your bidding. This is done by having the inviter, only, make the adjustment and only with the inviting bid. Then the partnership can rely on all other calls being standard, allowing more consistent decisions to be made by the partnership.
As a final note, in regards Grand Slam bidding, Barry Crane (and the Four Aces before him) had a commandment to never bid grand slam in Swiss Teams (my emphasis):

The caution about not bidding grand slams in Swiss Teams made a lot of sense particularly if
  your opponents are not all that skillful as nothing is more demoralizing than to go down one at
  seven while the other team only reached game. In fact, I remember the original Four Aces of forty
  or more years ago had a rule that if you bid seven once and went down you would be forgiven but
  if you did it the second time you were off the team.

Revisiting, for Matchpoints:
The above discussion is entirely intended to guide bidding in IMPS, Chicago, or Rubber scoring. In Matchpoints, different considerations apply.
In Matchpoints the amount by which you gain or lose compared to the field is irrelevant. Rather the number of times you are plus or minus to the field is paramount. This means that far more decisions should be made purely on a basis of
whether or not they succeed a straight 50% of the time.
Consider a touch-and-go game in a major that can be made only on a favourable lead and finding a subtle endplay. Here is a Matchpoint analysis for a case of likelihood for the four cases:
Contract                 Raw Score
& Result                  NV   V    #   MPs
Bid 4 making 10 tricks:  420  620   2  11.0
Bid 3 making 10 tricks:  170  170   2   9.0
Bid 3 making  9 tricks:  140  140   4   6.0
Bid 4 making  9 tricks:  -50 -100   4   2.0

In both case, simply making the 10th trick without bidding it is both sufficient to generate a good to excellent Matchpoint score, and avoids the risk of a terrible one.
In the nearly 5 decades I have been playing bridge, the quality of my game (at Matchpoints) has almost never been from the number of tops partner and I got - it is almost always a consequence of all the available bottoms that we didn't get.

To paraphrase Donald Trump (the Art of the Deal), "avoid the bottoms and the tops will take care of themselves."

In my understanding, vulnerability matters most in competitive bidding, especially when deciding whether to preempt or sacrifice, not strong openings. This page by bridge expert Richard Pavlicek, for instance, indicates that the strength of a preemptive bid should vary from 2-4 depending on whether the vulnerability is unfavorable, even, or favorable.

Do people do this? and Is it sensible? are two different questions.  There are systems that rely absolutely on this sort of thing: the Mini No Trump is opened on 10-12 points non-vulnerable and 12-14 vulnerable, and it's both legal and difficult to defeat.
But whether you should do it generally and without agreement is almost impossible to answer.  If you'll pardon a platitude, you should open only if you think you have a better than even chance of ending up with a plus score.  Whether your particular 12-point hand will give you that depends on its minor features (J109, doubletons, etc.), how active your partner and opponents are, and the comparative cardplaying skills of the four of you.  There are certainly 11-point hands I would open without hesitation and 13-pointers I would pass, and vulnerability is one factor in that; but only one.

Interesting response. What is your answer to this question? http://boardgames.stackexchange.com/questions/8308/in-bridge-are-there-some-13-point-hands-that-should-not-be-opened

@Tom: As ever, it depends on many things. But you should also consider that if you open a weak hand (or pass a 13-pointer) this time, your partner is less able to trust you next time.

I meant, suppose you AND partner have an agreement to open "light" at favorable vulnerability, and pass some 13 pointers when vulnerable vs. not.

@Tom: now I'm really confused. If your partnership agreement is to open borderline hands green but not red (perfectly normal though it should probably be declared at duplicate), then your other hand is a perfect example: is that really what you are asking?

If I understand your response, the answer would be yes.

