2 Drinks Problem

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Problem posed from a friend who delights in torturing me with unsolvable questions: there are 2 shots of black Russian on the table. Another friend has spit in one of the drinks. He tells me: choose one drink for myself, and he will take the other, and we both drink. He then takes one of the glasses and gives it to me.

Should I choose the drink he gave me?

Don't be too quick to whip out Baye's theorem: http://en.wikipedia.org/wiki/Two_envelopes_problem

(Actual outcome: too drunk to care. Can't even remember if the one I had was the spit drink or not.)

You should choose better friends.

You should know your friend well enough to win this, unless he built up an immunity to your other friend's spit. That would be how you win: you imply that he's gay.

When 2 statistics majors have a bet, you can be damn sure they've thought out the entire filtration of events.

Also, I later found out that it was quite a pretty girl who spit in the drink. Somehow, that makes it less gross.

DATA: I have several examples of Commander Riker's battle technique. At the Academy, he calculated a sensory blind spot on a Tholian vessel and hid within it during a battle simulation. And as a lieutenant aboard the Potemkin, his solution to a crisis was to shut down all power, and hang over a planet's magnetic poles, thus confusing his opponent's sensors.

TROI: And from these specifics, what general conclusion can you extrapolate?

DATA: Only twenty-one percent of the time does he rely upon traditional tactics. So, the Captain must be prepared for unusual cunning. Counsellor, Commander Riker will assume we have made this analysis, and knowing that we know his methods, he will alter them. But, knowing that we know that he knows that we know, he might choose to return to his usual pattern.

TROI: Wait, wait. You're over-analysing, Data. One cannot deny human nature. What kind of a man is Commander Riker?

DATA: A fighter?

TROI: Yes.

DATA: The weaker his position, the more aggressive will be his posture.

TROI: And he won't give up.

DATA: Then despite whatever options he is given, he must be-

TROI: The man that he is. Exactly.