MFA

33 hcp and almost balanced. 6NT should be very popular in any game. Odds 5:2 in the heart suit are overwhelming. I'm finessing.

3) There is more to this one than what I wrote. (a)......AQT7....................(b).....AQT7 ...(K954).....(83).....OR.........(K4).....(9853) ...........J32.................................J32 If east sometimes falsecards 8 or 9 from 98xx to induce us play the J on the second round, it means than when we don't see an 8 or 9 in the first round, the possibility of layout (b) should be discounted and thus it could easily be odds on to play for the layout (a) anyway. It's a convoluted game theory situation.

Same here.

Yes.

We might do so if we take a deep finesse because of restricted choice. An example: .....AQT6.............................AQT6 (K54).....(987).....OR.....(K854).....(97) .....J32.................................J32 Low to the T and then J, K, A. When we have seen 2 middle cards from east, restricted choice tells us to go deep on the third round to cater to 87 or 97 or 98 doubleton offside rather than 987.

On a more serious note - these are quite interesting and difficult. I'll give it a try. 1. Low to T, low to Q. 2. We want to scoop 78, 79 or 89 stiff. Low to T that catches 7, 8 or 9. Then we play J (covered), and if righty plays another middle card we are approx. 3:1 for a finesse on the third round (restricted choice). RHO can annoy us by falsecarding with 9875 or 9874. If he does so he will give us two more losing scenarios, three in total (987, 9875, 9874) to compete with three winning scenarios (98, 97, 87). One of the losing ones is a specific 3-3 and thus a little more likely. So if RHO falsecards always or almost always (guess: 95+%), we should fall back on low to T, low to Q. Otherwise we play J on the second round after seeing 7, 8 or 9. 3. We will always handle 98, but we might like to try to pin 9x or 8x by leading J the second time and go deep on the third round. But that would lose to 98x or 98xx (more likely in total), so it is not worth it. Should we drop an 8 or 9 on the first round, we could play the J on the second round to cater to 8 or 9 stiff. 98xx might have falsecard and there are three 98xx's compared to two 8 stiffs/9 stiffs. So if RHO falsecards more than 2/3 of the time, we should not play the J on the second round even if we see an 8 or a 9. 4. If we ever play the J, covered, we would not finesse for the 9 anyway. So leading the J on the second round really only caters to a singleton offside, which is clearly less likely than Kx onside. So we should play low to T, low to Q.

This new notation is killing me. Either we are having two deuces in the first one or a 14-card fit in the last one. Who invented that silly thing, Phil? :D

I can't figure out if you are being over-ethical or masochistic, but please just ask what 2♠ is next time. <_<

Vacant spaces is a rough model that can't handle partial information. Either cards are counted or they are not. It is usual much more accurate not to count in partial counts in the suits than to do so. I would expect 9:8 to be closest to the right answer of the numbers you present. If we cash one club, all we really get to know is that the suit is not 8-0 or 0-8. A very insignificant piece of information. And so on when we cash a second club and one or two diamonds.

Maybe it's a style question, but here goes: North's 2♠ is almost always a doubleton for me. So 3♠ can't be a bad 5card suit. I would have raised 1♠ to 2♠ in our usual precision system, even though 2♣ shows 5 for us. In this sequence, north's 4♠ would be unthinkable for us. AK, A, singleton and three trumps. We would have bid 3♠ forcing over 2♣ as south though to show a very strong suit that doesn't really need support. So in context I disagree with 2♣, 2♥ and 4♠ and would blame north for the bad result.

Or something that they think belongs in their pocket for the duration of the event. Sad but true.

2♠

I would try 1♠ only. If we bid three and catch partner with a singleton we could have blown the board already.

Double, surely.

62.3% to 37.7% is about the same as the 18:11 I suggested. I can recommend learning the method I am using, since the calculations are so easy that they can be performed at the table for instance within seconds.

Something is wrong. East is the one with KJ or KQJ in the suit, and since he is known to be short in trumps, KQJ as a specific holding is more likely than KJ as a specific holding.

Applying the principle of restricted choice to vacant spaces problems is quite easy, since we just have to multiply the relevant opponent's # of empty spaces with the number of ways he could potentially have randomized. That number is 2 in simple restricted choice situations and 3 in double restricted choice situations like this (with 3 equal honours where any of these could be saved for the third round). So vacant spaces makes this 11:6 in favour of the drop, since we can place seven cards with west and two cards with east so far. We multiply 6 by 3 because of the double restricted choice, and then it becomes 18:11 in favour of the finesse. If we like we could then proceed to speculate if the defender is randomizing well enough or if he is more likely to have KQJ for some specific sequence of the honours, etc. And we could evaluate if it is consistent with the bidding to hold KJ and 11 cards in two suits. But the starting point is a solid 18:11 for the finesse. EDIT: Small miscount of vacant spaces corrected (early in the morning :blink:).

I don't like double of 1♠.

Apparently west at your table completely forgot how many tricks one has to take to make 3NT.

2♥. I would not have overcalled 2m, but 2♥ has extra upside. I don't understand balancing with 2NT either. If we don't balance 3♥, then why not double? After double we can pass 3♣ in comfort, but if we balance 2NT, partner could be 3433 or something for a 3♣ preference.

Pass. In partner's shoes I would not necessarily double 1♠ just because I have four of them.

1. Pass. But I open in my usual precision context. 2. 1♠. I like playing 1♠ then 2♥ as not showing extras in this specific sequence 1m-1♥-1♠. So I bid 2♥ over 1N. If it would show extras then I don't have a strong opinion but would probably prefer raising to 2♥ rather than bidding 1♠. 3. 3♥. Partner's 3♣ shows 5 hearts as I play it, btw.

If you cannot get to dummy to lead a ♦ toward the KQ then you will loose at least 2 ♦ trick unless the JT are dub. Que? I think I did figure that part out...

A (too?) quick analysis: If we bang down ♥AK we need ♥Q to be double. If lead middle heart, we need ♦A to be double, but onside as well. So we should lead middle heart only if we estimate that the chance of sneaking past west's ♥Qxx is greater than the risk of ♦A offside. There are some minor issues with a stiff ♥Q or ♦JT tight also to consider. If we bang down ♥Qx double, we should play diamonds from the top rather than duck the first round, since a stiff T/J is in principle twice as likely as a stiff A.