execrable acbl bidding contest problems

[xcurt]

So I get the monthly dead tree from the ACBL in the mail today. Here are the bidding contest problems

 

(1) IMPs, they are vul and they do not bid Qxxx, AJxx, AJ9, xx 1D-1H; 2H-3S!; ?

 

It would never occur to me to bid 4D, yet this is the top answer. Although, 4H scored 90 so it's not like the scorer is making is an argument that either of the two superficially possible calls is actually an error. Is there a reasonable construction for the responding hand where 4D helps us get to a good slam? I can't find one easily.

 

(2) IMPs, both, they don't bid, QJxxxxx, AT, AJ, xx Partner opens a strong NT, you show a balanced slam try with a transfer and raise to 4S, and partner cues 5C. I think the responding action to this point is a pretty clear error since we either going to end in 4S anyway, end in 5S with no better idea of how to bid the slam, or face this guess whenever partner doesn't have the red kings and black aces or 3 kings and an ace and some other useful texture (and we don't want to be in slam with that opening hand most of the time). All answers other than 6S scored less than 50, but how satisfying is bidding 6S now? Isn't that auction worse than 1N-6S-P, and let them guess the lead?

 

(3) Matchpoints, they are vulnerable, RHO opens 4D Namyats and you have x, K9, QJT987, AJTx. The winning answer according to the scorer is to pass now and then bid 5D on the next round. Isn't that just losing matchpoints since we are taking the last guess? As a side bonus, we let LHO bid 4H to show slam interest. I don't see how the sequence P, 5D could ever be better than a direct 5D. If partner doubles 5S, we do have an ace after all. I suppose you could argue that passing throughout is better than bidding, but that's not what the scorer did.

 

(4) Matchpoints, they are vulnerable, we are dealer with JT8xxx, Kxxx, Kxx, -- P-P-1S-2D; 4S-Dbl-P-5C; ?

 

Again the top answer, 5S, scores much higher than the other reasonable answer, pass (50). Huh? We guessed to bash 4S and now RHO is guessing that his side has a productive minor suit fit. It's certainly possible that 5S is the winning call but again the scorer is advocating taking the last guess.

 

(5) An old chestnut where after 1m-1M holding a 3-suiter with 3-card support for partner we have to invent a suit. Today 1x-1M is 1H-1S and we have a soft 3613 16-count with the DA.

 

I would really like to see the ACBL run a better bidding contest. Steve Robinson runs one in the District 6 (Washington, DC area) magazine and the problems are of uniformly high quality.

 

The ACBL problems seem to fall over and over into the same categories -- (a) a guess (B) some standard expert treatment that gets a unanimous panel © problem where the answer is Dble and the real problem is next round (d) problem where the answer is cuebid and the real problem is partner's (e) problem where we erred at a previous turn and now have to guess (f) random guess about an infrequent auction.

 

Curt

[han]

(2) IMPs, both, they don't bid, QJxxxxx, AT, AJ, xx Partner opens a strong NT, you show a balanced slam try with a transfer and raise to 4S, and partner cues 5C. I think the responding action to this point is a pretty clear error since we either going to end in 4S anyway, end in 5S with no better idea of how to bid the slam, or face this guess whenever partner doesn't have the red kings and black aces or 3 kings and an ace and some other useful texture (and we don't want to be in slam with that opening hand most of the time). All answers other than 6S scored less than 50, but how satisfying is bidding 6S now? Isn't that auction worse than 1N-6S-P, and let them guess the lead?

 

I agreed with this 6S actually, it is not the same as 1NT-6S as (1) partner has shown a good hand for slam in spades and (2) partner has a club control.

[awm]

I disagree. What do you think these should be about? In my experience Steve Robinson's polls are often essentially platforms for him to tout his non-standard bidding preferences (i.e. opening 1M with five small in the major and six strong in a minor) often overruling the "expert committee" in doing so.

 

I think the purpose of these polls is to give advancing players an idea of expert judgement, especially in slam auctions or competitive sequences. For the hands you mention:

 

(1) I think this is a very reasonable problem. The question is "how good a hand do you need to cooperate with partner's splinter"? Is this hand with a "wasted" spade queen but four trumps and two aces and a side doubleton good enough? Or do you want a hand that truly has "nothing wasted" in spades? The poll suggests experts disagree.