The more I think about it, the more I believe that partnerships that are at unfavorable vulnerability ought to tighten up their bidding. But not necessarily the opening bidder, in the example I gave.
Someone needs to OPEN in order to get out information. They're not hugely vulnerable to doubles, because doubles of opening bids are usually for takeout. So you can maintain your opening standards when vulnerable.
It seems that it is the RESPONDER that needs to tighten up standards, e.g. respond at the one level with a full six points, at the two level with a full ten points, etc. Many otherwise makeable contracts are lost because dummy didn't have enough high cards to provide "transportation," and these are situations you want to avoid.
Also, one needs to be more careful about COMPETITIVE bids. Weak two bids need six cards, not five, and a good suit. Pre-emptive bids need two honors, not just seven cards in the suit. Raises of suits need honors to go along with spots. That's because THESE bids are most likely to be doubled. And if they are successful, the penalties (500 for down 2, 800 for down 3) will be large relative to the opposing game you are trying to "save."
A competitive bid that requires a high level of caution is a takeout double in the direct seat. If your partner has nothing, opener's partner will redouble, then (probably) double anything your team bids. At unfavorable vulnerability, you will need very good distribution (singleton or void in the opener's suit) for the likely penalty to be less than the game or slam the opponents can make.
Is it right to refrain from making a takeout double in borderline situations?

When vulnerable, the game bonus goes up more than the penalties for undertricks. At IMPs, you should bid "40% games" -- that is, games that have a 40% chance of making vs going one down. Quick math: assume you make either 9 or 10 tricks in a major suit. If it's 9, and you bid game and your opponents stay out, it's -100 vs -140 for 6 imps lost. If it's 10, and you bid game and your opponents stay out, its +620 vs -170 for 10 imps. That means you should favor being in game if your odds of making are better than 6:10 = 37.5%.
So it's not necessarily the case that you should be tighter when vuln.

@ruds: Absolutely, and the same point as made in my answer above.

Sadly I was unable to refer to your answer in my comment as it came 3 years later ;-)


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Can people win at Diplomacy using a "Qin strategy?"
The Qin was one of seven (yes, seven) "warring states" in China several hundred years B.C. During its rise to power, it often followed a policy of "ally with the three far states against the three near states."
Has anyone won (or lost) a game of Diplomacy using such a strategy? Does it work better using some countries than others (e.g. England, allied with Turkey, Austria-Hungary, and Italy against France, Germany, and Russia)? Or are there any good articles on such a strategy?

Being on the team of 4 in a 4vs3 certainly sounds like a good plan.. Not sure it deserves its own name though!

@NIck: 4 vs. 3. That's why the Qin won with it. But it is a sophisticated, complicated strategy fraught with pitfalls. Which is why the Qin made a name for themselves when it worked for them. I believe that's how CHINA got its name.

I have a hard time seeing this being successful.  The problem is that it doesn't mean much in the early game for England to be allied with Austria or Turkey.  So effectively you'd be playing EI versus FG, while Austria and Turkey teamed up on Russia.  The likely scenario is that the 2 v 2 battle doesn't go very far, and the 2 v 1 battle goes well, resulting in a stronger Austria and Turkey.  At that point, Turkey pretty much has to attack Austria or Italy, and either way doesn't seem to bode well for England.
In general, having an ally across the board is nice, but it isn't a replacement for having an ally that you can coordinate with directly, especially in the early game.  You'd need to look at it as more of a long-term alliance.  Perhaps as England you coordinate with Austria, Turkey, and Italy, but you start by getting Germany to help you take apart France quickly (with Italy's help), then activate your cross-board alliance to take out Germany.  It's debatable whether that really meets the criteria of a "Qin strategy" though.

It's close enough. "Qin" preached a particular strategy but didn't follow it dogmatically. And that's probably the key.

There are certain context for this strategy. Qin's strategy was only used for the major powers, any of which could crush others and were ready to do so. In general, there is great distrust among great powers, who cannot be permanent allies due to conflicts of major interests.
In that case, allying with your neighboring powers against farther powers is not a good strategy. Because first of all, maintaining interests faraway is costly; Even if you can afford it, neighboring powers would be threatened by the encirclement so that they alliance could not be genuine. Their betrayal could be deadly. Instead, working with farther powers is much easier. They have "common interests" (containing your neighboring powers who are more likely to threat their interests than you are) with you. Combined you are also in an advantageous strategic position. They can also be lured into an alliance by greed. The infamous example is the short alliance between Hitler and Stalin.

