JMStewy

The key insight is that this strategy causes there to be a strong correlation between the success of different prisoners.

As an example, let's say prisoner #10 opens his box and finds #21, then finds #5 in that box, then #84, then #51, then finally succeeds and finds his number 10 in box #51. These boxes form a cycle 10-21-5-84-51 (and then back to 10). Anyone who opens any of these boxes will eventually see the same set numbers that #10 did, so that means that we know prisoners #5, #10, #21, #51 and #84 will all succeed in finding their number by starting at their own box.

Compare that to the situation where they just randomly look in boxes and each independently have only a 50% chance to succeed - then the odds that those 5 prisoners all succeed would be (1/2)^5 = 1/32, or only about 3%. In every cycle containing n prisoners, instead of their success rate being (1/2)^n, now they all succeed together or all fail together.

Now that the success of every prisoner in the same cycle is perfectly correlated with each other, the prisoners' overall chance of success depends only on whether the random permutation created by the warden has any cycles >50 in length. If so, then everyone in that cycle will fail. If not, then all the cycles across the 100 boxes are short enough that all 100 prisoners will succeed.

That's a 終助詞 (shuujoshi) or "sentence-ending particle". Note that despite both being pronounced as "wa", the sentence-ending one is written as わ ("wa"), while the topic-marker particle is written as は ("ha").

In standard Japanese, わ is feminine and mildly emphatic (used for asserting an opinion or stating a fact).

Relevant discussion starts at 14:00 (15:47 to skip the intro).

It's the asker saying "you cannot," likely because of decisions he or she has already made about the setting and characters of the story that the green star will be in.

Your response would only make sense if it were an answerer trying to tell the asker what he or she cannot do.

The koan is commonly accompanied by the following:

"What I actually said was, 'If you wire it randomly, it will still have preconceptions of how to play. But you just won't know what those preconceptions are.'" -- Marvin Minsky

The average 1st grader is 6 years old. 8th graders are around 13 years old.

That's true for hold'em, but in stud variants you need to keep track of the cards held or folded by other players.

Thanks for linking, I enjoyed the talk. I'm currently in the middle of the "go back to school for CS" route into software development, and it was heartening to hear your success story. Between starting on CS a few years late and spending too much time on Hacker News, it's easy to feel discouraged at how little I know.

Being able to "check the further destruction of the retina" is a therapeutic benefit when it comes to macular degeneration. It's the best outcome you can hope for on any of our current treatments for it. The retina is still relatively poorly understood, and our treatments for the pathologies of it are unfortunately limited.