kgr

This! And: Axx Axx xxxx xxx : also 1D => I bid 1D if I prefer that partner plays 1NT and 1NT if I want to play it.

Well Done !!

1NT-2♣ 2♦-3X 2♦=forced 3X=4441 GF with singleton X (I think this is part of Heeman)

We play: 1♣-1♦ 1♥-?? 1♥=3c♥ and forcing We play that 2♦ is 5c♥ and asking strength/shortage (We don't have a good bid with a 4c♥ and slam interest)

DBL=♣ OR ♦&♥

2NT Natural invite. (Partner can be weaker with his balancing bid)

The hand you gave, is clearly a hand, that would break the transfer, i.e. will not bid 3C, since opener does not really want to play 3C. If opener bids 3C, this can happen, since the 2NT bid does not imply, that responder will bid again, he may well have 6 clubs and 4 spades, deciding, that it is a brilliant idea to make his long suit trumps. With kind regards Marlowe Aha, I missed then non-forcing 3♣. Then I agree that 4♦ should be an invite.

I have a rule that 4m is slam interest if it is possible (e.g not if 4m bidder did already limited his hand before). So slam interest for me (minorwood if I play that). Something like: ♠xx ♥AKxx ♦AKQxxx ♣A ...or should that bid 3♥/4♣ iso 4♦?

Why 1S and not 2S?: - Is 2S too dangerous vuln? - Or is it too good for a 3th seat 2S?

It was also my feeling that I had said enough with 1♦ but the first 2 answers to this post (before seeing both hands) seem to disagree with it. In IMPs I would probably have bid 5♦ anyway because of the ♣ support.

Thanks all for the answers. This was interesting. ...and of course a last question: If both opps still follow to a suit. What is the impact if you know for sure that they are not playing random, but allows from low to high (This is a realty against some opps). Can you then include it somehow in the vacant space theory or does it not make any difference? Thanks, Koen

Thank you Ceeb. I'm convinced now. - I guess that counting discards would give an even worse result. BTW: How did you come to 1/7400 and 1/360 in: ...Increases by 1/7400 knowing no club void. Increases by 1/360 knowing no club void or singleton.... Do you have a program for it or is there some logic to come to these figures?

Ben, My feeling says that South is more likely to have ♥Q because he had more Hearts initially. But I don't see how this relates to the Monte Hall problem and even less how it relates to my question.

[hv=d=n&n=sxhxdajxxxcakqjxx&w=saktxxxhakqxxdxcx&e=sjxxhjtxxdqxxctxx&s=sqxxhxxxdktxxcxxx]399|300|Scoring: MP[/hv] Not sure about all hands, but the above will be close. 1♣-(Pass)-1♦-(DBL) 3♦-(Pass)-Pass-(3♠) 4♣-(Pass)-Pass-(4♥) All Pass Is final Pass by South the biggest mistake? Rem: 4♥= because leader (not very strong) didn't take the ♠ finesse.

I messed up in the other post, let me try again: [hv=n=skjt9hxxxdxxxcxxx&s=saxxxhkqjt9dakcak]133|200|[/hv] contract 6♠. LHO leads ♥x, RHO takes with the ACE and return a ♥ for LHO to ruff. LHO plays ♣ and you take ♣A, (♣K, ♦A, ♦K all follow) ♠A, You play small ♠ and LHO follows small. Probability that LHO has ♠Q? Vacant Spaces: 13-1(H)-3(S):13-4(H)-1(S)=9:8=0.529412 Also take other suits into account (HOW WRONG IS IT?): Played ♣A: 13-1(H)-3(S)-1(C ):13-4(H)-1(S)-1(C )=8:7=0.533333 Played ♣A, ♣K: 13-1(H)-3(S)-2(C ):13-4(H)-1(S)-2(C )=7:6=0.538462 Played ♣A, ♣K, ♦A: 13-1(H)-3(S)-2(C )-1(D):13-4(H)-1(S)-2(C )-1(D)=6:5=0.545455 Played ♣A, ♣K, ♦A, ♦K: 13-1(H)-3(S)-2(C )-2(D):13-4(H)-1(S)-2(C )-2(D)=5:4=0.555556 What is the real probability of these last? Is it closer to 0.529412 or closer to the wrongly calculated?

[hv=d=n&v=n&s=sqxxhxxxdktxxcxxx]133|100|Scoring: MP[/hv] 1♣-(Pass)-1♦-(DBL) 3♦-(Pass)-Pass-(3♠) 4♣-(Pass)-Pass-(4♥) Pass-(Pass)-?? 1♣=2+ (you open 5542) Do you agree with the bidding and what now?

