Blofeld

As pointed out, some of these problems seem to have been garbled from their standard forms, presenting us with either a problem with not enough information or one with a trivial solution. I'll skip the large-numbers-estimations because I'd encourage others to try these (they're fun and not too hard). But some of the other questions haven't been adequately answered, I think, so I'll have a go. 2. Standing on the blades seems to be asking for trouble. For one thing, my experience of blenders tells me that stuff is sucked down in the middle (and thrown up around the edges). At any rate the net airflow up/down must be zero. I'd rather not get stuck in a turbulent flow of this kind when another option presents itself: I jump out. I'm not quite sure how big a nickel is, but it doesn't matter. Say we're being shrunk to 1/n of our normal size in linear dimensions. Then muscle strength, which is proportional to cross-sectional area, will be 1/n^2 normal. Our legs will be able to push us from the ground for 1/n the normal distance. Using E = Fs (E = Energy, F = force, s = displacement) to get kinetic energy gained from jumping, we should have 1/n^3 the normal amount. But our mass is also 1/n^3 normal, so when we leave the ground our velocity is just the same as when we jump at full size. If we neglect air resistance we'd thus be able to jump to the same height. Air resistance will play a bigger role on small-us, but not sufficiently big that we shouldn't be able to clear the blender walls. 9. If we assume that everyone involved is entirely logical and knows all the others to be so, then on the hundredth day all the wives kill their husbands. [Claim: if precisely n husbands have been unfaithful then their wives will kill them on the nth day. Obviously true for n=1. Proceed by induction.] 11. Probability of not observing a car in 30 minutes = 0.05. Therefore probability of not observing a car in 10 minutes has to be the cube root of 0.05. Probability of observing a car in 10 minutes is 1 minus this, or roughly 0.63.

I think this is a restriction of option (a); a proper combination of (a) and © would include some three-suiters missing a major suit (or count 5431s as 3-suiters, allowing a trebleton in a major). Showing "both majors" doesn't seem to specify that the hand must be "two-suited" (whatever that means).

I would show strength, but not with 2♥. Rather I think 1NT is a reasonable description of the hand in context. We seem to merit another call, but 2♥ is rather higher than I think is safe, and 1NT has the added advantage of showing stoppers. 2♣ is quite a misrepresentation; it should show at a minimum a 6 card suit.

I think it has to start (3♠) Pass (Pass) 3NT (Pass) Pass (DBL) Pass (Pass) ? Now as East I would run. If Redouble was for rescue I'd bid that (as it has to be a two-suiter), but I wouldn't normally have that agreement, so I guess I'd pick a minor. As far as I can see I'll just be playing in whichever minor it is, so I'm not sure which I'd go for.

(I'm a 5♥ bidder, but my reasons have been given above. I'm also an optimistic 5♥ bidder and prepared to raise 6♣ to 7, just signing off over 5♠)

I confess that I'd like to make another move.

Surely worth another move. I think I just bid 6♣, though. How much worse could we be for that bid?

I agree with 4♣, but think we're just shy of another bid now.

Lol, I have no idea what this post said before, but seeing this made my day :) It was another hand where a heart lead takes the contract down, this time exactly as much as a club lead would.

Opening hand, stiff spade, 345 in the other suits - nothing other than double even occurs, which makes me worry that I've missed the point of the problem.

Cash the ♣A and ♥A, run five diamonds. S must keep a club and two hearts, so has to throw a spade. Now exit in spades to N. N can cash three spades but then has only hearts left, leading into the tenace in dummy and giving the tenth trick.

I voted for my expectation of the percentage, which is around 30-40%. I think the actual percentage will very rarely be in this range.

I overcall and think it's close-ish, but not so close that I wouldn't do it without the ♣J.

Wow! I'm glad to find someone else who has seen the light! 4C as always Gerber just avoids so many misunderstandings!!!!1oneone

If partner can overcall to the 2-level, opponents won't make 3♣x, so Dbl is safe... That obviously wasn't Han's point - if you don't raise the suit, partner won't expect you to have anything in the suit, so using double to show you really don't have anything in the suit is waste of a very useful bid. I had the same reaction as Han and Arend, but on inspection I think Frederick must be saying that he inverts the meaning of pass and double here - is that right? You'd give the opponents more room when you don't have a raise but less room when you do have one. I think that the main problem would be memory, and working out when it does or doesn't apply. Double with that meaning may be safe here, but I don't think it would be if p made a 1M overcall and the cue was 2M.