In Diplomacy you are not playing countries; you are playing your opponents. There are tremendous advantages to allying with nearby countries; as there are tremendous advantages to allying with non-adjacent countries. Which is better in any particular game has more to do with the players, than the countries. That is why the difference between countries diminishes as the player quality increases.
In a really strong game I don't see any particular disadvantage to playing Italy or Germany, but in a weak game it is important to be Britain or Turkey.
Update:
Every country starts with three neighbors, except Italy and Russia who start with four. Anyone who starts by quickly making enemies of all neighbours is on the fast track to finish seventh. A strategy like the Qin strategy (which of course was also popularized by Machiavelli) only works for someone who is actually stronger than his collective neighbours, or can at least withstand them singlehanded. In Diplomacy, as in Survivor, you win by having more allies than your enemy does.

This doesn't really seem to address the question at all.  If you're saying that the question can't be answered, that probably makes more sense as a comment.

@bwarner: It worked in "real life," which is why I asked if it might work in Diplomacy. But the connection might be hard to make on a gameboard.

@bwarner Yes it answers the question. Because it says you choose allies in diplomacy by player, not by "farthest 3".

Is winning a diplomacy tournament like winning a session of matchpoints? That is, do you win a tournament by finishing average (fourth) or better in all games, and getting the occasional "top", and avoiding the bottoms (or even fifths and sixths)?

@TomAu: That's like asking about a Backgammon Tournament: "Do you win by declining a double?" - It depends on the tournament rules and situation. The one Diplomacy tournament I participated in, First Year University, scored best 4 results over the year. I won with a 1st, 2nd, 3rd, and 4th. Games counted if they started with at least 6 players, and (IIRC) scored  7:6:5:4:3;2:1 for 1st through 7th place. That 4th place result was as A-H and being backstabbed on the first turn by Italy's "F VEN - TRI". A fun game after that scrambling for a 4th place.

In your tournament at least, you were awarded 1 additional point for each place over the bottom like in matchpoints (whose structure might be more like 6:5:4:3:2;1:0). You said that in matchpoints, the key was to avoid the bottom scores, and the tops would take care of themselves. You won by getting one top out of four (more than your 1/7 share) and less than your share (0) of below average scores. That's what I wanted to know.

@TomAu: To continue: Italy, playing your Qin Strategy by allying with 3 farthest and backstabbing a neighbour: came in 7th, After the first turn backstab, no-one trusted Italy again in either that game - or the next couple. A fast track to last place in the tourney.


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In bridge, are "sequences" more valuable than non-sequences of similar point count?
In backgammon, for instance, sequences of "points" are more valuable than the same number of points out of sequence. That is the 6-5, or 6-5-4 points, are more valuable than the 6-4, or 6-4-2 points respectively. In "hold 'em" (poker), a T-9 is more valuable than a J-9, even though the J is higher than the T (because of the greater potential of the T-9 to make a "two-sided" straight.
Similarly, are sequences of cards considered more valuable in bridge than non-sequences with similar higher HCP? That is, could KQJxx of a suit be more valuable than AQxxx of a suit, even though they both amount to 6 HCP? And could QJTxx be worth more than KJxxx (x being seven or less in both cases), even though QJT is nominally 1 HCP less than KJ?