What is the logic about this? (Before I read this I thought making a post to ask this & I was almost sure that you could do it always.) Logically you would think that if LHO leads a Heart then vacant spaces are 12:13..? I can only remember this if I understand it. Because vacant space calculation is an approximation in some situations. For example, suppose opps have 8 spades, you draw two rounds, both follow. Therefore, spades can't be 8-0 or 7-1. However, 6-2, 5-3, 4-4 are all possible, so you just don't really know the exact distribution of that suit. In this sense, you can't include this suit into your calculation. All you know is that spades distribution is rather unknown and it's impossible to be 8-0 or 7-1, which is still a very small percentage comparing with all the possible spades distributions. Therefore, It's still fairly good approximation to assume that you don't know the spade distribution at all. In the other thread talking about the probabilities, one post was very well said: what's the average number of your heart suit if you open 1H showing 5 or more? I guess it can't be 6 and should be in the middle of 5-6, because frequency of 5, 6, 7 hearts holdings are very different. In this case, it's the same logic. When they hold 8 card, even if you know the distribution can't be 7-1 or 8-0, you still don't know the exact distribution and 7-1 8-0 are very rare events, so you can't really take those out of your approximation easily. Therefore, you'd just stick to what you have and consider the distribution of spades is unknown. The real percentage can be calculated by computer simulations in a quite accurate way, which should be slightly different from the vacant space calculation. However, at the table, vacant space counting is still your best friend. Still, in many situations, vacant space counting actually gives the accurate result. Thanks for the effort. I want to believe the above, but I wonder how far off both methods are: [hv=n=skjt9hkqjxdxxcxxx&s=saxhxxxxxdakqcakq]133|200|[/hv] ♠ is trumps. LHO leads a small ♥, RHO return a ♥ and LHO ruffs. LHO plays a random ♦ and RHO follows that suit. You cash ♠A and lead a second round. All follow with small ♠'s. Probability that LHO has ♠Q according to vacant space theory: 13-1-3:13-6-1=9:6=0.6 Probability if WRONGLY taking the ♦ play into account: 13-1-3-1:13-6-1-1=8:5=0.615385 If Playing ♣/♦ before the 2nd trump then: - for Vacant Spaces this will always be 0.6 - for the WRONG calculation this will be: 1 minor: 0.615385 2 minors: 0.636364 3 minors: 0.666667 4 minors: 0.714286 5 minors: 0.8 ==> Is anyone able to calculate the real probabilities? BTW: Does it make a difference for vacant space theory if opps always play their small cards from low to high?

The problem with that is I only get an hour to play a day, so looking up histories on every pickup partner cuts into that time severely. Getting up from the table is also a waste of precious time. .... I think that people who are against a rating system should try this. Log in on BBO, start playing asap for 1 hour and then stop. Do that for one week and you see that a rating system could also have advantages. (I used to play a lot like that on BBO, but now I almost never play anymore)

Actually yes, IF LHO picked a totally random card to lead, and that you need to make a decision right before RHO plays. After trick 1 is completed (assuming RHO follows heart), the vacant space is back to 12:12. Are you saying?: that if LHO leads a random card then probability that RHO holds another not shown specific card is 13:12. that if LHO is a bridger and leads a card then probability that RHO holds another not shown specific card is 13:13. (what if LHO is a beginner and does not have a clue what he is doing??)

I didn't understand it. I'll reread it later

What is the logic about this? (Before I read this I thought making a post to ask this & I was almost sure that you could do it always.) Logically you would think that if LHO leads a Heart then vacant spaces are 12:13..? I can only remember this if I understand it.

Thanks all for the answers!! Below the actual hands dealt by Jack [hv=n=s64ha952d95cakq65&w=sq83hq87daq7cj743&e=sajhkj64dj8642ct2&s=skt9752ht3dkt3c98]399|300|[/hv] Jack thinks that ♥A at trick one is slightly better (98.3 vs 88.1) and would continue with a low ♠ in trick 2. (It is taking 1000 samples to do this. But I can imagine that playing ♥A is better if you know double dummy what the best play is in trick 2; while in reality it is possible that ♥ duck is better).

- I would always go to 4♠ with your example hand - I don't see why you should always upgrade if LHO DBL's (If partner has extra length in ♠ then he will upgrade his hand). If partner has no extra length then it is a bit more likely that ♠ are 4-0 - After the DBL: - xx in ♥ and ♣ is not good. partners honous are more likely to be covered by RHO. - But I wouldn't downgrade the hand; Seems like ♦'s will be worth more and maybe LHO will not have an entry to play through ♥xx or ♣xx.

Why is ducking ♥A so much better?

Partner had a ♣ void. I think his hand was something like: ♠xxx ♥Axxx ♦QTxxxx ♣