David: Wow! I hadn't thought about the problem enough. I find it very interesting, as well as highly counter-intuitive, that there can be a distribution such that the expectation is always higher when you swap[1]. Thanks for doing the analysis on that. [1] Though it perhaps shouldn't be a surprise that this kind of distribution leads to counter-intuitive results. After all the "gambler's fallacy" is a guaranteed way of making money even with 99% odds of losing each bet, if there is no limit to the funds available to you (or to the size of stake you can wager).

I just voted on this. But I have an admission to make. I didn't try to pick a random number. Instead I tried to pick a number to counteract the patterns other people would make. I went for 4, and this seems to have worked, to a reasonable extent. But that's playing psychology, not trying to pick a random number. Unfortunately I didn't realise what I was doing until after I'd voted.

Yes, this makes a difference. Now the argument with expectations works because you know you've got 50% chance each of getting half as much and twice as much, so you should pick a white envelope (assuming your aim is to maximise expected winnings).

I don't really like this argument but I agree with the rest of your post. (although you shouldn't call it "Han's argument" because I didn't come up with it myself, it's a well-known problem). OK, I admit that I don't really like that argument either.

Han is of course correct. The fallacy is this. Although you have picked between the two envelopes randomly, it is in general false that the other envelope will have more money in 50% of the time. To see that this cannot be true, imagine you open envelope A and find 1 cent in it. Envelope B can't have half a cent in, so must have 2 cents - and the probability it has more money is 100% rather than 50%. This is just an illustration of the fact that our intuition in this area is often wrong, and relies on the accidental fact that money isn't infinitely subdivisible. If you allow for arbitrarily small amounts of money, the argument doesn't hold. But the one that Han gave prevents any distribution of possible amounts of money to envelopes that always has a 50% chance of having more money. In fact, what the "paradox" shows is precisely that such a distribution cannot exist!

I think both of Richard's ideas for reducing dropouts are good. I particularly like the permanent floating individual -- rather like the MBC but with different partner and opponents each round. I think this would be very popular.