Yes, it is possible, but it might vary when you are considering the offensive/defensive potential.
Consider your example KQJxx vs AQxxx
Suppose this was the trump suit and say partner has Txx.
With KQJxx, you likely have only one loser. But with AQxxx it is quite possible that you will have 2 losers.
offensively (i.e if that suit is trumps) KQJxx can probably said to be "better" than AQxxx.
Defensively (i.e when you are defending and this is a side suit), AQxxx tends to be more valuable. This is worth an almost sure trick, and is a reasonable chance that you can make 2 tricks.
With KQJxx, you might make one trick, but the second one might be unlikely.
So defensively, AQxxx is "better" than KQJxx.
Of course, I am yet to come across a hand where this difference seems relevant (perhaps we can construct an artificial hand where there is a choice of trump between two suits).

Very good answer. (I'm going to wait a day or two before making a decision on acceptance.) Would you then agree that connected sequences KQJXX are better for offense and "broken" sequences AQxxx are better for defense, and be more inclined to overcall with the former than the latter (all other things being equal of course)?

I find the distinction arises most often when choosing between offense and defense -- e.g., do I bid 3 spades in a competitive auction or do I let the opponents have it at 3 hearts? It does affect overcalls too, but overcalls can also serve to direct leads if you end up on defense, so for me the distinction is less important there.

@DanielGottesman: I usually rely on length (law of total tricks) rather the suit strength when determining to push one level further, in competition, but you are right it might make a difference. Of course, what I was talking in the last paragraph was about comparing KQJxx to AQxxx on the same hand.

@Aryabhata, I agree suit length is more important, so this is mainly a consideration for borderline cases.  In fact, honor holdings like the ones we're discussing can result in a 1-trick adjustment of the law of total tricks precisely because they differ on offense and defense.

@DanielGottesman: I see, you might be right. Never went that deep into LOTT. Too much effort :-)


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In bridge, what caused bidding "standards" to decline post Goren?
I was weaned on "Goren" in the 1960s, and as some readers of my other questions have pointed out, am not totally comfortable with "Standard American" or other newer standards. These may be some examples why:
1) A "strong" (Goren) 1NT was 16-18 points, now it's 15-17.
2) "Five card majors" now means "any five cards." Goren preferred suits led by at least one honor.
3) Goren had stringent high card point requirements for raises of major suits. Nowadays, people like Larry Cohen and Marty Bergen advocate raising with "trumps rather than points."
What led to the above "weakening" of Goren's standards? Has declarer play improved more than defender play? Has there been a change of ethos from "don't go down if you can avoid it" to "don't go down more than your opponents' likely score?"
And speaking of which, is this why penalties were stiffened for doubled, non vulnerable from 100, 300, 500, 700... to 100, 300, 500, 800...?

You presume that standards have fallen, when in fact they have risen
substantially. Bidding accuracy from the local club game to the highest levels is
substantially higher than 50-60 years ago.
You are comparing apples to oranges with your strong 1NT example.
The modern 15-17 strong NT is all High-Card Points; Goren's 16-18 NT
included distribution points for a doubleton honour. If you carefully read Goren's works, you will see that he explicitly states
that the "distribution" points in his system are for hand shape,
not ruffing. Strong modern players will subtract a point for a 4-3-3-3 hand, making the modern 15-17 HCP identical to the Goren 16-18.

Update:
The strong players of the 50's and 60's were not cautious players. Culbertson was an aggressive player, Goren was an aggressive player, and Barry Crane was as aggressive as possibly any player in history.
The Italians were opening light hands more aggressively than some because their system allowed it. Kaplan & Sheinwold were amongst the first (in North America) to introduce a 5-card major system to improve slam building, but also "systemized", for club players, a means of recognizing hand shape more accurately than Goren's point count.