 

(2) Bidding transfer...4♠ gives partner the option to pass if he doesn't like his hand. This is much better than blasting 6♠ opposite a partner who could have xx in spades (for example). If anything this problem is "too easy" but evidently from your comments it is not. :rolleyes:

 

(3) There is no "guess" -- bidding a delayed 5♦ or a direct 5♦ gives the opponents the same information about whether to bid on. The point is that a direct 5♦ might trick partner into bidding slam when slam is awful, or doubling 5♠ when it's cold. In exchange, you do give the opponents the chance to make some kind of slam try (i.e. bid 4♥ direct). I think it's an interesting question how this tradeoff works out -- evidently the expert panel feels that clueing partner in is more important than taking away a little space from opponents (especially since opener's hand is pretty well described already). Passing throughout could also conceivably be right. But I see nothing wrong with this problem or with the scorers action. Again, the scorer's choice is usually the consensus choice of the expert panel (unlike Steve Robinson's choices, at least in my limited experience, which often express his own judgement/opinion regardless of what the polled experts think).

 

(4) Why is this the last guess? Won't opponents have to guess whether to double 5♠? Really this "last guess" rule is nonsense anyway. A better rule is that if you are sure what your opponents right action is over your call (and it's not "pass it out") then you probably bid either too little (if their right call is obviously to compete) or too much (obviously to double). Here, it is far from obvious to me whether they should double 5♠ or compete over it. It is clear that selling to 5♣ is wrong. I suppose we could've bid 5♠ directly, but sometimes 4♠ does buy a hand.

 

(5) Well it's an oldie, probably has appeared too many times on these sorts of polls. But if the old BW death hand doesn't pop up once every year or two, how are newer players to hear about it?

[han]

(3) Matchpoints, they are vulnerable, RHO opens 4D Namyats and you have x, K9, QJT987, AJTx. The winning answer according to the scorer is to pass now and then bid 5D on the next round. Isn't that just losing matchpoints since we are taking the last guess? As a side bonus, we let LHO bid 4H to show slam interest. I don't see how the sequence P, 5D could ever be better than a direct 5D. If partner doubles 5S, we do have an ace after all. I suppose you could argue that passing throughout is better than bidding, but that's not what the scorer did.

 

Didn't Meckstroth argue for a direct 5D for pretty much the same reason? Not the worst to agree with. I think that the best argument against the 4D bid is that we don't want a diamond lead against a slam. So it makes some sense to first look if they are going to bid slam and if not then bid 5D. It's not like they have a lot more information if it goes 4S - p -p - 5D next.

[jdonn]

On 1 I agree with you, on 2 I don't know what the heck you are talking about, what's wrong with trying for slam then bidding it when partner accepts your try?

 

After that I got tired of reading.

[Guest Jlall]

I agree with the general sentiment that It's Your Call is poorly run with poorly chosen problems.

 

I agree that 4D is bad on board 1 but I am only one person, that's why they call it a bidding problem. If you think the experts are wrong (I do on this one), well maybe you will learn something from their answers or maybe they're just wrong. The panel isnt perfect. The scoring seems to reflect that it's a close decision.

 

I disagree strongly with you on the 6S hand (agree with han's comments).

 

I agree with you strongly about the namyats hand.

 

I agree with boredom about problem 5.

[han]

(4) Matchpoints, they are vulnerable, we are dealer with JT8xxx, Kxxx, Kxx, -- P-P-1S-2D; 4S-Dbl-P-5C; ?

 

Again the top answer, 5S, scores much higher than the other reasonable answer, pass (50). Huh? We guessed to bash 4S and now RHO is guessing that his side has a productive minor suit fit. It's certainly possible that 5S is the winning call but again the scorer is advocating taking the last guess.

 

Agree with many in the panel that 4S wasn't right and also agree that now we shouldn't pass but bid 5S. 14 out of 18 experts are bidding, only 4 pass, so it seems right to give pass only 50 points.

[P_Marlowe]

Hi,

 

#1 Depending on the meaning of 2H and 3S, 4D is fine.

If you regular raise responders mayor with 3 card

support, the known 9 card fit is a plus.

If 3S shoed values, than your 4 card spade suit with

the Queen will fit nicely.

You showed a min, but depending on your partnership

agreement, the hand may well be a suitable min. making

slam a possible option.

For that matter I dont need to construct hands for partner,

I just need to ask myself, "How bad could my hand be?",

thanks too S.J. Simon.