Yes, I'd double with a 4441. I produced 20 hands where we hold this and West has 7+ spades, 10- points: ------------------------------ S: 4 H: J95 D: AKJ6 C: K9874 S: AQJ8765 S: KT9 H: 6 H: Q8743 D: Q7 D: T854 C: J65 C: T S: 32 H: AKT2 D: 932 C: AQ32 Partner might double, but it's borderline. If partner passes initially then doubling turns +50 into +600 -- if partner doesn't bid slam. I think if we posted this as a problem then a significant proportion of people would either double initially or bid slam with the north cards. Though possibly not the same people as those doubling with South. -------------------------- S: A H: QJ8743 D: KJ7 C: KT6 S: QJT9864 S: K75 H: 65 H: 9 D: AQ5 D: T864 C: 8 C: J9754 S: 32 H: AKT2 D: 932 C: AQ32 Partner would have acted (double/5H according to preference), so this one is out. -------------------------- S: K H: 8753 D: KJ7 C: KJT64 S: AQT9876 S: J54 H: 9 H: QJ64 D: AT D: Q8654 C: 975 C: 8 S: 32 H: AKT2 D: 932 C: AQ32 If partner passes 4Sx then we turn +50/-420 (according to whether they guess trumps right ... probably they won't) into +100/-590. If partner bids we land in 5C or 5H, both going down. I'd tend to bid with the north hand - I expect to make a vulnerable game opposite a normal takeout double, and if we're going down then 4S may well be making. -------------------------- S: AQ H: QJ985 D: T74 C: K54 S: KT98764 S: J5 H: 74 H: 63 D: KJ D: AQ865 C: 98 C: JT76 S: 32 H: AKT2 D: 932 C: AQ32 turns +150 into +500 if partner passes, but again it's not clear that they will when we probably have a game and possibly a slam; 5H is -100. -------------------------- S: KJ H: 753 D: QJ8 C: KT987 S: T987654 S: AQ H: QJ4 H: 986 D: K7 D: AT654 C: 4 C: J65 S: 32 H: AKT2 D: 932 C: AQ32 This is at the stupidly aggressive end of 4S, but doubling leads to -590. (and 5C is 4 off on the right defence!) -------------------------- S: K H: J963 D: AK4 C: KJT85 S: AQ98754 S: JT6 H: 87 H: Q54 D: J87 D: QT65 C: 9 C: 764 S: 32 H: AKT2 D: 932 C: AQ32 Partner would have doubled, so not relevant. -------------------------- S: 8 H: QJ976 D: AKQJ4 C: T4 S: AKJT976 S: Q54 H: 53 H: 84 D: 6 D: T875 C: J86 C: K975 S: 32 H: AKT2 D: 932 C: AQ32 I think partner would have doubled/bid 4NT ... but pass is possible. In which case double turns +100 into +680/+1430. -------------------------- S: 6 H: 86543 D: K864 C: KT8 S: KT98754 S: AQJ H: 97 H: QJ D: 5 D: AQJT7 C: 974 C: J65 S: 32 H: AKT2 D: 932 C: AQ32 Double turns +100 into +300 (everyone passes as north, right?) -------------------------- S: Q6 H: J9765 D: KT4 C: K96 S: AJT9874 S: K5 H: 4 H: Q83 D: Q5 D: AJ876 C: 875 C: JT4 S: 32 H: AKT2 D: 932 C: AQ32 +50 into +100. -------------------------- S: A H: 5 D: KQT865 C: K9864 S: KQJ8764 S: T95 H: J974 H: Q863 D: --- D: AJ74 C: T7 C: J5 S: 32 H: AKT2 D: 932 C: AQ32 Partner wouldn't have passed. -------------------------- S: KT8 H: 8653 D: KQ75 C: J5 S: AQJ9764 S: 5 H: 4 H: QJ97 D: T6 D: AJ84 C: K97 C: T864 S: 32 H: AKT2 D: 932 C: AQ32 +50 into +100, I think? possibly 2 down. -------------------------- S: A98 H: 9754 D: A86 C: KT8 S: KQJ7654 S: T H: J H: Q863 D: Q54 D: KJT7 C: 97 C: J654 S: 32 H: AKT2 D: 932 C: AQ32 +100 into +300. -------------------------- S: J H: 853 D: AKQ854 C: T87 S: AKQT985 S: 764 H: 94 H: QJ76 D: T6 D: J7 C: J6 C: K954 S: 32 H: AKT2 D: 932 C: AQ32 +150 into a probable -100 in 5D. -------------------------- S: T9 H: J64 D: AQ7654 C: 74 S: KQJ87654 S: A H: 3 H: Q9875 D: J D: KT8 C: KT8 C: J965 S: 32 H: AKT2 D: 932 C: AQ32 -420 into -590 (-300 or -800 if p bids 5D ... do you double as east?) -------------------------- S: 8 H: Q74 D: KJ4 C: KT9764 S: AJT9654 S: KQ7 H: --- H: J98653 D: AT865 D: Q7 C: 8 C: J5 S: 32 H: AKT2 D: 932 C: AQ32 -450 into -690 or -100 depending on what partner does (actually east may well compete to 5S ... so -450 into -450 unless partner now doubles). -------------------------- S: K96 H: --- D: AKT65 C: JT874 S: AQJ8754 S: T H: Q65 H: J98743 D: J D: Q874 C: 65 C: K9 S: 32 H: AKT2 D: 932 C: AQ32 +200 into +800 (or +600 if partner bids) -------------------------- S: J H: J973 D: AQT76 C: T87 S: AKT8765 S: Q94 H: 65 H: Q84 D: J85 D: K4 C: 4 C: KJ965 S: 32 H: AKT2 D: 932 C: AQ32 +50 into +100/-100 depending on what p does -------------------------- S: T H: Q863 D: AKQ84 C: JT6 S: AJ98764 S: KQ5 H: 94 H: J75 D: 5 D: JT76 C: K95 C: 874 S: 32 H: AKT2 D: 932 C: AQ32 Partner might double 4S; if not double turns +100 into +650/-100 (if partner drives to slam). -------------------------- S: AJ H: QJ94 D: A854 C: JT6 S: KQT9864 S: 75 H: --- H: 87653 D: KQT6 D: J7 C: 85 C: K974 S: 32 H: AKT2 D: 932 C: AQ32 +50 into +100. -------------------------- S: Q87 H: J83 D: KQ765 C: T4 S: AKJT654 S: 9 H: 97 H: Q654 D: T D: AJ84 C: J95 C: K876 S: 32 H: AKT2 D: 932 C: AQ32 +100 into +300. -------------------------- Which leaves me less sure than before which is going to be better!

Thanks for the explanation, Mike. And I like the point about the opponents being overly aggressive at these colours. --- Rebound, if you're taking the aggressive call whenever it's a close call, doesn't that just mean that you move the boundary of what counts as close slightly? --- To all those doubling, would you double in the direct seat?

Helene, what's wrong with asking? I don't think that asking why a player made a bid has any implications of cheating/concealed agreement or dumping. It just helps to understand what's going on.

Frances, would partner have played this way in trumps with KJT?