The word "break" has so many meanings, not as many as "pass" and "set", which are the two words with the most meanings in the standard dictionary, with the latter winning by a landslide. Even in games and sports its meanings differ, with a break in snooker being a long run of pots, while a break in darts is to win the leg when the opponent throws first. Take a Break is a very successful magazine which combines rather mindless puzzles and word searches with "soap and star stories".
Even in bridge, break has more than one meaning. A bad break would usually be a 4-0 or 5-1 trump break. To break a contract is to defeat it. But also a break is the "non-completion" of a transfer as happened on the hand below. Fred Pitel judged very well to bid slam when his partner broke the transfer:
2NT was 20-22, 3D was a transfer to hearts, and 4H showed 4 or more hearts and a good hand. I am surprised that other tables who had the same start did not bid slam now, and I think 4NT, Roman Keycard Blackwood, is best although it could lead to a slam off the ace and king of spades. After North showed 1 or 4, South bid 5H which said "if you have only 1 pard, we are too high!" North had an easy 6H, although I might have even bid 5S here to show the king of spades in case South has extras.
The play was interesting. Declarer drew trumps, cashed the top spades and ruffed a spade and played ace and another diamond. When the queen lost to the king, he now took the club finesse. So, the slam was 75% requiring one of two outcomes (with a small extra chance of a singleton king of diamonds or Kx with East). The chance of AT LEAST one of two coin tosses being a head is also 75%, which some people get wrong. That reminds me of another poser. A friend covertly tosses two coins and tells you that one of the two results was a head. What is the chance that the other coin is a tail? I will leave that with you.
That poser is a Monty Hall/Restricted Choice, no?
ReplyDeleteIf one coin is head (50% of the time), your friend will tell you that one, and the other will be a tail.
If both coins are heads (25% of the time), he can pick either, and the other will be a head.
So the answer is 2/3 = 67%?
I would not bet on the other one being a tail at any element of odds on. This is a sort of "double restricted choice" where he has to choose heads or tails when they are both the same, but when they are different he can choose either, and should do so randomly. This time the chance the other one is a tail is 50%.
DeleteOkay, I read that as your friend telling you that a *specific* coin was a head, rather than that one of the two is. And that his statement would be true (so you'd excluded the 25% of Tail/Tail). Obviously if lying is allowed, then his statement is irrelevant and you're back to 50/50.
ReplyDeleteWe will assume lying is not allowed. But he could equally well have said "one of them is a tail" if that was true. With HH or TT he has to say "one of the is a BLANK" but with HT or TH he has a choice.
Delete