 

#2 You now know, that partner will have a suitable hand

for spade slam, if you just shoot, you dont have this

information. So the given auction to 5S is clearly a lot

better than the auction you suggested, because you have

more information.

 

...

 

With kind regards

Marlowe

 

PS: The question is always, how do they get the bidding problems,

in Germany they get send by readers, not all, but too a large degree.

=> Several themes will reoccur again and again, but thats ok.

Because if you would just present problems from high quality turneys,

involving highly artificial bids, those problems wont help the average

player, and my guess is, the ACBL magazine is aimed at those, and

this includes the bidding poll.

[jtfanclub]

I really wish for these that they would grade them either by straight % of experts or with a double-dummy problem solver. I really don't care what the author thinks is the right answer (since he's almost never as good as the experts polled).

[xcurt]

I disagree. What do you think these should be about? In my experience Steve Robinson's polls are often essentially platforms for him to tout his non-standard bidding preferences (i.e. opening 1M with five small in the major and six strong in a minor) often overruling the "expert committee" in doing so.

 

Well, for about one problem per month, that's true about the scoring. Steve also likes the Law a lot and does advocate following it fairly blindly. But the problems are really, really good. Take this one from this month:

 

mps, they vul, in 4th you have

 

Ax, KTx, QJxxx, AJx (if i recall correctly)

 

1S-Dbl-3S-???

 

I predict there will be at least 5 and possibly 6 answers from the solvers.* Less from the experts since I think a few of these are hopeless calls, but any problem that fetches 5-6 different answers from the solvers is an excellent problem.

 

* I expect to see P, Dbl, 3N, 4D, 4H, 5D all get called.

[jdonn]

mps, they vul, in 4th you have

 

Ax, KTx,  QJxxx, AJx  (if i recall correctly)

 

1S-Dbl-3S-???

 

I predict there will be at least 5 and possibly 6 answers from the solvers.*  Less from the experts since I think a few of these are hopeless calls, but any problem that fetches 5-6 different answers from the solvers is an excellent problem.

 

* I expect to see P, Dbl, 3N, 4D, 4H, 5D all get called.

Just because a few dingleberries might bid P, 4♦, or 4♥ doesn't mean the selection of those 'choices' made the problem any better. I think the acbl bulletin problems are fine for the audience toward which they are geared.

 

Now that I read all your comments, I agree with you on 1, still think you are nuts on 2, think you are simply unwilling to learn anything on 3 or 4 regardless of the right answer, and think you are being nothing but whiny on 5.

[pclayton]

1. I happen to agree with 4♦. My four hearts are great. My doubleton club is great. Sure, my black mariah is wasted, but how often do we have a splinter auction where 100% of our hand is working? 4♦ doesn't commit us to slam either, it just cooperates.

 

2. Partner is making a slam try off both red aces. He could have key carded, and the inference he is missing one red king is strong, but its not certain. I think 6♠ is fine. I think pard has great trump and good clubs or vv.

 

3. Why would you want to overstate your hand with a direct 5♦? Yes I know its NAMYATS and I can see the colors, but we will usually have the luxury of passing and then saccing.

 

4. 4♠ isn't a marginal action designed to 'give the opps the last guess' It's clear cut. If RHO overcalled 4N instead of overcalling, wouldn't we be bidding 5♠ here? 5♣ gives us a real problem and this looks like a 'bid one more hand'. Maybe a 4♣ splinter on the last round would be a better call - if its not a FJ.

 

5. Yawn.

[xcurt]

(2) Bidding transfer...4♠ gives partner the option to pass if he doesn't like his hand. This is much better than blasting 6♠ opposite a partner who could have xx in spades (for example). If anything this problem is "too easy" but evidently from your comments it is not. :P

I am not advocating blasting 6♠. I am suggesting that, if we bid this way, we are behind a hypothetical other table where the player with our cards bid 6S. If the expectancy of partners continuation over 4S whenever he has a suitable hand for slam is dominated by 5C, then our bidding plan was poor. Looking at our hand, he will be bidding 5C whenever he does not specifically have both red kings since he can't Blackwood, and without both red kings he my initial reaction is that he is a strong favorite to have one of the club tops. Give him AKx, KJxx, xx, ?? and he needs the CK to have a strong NT. I suppose he might have AKx, KQxx, Qx, QJxx, but there are no guarantees in this life. I don't have a copy of dealer handy to check all of this, but I will later if nobody else has.