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In bridge, does a declarer "need to" locate all 52 cards during the play of a trump contract?
This was recommended by author Terence Reese (and several members of the site).
But I was taught differently, at least as declarer.
That is, I was taught to count "trumps and honors." So, if you are declarer in a trump contract, with, say, 26 high card points and an eight card trump fit, you will be most concerned about the five outstanding trumps, and the outstanding five or so, of the 16 face cards in your opponent's hands. Assuming no overlaps, your primary concern would be over TEN opposing cards, not 26.
If there is a critical side suit in the play, you might worry about five or so additional cards in that suit as well. Then I have worry about 15 of my opponents' cards, but not all 26.
On the other hand, suppose you have a singleton, x in the dummy of your opponents' best suit, and xxx in your own hand. They start off with AK of the suit, and you ruff the second round. You've seen four of your opponents cards, and you don't have to worry about the remaining five cards in the suit (assuming that both follow when you ruff your last x). Then you only have to worry about the remaining 19 opposing cards. And of these, the most important ones are the outstanding trumps, and the two honors or so, outside their main suit.
Is this right, at least regarding a trump contract (no trump is a different animal)? Or is there something that I am missing?

Terence Reese is widely regarded as amongst both the best bridge players of the 20th century, and the best bridge writers of the 20th century. When you can legitimately aspire to one of those achievements, your proposed new approach to declarer play can be taken seriously.

@PieterGeerkens: Maybe it was a badly worded question, which was really about the (economic) "law of diminishing returns." Of course "more is better than less" and 52 is better than 51 or 50 (nonsatiation). But if Reese is 100, can one get to e.g. "90" by counting 35-40 cards, or does one need to count 46-48? Put another way, while the ability to go from 26 to 36 increases your skill by a LOT, is there all that much difference between say, 46 and 52?

Now that is a more sensible comment, though incorrect. I will expand on my answer to address it.

@Tom: What exactly do you mean by all 52? Down to the spots? Or are you talking about the hand distribution, with possibly not knowing all the x's, like "LHO has AJTxx"?

@Aryabhata: Good question. I fear Pieter means "down to the spots." But yours truly was "talking about the hand distribution, with possibly not knowing all the x's, like LHO has AJTxx." Is either description more useful than the other in practical play?

I sense a misunderstanding here. On the one hand, remembering every card played in every hand is a good thing, as there is always a small chance that the setting trick will turn on the 4 against the 5. This does not mean that striving for this perfection is the best  way to improve your bridge, nor that anyone who can't do it is a bad player. On the other hand, it is only necessary to keep track of significant cards; but the 4 as against the 5 may be significant as a signal or indicating a split (assuming a defender played his lowest trump under the A). You're not actually disagreeing.

@TimLymington: How are you reading the count signals by Partner/Defenders if you are not noting the spots carefully? How are you detecting false carding by the opponents if you are not watching the spots carefully? There are only six cards 2 through 7 in each suit, for 24 in the deck. (All other cards start as significant a priori.) You and Dummy hold 12 on average. After the first three tricks, typically in at least two suits, anywhere from 3 to 6 of those remaining 12 are located. Far from diminishing returns, noting the spots pays increasing returns.

@Pieter: that comment, while correct, seems out of place. I explicitly said it is a good thing to remember; but if you are dealing with non-professional humans, saying "Remember every card and make every appropriate deduction or you will always be a bad player" is unhelpful. OP is asking about  "LHO has AJTxx", and yes, that is a good thing to know, though not the best.

It's not completely a matter of the number of cards that you know as much as knowing the important features of the cards.  For instance, it might be valuable to know that East holds one more small heart even if you don't need to know precisely which one it is.
As Pieter Geerkens says, every card is potentially important, so it's definitely worthwhile to locate as many as you can as accurately as you can.
In the interest of prioritizing, here are my suggestions for what is most important.  There are two axes: One is which cards to pay most attention to, and the second is what methods to use to locate them.
For which cards to pay attention to, I would suggest the following priorities:

