Are you a one-boxer or two-boxer?
Let me get straight to the point:
You are presented with two boxes, Box A and Box B.
Box A contains $1,000
Box B contains either $1,000,000 or nothing
This is what we know about the game.
The amount of money in Box B is determined by Omega (a supernatural being) who is "almost certainly" accurate in her predictions. If she predicts that you will take home both boxes, then no money will be put into Box B. If she predicts that you will take home only Box B, then $1,000,000 will be placed into the box.
Omega has never been wrong so far. She has been correct on all observed occasions so far - everyone who took both boxes has found box B empty and received only $1,000; everyone who took only box B has found Box B containing $1,000,000.
When you are presented with both boxes, Omega has already left. The prediction will already have been made by the time the game starts, and the amount of money in Box B is already fixed.
You cannot first choose Box B and then open Box A. You either take both boxes or take only Box B.
If Omega predicts that the player will choose randomly, then box B will contain nothing.
Assuming you want to win as much money as possible, will you take both boxes or just Box B? Are you a one-boxer or two-boxer?
Some of you may know this game as the Newcomb's Paradox. I assume many HackerNews readers are programmers - extremely logical people. I am curious whether the HN community skew towards a one-boxer or two-boxer.
Vote & view results
(Please make a choice first before continuing...)
Analysis
Why should you pick only Box B?
Since Omega has shown to be never wrong, it makes sense that by taking only Box B, you are almost guaranteed to get the $1,000,000. However, if you take Box A as well, it will turn out that Box B is empty, since Omega would have predicted that, and you will lose the million dollars it would have contained had you not taken both boxes.
Why should you pick both boxes?
By the time the game starts, the prediction has been made. Hence, it makes no difference to the outcome whether you take one or two boxes. By taking both boxes, you will always get an extra $1,000, whether Box B is empty or contains $1,000,000. After all, if Box B is empty, it will remain empty, even if you take only Box B away with you.
All possible outcomes
Predicted choice Actual choice Payout A and B A and B $1,000 A and B B only $0 B only A and B $1,001,000 B only B only $1,000,000
My choice...
The first time I read this question, I never knew why there's a paradox. I am a one-boxer. This may be due to the fact that my quick read led me to assume that Omega is 100% accurate. Since Omega is 100% accurate, it seems perfectly logical to me to pick only Box B. However, after re-reading the question again, it was never clear to the player whether Omega is always 100% accurate. Omega is shown to be never wrong so far, but that does not mean that Omega will never make a mistake.
Of course, it is also perfectly logical to many others that the contents in Box B have already been decided by the time the game starts. Hence, it is illogical to only pick Box B regardless of how accurate Omega is. (I am not about to start a deterministic metaphysics debate.)
To me, this paradox comes down to the player's confidence level with Omega, and what "almost certainly" means to the player. Till now, I am still a one-boxer. I see Omega as someone who is 100% accurate, or extremely close to 100% accurate. In that sense, I think taking only Box B makes total logical sense.
More about this game
This thought experiment was devised by the physicist, William Newcomb, in 1960. To this day, this experiment is still widely discussed because there is no generally agreed solution. Apparently, people are evenly divided between one-boxer and two-boxer.
If you want to go more in-depth about this paradox, you should read more about Causal Decision Theory. http://plato.stanford.edu/entries/decision-causal
Follow me @lominming for more philosophical discussions.