 

Yes, I'm aware that there might be a Condorcet cycle among three or more bidding plans.

[jdonn]

(2) Bidding transfer...4♠ gives partner the option to pass if he doesn't like his hand. This is much better than blasting 6♠ opposite a partner who could have xx in spades (for example). If anything this problem is "too easy" but evidently from your comments it is not. :P

I am not advocating blasting 6♠. I am suggesting that, if we bid this way, we are behind a hypothetical other table where the player with our cards bid 6S. If the expectancy of partners continuation over 4S whenever he has a suitable hand for slam is dominated by 5C, then our bidding plan was poor. Looking at our hand, he will be bidding 5C whenever he does not specifically have both red kings since he can't Blackwood, and without both red kings he my initial reaction is that he is a strong favorite to have one of the club tops. Give him AKx, KJxx, xx, ?? and he needs the CK to have a strong NT. I suppose he might have AKx, KQxx, Qx, QJxx, but there are no guarantees in this life. I don't have a copy of dealer handy to check all of this, but I will later if nobody else has.

 

Yes, I'm aware that there might be a Condorcet cycle among three or more bidding plans.

I honestly don't understand what you are talking about at all. Why is it a bad thing that if he is not passing he probably bids 5♣?

[xcurt]

I honestly don't understand what you are talking about at all. Why is it a bad thing that if he is not passing he probably bids 5♣?

Because if partner is going to bid 5C with most hands he might hold, we haven't learned very much at all. We also aren't in any better position -- we have no way to find out about the spade tops, and we don't know which red suit partner is missing so we don't know how to help him make the final decision about slam. We have, however, helped the opening leader a fair bit.

[jdonn]

I honestly don't understand what you are talking about at all. Why is it a bad thing that if he is not passing he probably bids 5♣?

Because if partner is going to bid 5C with most hands he might hold, we haven't learned very much at all.

We have learned we have clubs controlled, and that partner likes his hand for slam. Seems like plenty to bid slam to me.

[pclayton]

I honestly don't understand what you are talking about at all. Why is it a bad thing that if he is not passing he probably bids 5♣?

Because if partner is going to bid 5C with most hands he might hold, we haven't learned very much at all. We also aren't in any better position -- we have no way to find out about the spade tops, and we don't know which red suit partner is missing so we don't know how to help him make the final decision about slam. We have, however, helped the opening leader a fair bit.

? He's cooperated in a slam try and he didn't bid 4N or 5 red. We've learned plenty.

[xcurt]

He's cooperated in a slam try and he didn't bid 4N or 5 red. We've learned plenty.

We can simulate the situation after transfer, 4S by responder. Conclusion is that we have already misbid. At the point of the auction given, this was a poor choice of a bidding panel problem.

 

Details......

 

Facing a random strong notrump drawn from the 39 unseen cards,

 

we have enough key cards 85% of the time

6S is 80% or so on double-dummy defense

7S is 2% or so

the lead matters about 30% of the time

 

Furthermore, when partner moves over 4S, assuming he bids Blacke when he has all off-suits controlled and makes his cheapest cuebid otherwise, the relative frequency of his calls is

 

4N -- 20%

5C -- 70%

5D -- 8%

5H -- 2%

 

What the best strategy is will depend on our assumptions of what hands partner would move with over 4S, and furthermore, how well the opponents lead and whether they can profit from listening to our auction. However, any reasonable construction of the payoff matrix for bashing vs bidding as we did suggests that partner needs to be moving much more than half the time over 2H...4S from the responding hand. He won't move over 4S on "most hands", that just doesn't fit with the definition of this auction. But if he is moving frequently, there is not much implication from his call of 5C, since the frequency of 5C dominates 4N, the other call that keeps slam in the picture.

 

Curt

[mike777]

hmm are you saying over a strong nt 6s is 80% just looking at our responder hand, deal two, and before any other bids other than 1nt?

 

If so why did not one expert say this, not one?

[xcurt]

hmm are you saying over a strong nt 6s is 80% just looking at our responder hand, deal two, and before any other bids other than 1nt?

 

If so why did not one expert say this, not one?

Sorry I mistyped. Too tired. I meant "it's right to be in 6S 80% of the time facing a random strong NT."

 

Slam is making about 65% of the time if the opponents lead randomly from among the three offsuits.

 

The conclusion still holds though, partner won't move enough after 2H... 4S for 2H... 4S to be the right responder action.