High cards and distribution: Honors are probably self-explanatory, but distribution (and not just of trump) is frequently even more important.  You often need to know if a suit is set up, if someone can ruff, etc. At this level, you just want to know how many cards in a suit are out/are held by someone, and don't care too much about which ones they are.
Potential signals: If you are defender, you need to know if your partner is playing high-low or low-high, and as declarer, you also want to be able to read defenders' signals.
Spot cards likely to be important because they can create or defeat endplays or entries: For example, it may be crucial to know that the last of a suit out is higher than your last card in that suit, so it can be used to throw in an opponent, or that you can get to partners hand when partner doesn't have other high cards using your 7 since the 8 is still out, or that all cards 6 or higher have now gone so the 5 over your 3 in the other hand can be used as an entry to a weak dummy that contains a long suit or is key to a finesse. (Added)
High spots: It's very common that the 9 or 10 is high after a suit has been played twice, so you need to know that and where they are.
Other spots: Usually you can get away with not knowing the exact values of the rest of the cards (although remember, you want to know how many each person has), but occasionally it still becomes important.

Whether #2 or #3 is more important depends on the hand.  #1-#3 are all pretty important, but I think you start to face diminishing returns by #4.
Methods:

Know which cards have been played already and which are in play: This is a critical beginner skill.  I have seen many beginners miss tricks simply because they didn't remember that their Q was high.  I still get bitten by this myself occasionally if I don't remember whether someone sluffed an 8 (making my 7 high) or a 6 (meaning the 8 is still out).
Assemble a picture of the hand: At this level, you start doing deducing distributions from the two hands you can see and the cards already played.  For instance, if you know East started with 2 hearts because he has shown out, and can have started with only 1-2 spades because you and dummy have 10 and West has already played 1, then you also know that East started with 9-10 cards in the minors.  As you get more information, update the picture.  E.g., West turns out to have a singleton club, meaning East has 6.  Therefore East started with 3-4 diamonds.
Make inferences from the bidding and play: Put in information you have from bids and plays that were made.  If someone overcalled hearts, they probably have 5+ hearts -- that narrows the distribution down further.  If West lead and East put in the K, East should not have the Q (unless East is a beginner or using some unusual signalling conventions, or conceivably has KQ doubleton).
Make inferences from things that were not bid or played: For instance, if East chose not to open, and if you have located 10 HCP with East and you are trying to identify the location of a king, you can probably infer that West has the missing K.  Ask yourself questions like: Why didn't West lead partner's suit?  Or I know East has 6 diamonds, why didn't he bid them?  (Too weak for a weak two, perhaps?)

In this axis, #1 through #4 are all very valuable, it's just that the later ones tend to be harder.  #3 and #4 tend to involve some inherent uncertainty, which means you have to be a bit cautious in inferring information.  You should try to evaluate how likely it is that your inferences are correct, and perhaps try to identify alternate scenarios.

Declarer never needs to count all 52 cards, just like declarer never needs to make the contract. To be consistently successful declarer simply needs to be counting more cards than defenders are counting. Of course if the defenders are counting at least 26 each, declarer should be counting a full 52.
There are two fundamental reasons why one must aspire to count all 52 cards:

You get expanding returns, not diminishing returns, as every card you count increases the ability to locate and count the next card. The reason for this is that each located card reduces the number of cards remaining to be counted.
All of the advanced play techniques (single-, double-, and repeating-squeezes; throw-ins, etc.) require an exact, or nearly exact, count. One cannot aspire to perform any of these reliably without an exact count; neither can one effectively defend against them without an exact or nearly exact count.

