| Re: Prisoners' Dilemma |
[Jul. 23rd, 2008|04:22 pm] |
So still no solutions.
It occurred to me that I don't have a proof that the following is optimal (though I'm pretty sure it is, as it stores useful data of length n into blocks of length n, in the sense that it allows every prisoner to infer the previous box by looking at any box). It's optimal for small numbers, anyway.
( Gory details )
The integration rule tells us that this is less than the integral from n/2 to n of 1/i, which basic integration tells us is ln(n) - ln(n/2) = ln 2, which is about 0.7. In other words, using this strategy, our prisoners can win just under a third of times they normally would, and by the arbitrary rules, survive.
It turns out that this is too much of a hassle for the warden, especially since his apparently mathematically minded victims aren't dying, so he's now picked a new problem (for which answers can be found online, as this also is not an original problem). He groups the prisoners into tables of 3, and places black or white hats on their heads. They have long peaks, so prisoners can't see their own hat colour. The challenge is that the prisoners around the table must either guess their hat colour or pass.
If they any prisoner guesses incorrectly, the warden will not feed any of them. If at least one guesses correctly and the rest guess correctly or pass, they get fed. If they all pass, the hats are re-picked randomly and they can have another go. Servings are reduced, so the prisoners will die if they don't eat strictly more than half of all mealtimes. Can they survive? If so, does the warden have a tactic to defeat this survival by picking hats in a nasty way? |
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| DDoS attacks - why do they work? |
[Jul. 23rd, 2008|04:57 pm] |
So, 4chan is under a massive DDoS attack right now, causing it to be completely inaccessible. This doesn't exactly bother me as I rarely use it. But it does bring me to wonder: How can such an attack persist?
DDoS attacks are a result of many small internetted machines sending large amounts of data to the target until it crumbles. This data presumably gets routed through a number of routers: The breached computer's ISP, their upstream, large hubs, the victim's upstream, the victim's ISP and finally the victim.
Obviously when this sort of thing happens there's a block at the recieving end, presumably as far up as they can go to save the costs of recieving all the spam. My question is why can't the blocks happen at the sending end?
DDoS attacks must be readily recognisable with minimal inspection. It seems most routers nowadays use connection tracking and it's pretty unlikely anything can make a connection to the target under all this abuse, so one is led to suspect that all this data is sent via SYN or maybe RST packets over TCP, UDP spam or ICMP spam. The thing is, all of these things should be expected to be of a fairly low volume. UDP is used for DNS and gaming, which shouldn't be too high bandwidth, ICMP is used for basically nothing so can almost certainly be safely limited, and it's pretty rare for a machine to need to make more than 10 connections per second, so a burst of 100 and an average of 15 ought to sort that out.
Not only is it useful to stop the spammage, but it must also be useful to be able to mail customers with "we suspect you've been rooted" when traffic consistently breaches these limits, with cutoffs threatened after a week or so without adequate explanation.
So, like I say, why doesn't this happen? Is it just too hard to track the data? Am I wrong about connection tracking being common? |
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