 

Bashing is about a wash if the opponents lead randomly against the 2H...4S auction. It's going to be a gainer if the opponents can exploit the information gained from the auction.

 

Bidding slowly (How? Thats my point -- the action over 1NT is the real problem!) could be a big gainer over 2H...4S if we can avoid the 20% of the hands where slam has no play on any lead or is off two cashing tricks.

[mike777]

hmm are you saying over a strong nt 6s is 80% just looking at our responder hand, deal two, and before any other bids other than 1nt?

 

If so why did not one expert say this, not one?

Sorry I mistyped. Too tired. I meant "it's right to be in 6S 80% of the time facing a random strong NT."

 

Slam is making about 65% of the time if the opponents lead randomly from among the three offsuits.

 

The conclusion still holds though, partner won't move enough after 2H... 4S for 2H... 4S to be the right responder action.

 

Bashing is about a wash if the opponents lead randomly against the 2H...4S auction. It's going to be a gainer if the opponents can exploit the information gained from the auction.

 

Bidding slowly (How? Thats my point -- the action over 1NT is the real problem!) could be a big gainer over 2H...4S if we can avoid the 20% of the hands where slam has no play on any lead or is off two cashing tricks.

Ok, you say across from strong nt opening 6s over a strong 1nt is a big fav, more than 51% :) My main response is not one person in the article said this. This seems like a big thing to not mention for us nonexperts.

 

If true, and I do not mean to doubt you, it would really help to tell us, teach us how to know that. Trust me alot of readers will not know this.

[xcurt]

If true, and I do not mean to doubt you, it would really help to tell us, teach us how to know that. Trust me alot of readers will not know this.

Sure, I'm happy to talk about this. I apologize for the long post but I want to express my thought process.

 

To attack problems like these, first get a copy of a hand dealing program. I use Hans van Staveren's venerable dealer program (see http://www.xs4all.nl/~henku/html/dealer/body_dealer.html). If you are not a *nix guru you probably want to try one of the more recent Windows programs. Dealer can write some ugly output and you will probably want to hack up some perl code or similar to generate input files and work with the output.

 

All of these programs allow you to randomly deal some or all of the cards, select hands based on conditions, and write the hands or compute statistics over the hands.

 

Now you get into the philosophy of simulation. Personally I think that double-dummy solver analysis while useful is not the most direct route to the truth of a hand. I prefer to do two things.

 

First, calculate some statistics about partner's critical holdings. Here, we can simply predeal ourselves the 13 cards we see. We don't need to impose any conditions on the opposing hands since they are probably so weak they will never bid without extreme shape. We impose a strong NT condition on partner's hand. There will be some edge cases where you look at the hand and say "I would not open that 1NT!" If you see such a hand disregard it. It will probably be infrequent enough not to distort the statistics too much. In this case, we have a bidding problem in part because our high honors are not where partner will most likely expect them -- in our long suit. We also have a bidding problem because we have a suit with two fast losers. So we need to find out at least two things to bid slam with greater accuracy than just counting points or just bashing. We need to know that they can't cash the CAK, and we need to know that they don't have the CA and some trump holding that is likely to produce a trick. If we ask the dealer program how often partner has only one key card for spades, we find out that it's about 15% of the time. So while this is a problem we would like to resolve in the auction, it might not be the most important problem to resolve.

 

Second, deal partner a number of hands consistent with the auction and look at each one and think about where we would like to end up and whether or not given actions from us will produce the desired result. We need express the results in terms of IMPs or matchpoints against other tables that take other actions on the same hypothetical deal. I have found that this is very effective at helping me understand what is going on on a deal. In the case of this deal, I looked at 40 hands, single dummy. On each hand I looked at how would I play the hand. This was pretty easy since with a big 1-suiter there usually aren't that many lines of play. If you are looking at something like

 

Ax, KJxx, Qxxx, AJx

 

you would say on a non-club lead I would finesse the diamond first to set up a club pitch if it lost, then try the spade. You can figure out that you play this spade combination for 0 losers about 20% of the time, 1 loser 50% of the time, and 2 losers 10% of the time since you have too many trumps to pick up KTxx on your right with a coup. If the diamond finesse fails you make 20% of the time (edge case of 6-1 diamonds), if it wins you make 20% of the time plus 25% more of the time (spades for 1 loser and hearts to pitch the club or some kind of endpotision). There are a few additional chances in the endgame here like DKxx on and you might not need the HQ on. Since the edge cases will cancel out a little you don't need to be totally exact. So we write 37.5% for this one. We also have to estimate the chances partner would cue 5C with such a hand. If we always think partner is moving over 4S we have probably done something wrong since most of the time the auction goes tranfer--accept--game in the major it plays there.