The gain in play by having a solid familiarity of advanced techniques, can approach a trick over the play of a good intermediate player who has not studied these techniques. That is like being dealt 2 or 3 extra points every hand. If your partner has likewise studied these, (s)he also gets these extra points.
Imagine how many more successful contracts you will bid, and how many more opposing contracts you will set, if you and your partner are each dealt an extra queen each hand. That is the advantage one obtains by first learning to get an exact count early in the hand, and then studying the advanced techniques that allow you to take full advantage.
This analysis may also bear o your question here concerning cycles of over- and under-bidding. If one considers the very aggressive bidding of the Meckwell partnership (Eric Rodwell & Jeff Meckstroth), it is their excellent declarer and defender play, combined with superb table feel and intuitive hand evaluation, that allows them to be successful playing this way. Barry Crane played a similarly aggressive style in his day.
Weaker players tend to emulate the best known successful players of the day, without having the skill set to support the style. Goren addressed this by developing a more conservative system for weaker players, which was popular for many years. However don't be misled to think that Goren played passively in tournaments; Goren played his own system very aggressively, because of possessing the intuition and skill to do so successfully.
Update:
Yes, there are in many hands low spot cards that one does not need to remember exactly; thinking of an x is sufficient. However, the bridge literature is chock full of examples where the careless play of a deuce or trey instead of 5 or 6 has blocked a key suit. One never knows for sure which low spots are irrelevant until the full hand is counted.
I remember well an argument between two mentors, during my formative bridge years, as to where two small diamond spots had been, on a hand played 4 years earlier. Yes, that was the key hand in an important hand in a lost final; but one cannot even attempt to remember that far back if one doesn't remember at the conclusion of the hand. (Corollary: they both agreed on the location of the other 50 cards.)
Remember this: As declarer, the opponents are using those spot values to communicate with each other; as defender, your partner is using those spot values to communicate with you, and you are using those spots to communicate with partner. Nothing is more frustrating than to lead a small spot to partner asking for the suit to be returned, and having partner return another suit instead allowing a FAMOUS declarer to make an unmakeable contract (Sorry Dan! Too good an anecdote to leave out; I'll buy you a beer.)

I think your count, and Tom's count mean different things. Counting distribution and location of relevant cards is all one needs to do. Not necessarily all the 52, down to the spots, which is what Tom is getting at I presume.

@Aryabhata: I think you need to re-read my post, without preconceptions.

Ok, please clarify by what you mean by count? Do you mean down to the spots? (like at trick 7, you know who holds the spade 4?)

@Aryabhata: Yes, every spot of every suit until one knows the spot-value is irrelevant. This will happen sooner in some suits, and on some hands, than on others. I will not claim to be that good (yet), but I do aspire to that level because I understand the value of doing so.

@PieterGeerkens: It seems like "how many cards do you count?" is tied to "how far do you want to go?" Maybe "26 to 36" gets you from beginner to high intermediate, while "36 to 52" gets you from high intermediate to world class, with "advanced" somewhere in the 40s.

@TomAu: Listen well, if you really want to improve. 52 gets you to advanced beginner. Getting to 52 at trick 3 or 4 (or earlier at times) gets you world class. 52 at trick 8 or 9 gets you to average or average plus in a typical club game. 52 at trick 12 or 13 is back to advanced novice. Also, it is an exercise in discipline, not of intellect. Any determined player of average intelligence can count all 52 cards; if they practice it and really want to improve their game. And the best players in every club will play an occasional game with anyone who counts the cards.

@TomAu: Counting all 52 cards is really the definition of early intermediate. If you are not doing that on most hands, you are simply not an early intermediate yet. Counting is the most fundamental single skill for a successful bridge player, bar none.

Getting to complete 52 (down to the exact spots) at trick 3-4? I call complete BS on this, sorry. By end of trick 3, there is at least one suit which hasn't even been touched. How will you know the spots there? You might know the distribution, but the spots? And while ability to count is absolutely essential (no question there), trying to associate it with skill levels like that is pointless and misleading. It is what you are able to do with the information you have that determines your skill level.

@Aryabhata; I am by no means a world class player, yet  in 1-2% of hands (one hand every 3-4 sessions), I will know where every significant card is as soon as the first trick is completed, sometimes as soon as dummy comes down.

@PieterGeerkens: The key word being "significant". While it is an admirable goal to see if you can nail down the whole hand to the exact spot cards, the question Tom is asking, is, is it really practical to do that on every hand. Of course, what he actually asked (trying to set a limit like 32 or 40 cards) has no answer: some hands require to know where the heart 6 is, while in some you don't care who holds the outstanding four Aces. Knowing where to (and where not to) spend your mental energy is an important skill which many non-world class players lack.

authors: Павел Серышев