 

Having done this for 40 hands or however many you think has given you a feel for how things are running, you now add up the probabilities. Some of these probabilities will be conditional (eg make slam given that partner has a cueing hand over 4S) and you may need to estimate the conditional probabilities. It helps to know something about Bayes Law here.

 

On the problem hand it becomes pretty clear quickly that when slam is bad it still has some chances (unless off the CAK or two aces -- which we know is only 15% of the time from a 1 million hand simulation so we know that number pretty accurately since the computer will count it for us). If slam is good it is usually cold or on one of two finesses or on the wrong lead or a finesse. It's good on most of the hands. So the real crux of the problem becomes how often partner is moving over 4S. I found it too hard to accurately evaluate each hand (judgement becomes colored by knowing the responding hand) so I considered what would happen if partner moves exactly half of the time. That's probably an over-estimate and you could answer that by going through a database of hands from BBO or OKB and asking how often partner moved over this auction. We now work through the algebra computing our IMP expectation against bashing knowing that

 

50% of the time one table is in slam and the other is not

50% of the time

85% of the time we have enough key cards and both tables are in slam (I ignore the increased

expectancy of having all of the key cards since partner moved)

15% of the time one table is in slam and the other is not

 

I won't reproduce it all here but you get something that suggests that even if

(a) the slow auction never bids a hopeless slam -- and some of the slams are hopeless because partner has all the missing quacks and we have two slow losers) and

(:) the opponents lead no better than against the bashing auction

that you are going to break roughly even by bashing if your only other choice is to bid as given in It's Your Call. In practice both (a) and (B) are not likely to be as optimally distributed for the slow auction, so bashing should have a positive IMP expectancy against the slow auction.

 

Finally, there are other bidding plans out there. I would have bid 6S at the point given in It's Your Call, but at the table I would not be in that particular pickle. I really wish this had been given as a MSC multiple choice style problem after 1NT-?.

 

Curt

[mike777]

1) I have to admit I am sure this is all brilliant

2) I have no idea how this helps the mass of readers of this column at the bridge table under pressure to bid 6s direct over 1nt.

3) I am looking at deal one now. I would bid 4h since I think my hand is garbage but I see Larry Cohen, Lawrence, Jill, and Stansbys/ Freeman bid 4d. I think the write is up is bad but then I think it would take 20 pages or more to do a decent write up. In other words....great problem.

4) If cuebid is 100% with anything less than a dead dead minimum I understand 4d. But this is a big if and what is a dead minimum here.

[awm]

So your simulations indicate that with ♠QJxxxxx ♥AT ♦AJ ♣xx, you are making slam more than half the time on hands where opener would not move over the quantitative 4♠ invite?

 

I find this somewhat hard to believe. Surely with only 28 hcp between you or so, you could easily be off two aces or an ace and the trump king, or the club ace-king, etc. None of these hands land in slam when you bid quantitatively (you might get to 5♠ on a few) whereas all of them are in slam when you bid 6♠ directly.

 

My count is, over 30 hands:

 

6♠ cold: 4

6♠ better than a finesse, not cold: 4

6♠ on a finesse: 5

6♠ worse than a finesse but some play: 11

6♠ no play: 6

 

This suggests that blasting 6♠ may well lead to going down more than it leads to making. If we assume that the quantitative approach bids the "better half" of the slams you can see that it's a huge winner over blasting slam. More realistically, even if the quantitative approach just keeps you out of the "no play" slams and randomly gets you to slam on half the other hands, it seems substantially better than blasting.

[cherdano]

Furthermore, when partner moves over 4S, assuming he bids Blacke when he has all off-suits controlled and makes his cheapest cuebid otherwise, the relative frequency of his calls is

 

4N -- 20%

5C -- 70%

5D -- 8%

5H -- 2%

What kind of assumption is this? Usually partner will pass or bid 6S, only when he has a specific concern (lack of keycards, one suit uncontrolled etc.) but otherwise good cards will he bid anything else.

 

Where did you get your percentages of 6♠ making from, btw?