A very cool problem! Thank you for sharing it and helping us along with the discussion.

You're right that I ruled out the opponent voluntarily using rock, based on the informal idea that it could only make things worse, since the weakness of the opponent comes from what is already a strategy with too many rocks, which will be countered. I also ruled out ever using scissors against that rock-heavy strategy in a similarly informal way. And this makes the problem fairly easy to calculate.

So, here's something I haven't thought about yet: What is the opponent's optimal strategy on the turns where he gets to choose what he throws?

So here's what I have:

First, there is some uncertainty about what ratio of your opponent's throws will be paper. Let's call that ratio x. This means that we can define the likelyhood of his throws this way:

HeDoesRock = .5, HeDoesPaper = x, HeDoesScissors = .5 - x

Now you need to figure out the optimal winning ratio of your throwing either rock or paper.

YouWinIfRock = HeDoesScissors = (.5 - x); YouLoseIfRock = HeDoesPaper = x
YouWinIfPaper = HeDoesRock = .5; YouLoseIfPaper = HeDoesScissors = .5 - x

Winning Margin = FreqRock[(.5 - x) - x] + FreqPaper[.5 - (.5 - x)] = FreqRock(.5 - 2x) + FreqPaper(x)

Now take the first derivative of winning margin and set it to zero to find the maximum:
d/dx .5FreqRock - 2FreqRock(x) +FreqPaper(x) = -2FreqRock +FreqPaper = 0

So 2(FreqRock) = FreqPaper, so you should throw paper twice as often as you throw rock. And surprisingly, you can get this result without ever needing to know x, the optimal ratio of your opponent throwing paper. Is that right?

To figure out what you should do, first assume your opponent is rational, and will make good choices whenever he is able. Since he knows that you will play a paper-heavy strategy to counter his rock-heavy strategy, it would not be rational to voluntarily choose more rocks. That could only make things worse.

But if he tried to exploit your paper-heavy strategy by throwing scissors on turns when he gets a choice, you'd have a perfect strategy against this: All rock. On forced rock, you get a redo, and on non-forced rock, he does scissors and you win. So on first pass, I think that your opponent should favor paper when he can choose. It's not like you'll ever do scissors. That's auto-lose half the time - basically a complete surrender of your advantage. So paper is a safe move for your opponent.

The problem is that if he did 50% rock and 50% paper, then all-paper will be your perfect counter. He won't let you do that, so he'll have to throw in some scissors. Just how many? It looks now like you will both simultaneously have to determine optimal strategies in order to answer that question, and this will require derivatives of two sets of optimal-choice equations - so that you can solve for the two maxima. Sounds like a fun problem!

Good point.

I was dumb enough to follow that link, and WTF!?! You sent me anti-Semitic Nazi propaganda, totally unconnected to what I said?

If I still lived in California I would also have been "virulently opposed" to prop 8, but I hate the idea of judging someone's employability based on how they vote. To suggest that Google would treat Mozilla differently simply based on a single-issue stance of its new CEO is really selling them short. They invest in Mozilla for strategic reasons. (Mozilla isn't some sort of lazy couch-crasher that Google supports because of Mozilla's charming personality.)

And for that matter, I don't think we should judge products based on the ideology of the people who created them. To save us some time, I'll get straight to a Hitler example, noting that Hitler personally played an important role in the design of the VW Beetle. But hippies can still drive Beetles without thereby supporting Hitler.

Generation ships are pointlessly risky, heavy, expensive and tedious for the inhabitants. Accelerating a city of humans to acceptable speeds is just bad scifi. Rather than the colonists being born en route in some miserable spaceship full of stressed cooped-up people, I say it's better that they are born at their destination, in an orbiting nursery that could partially be constructed from local materials. The parenting would have to be done by AI and the gestating would happen in an artificial womb, but both of these technologies will be ready long before a suitable propulsion system is perfected. There are already independent reasons to pursue both parenting/tutoring AI and artificial wombs for terrestrial applications, and I expect that both systems will be usable in the lifetimes of some of today's slashdotters. Children being raised by AI is potentially controversial, but before long, AIs will be better at parenting than the many millions of bad human parents in the world today, who still get to keep their kids. And it will keep improving, even if human parents don't.

The worries about genetic diversity are just stupid. We could easily just bring along frozen fertilized eggs, which will remain viable with proper shielding for even a century-long trip. These could be gestated by the early generations of colonists, or by the artificial wombs that they brought along. But I would think they'd serve as a backup. Much less cumbersome would be to simply transmit some suitable DNA sequences from Earth once the colony ship arrives, and print it to DNA using Venter technology that we basically already have. The process is less likely than freezing to introduce errors. The privilege of instantiating your DNA in another solar system could be a reward for super-awesome human beings that do cool stuff in the decades that the ship is en route - a kind of Nobel Prize for being a worthwhile person.

The point of any stellar colony ship is to travel light - as light as possible. That means bringing 3D printers that could use materials at the destination to make the stuff that the colony will need: initially, a space station and its facilities. If this payload is light enough - just tools that are able to make the necessary tools on site - then conventional nuclear propulsion might be enough to accelerate the ship to an acceptable speed, and we'd be ready to launch in a mere 150 years. In comparison, a cumbersome ship that hosts a city of 40,000 people, plus all the farms they will need to stay alive for a century, plus all the facilities they will need to keep from going insane, will launch ... never. Because it's a stupid, stupid idea.

I've been looking for a router that can also host a HDD for network storage, and give me global access the data on it through FTP and HTTP. I've done this with various USB routers running TomatoUSB and the like, but the USB bus on those is so painfully slow that it's basically useless. This thing wouldn't suffer from the same problem, and the price and energy consumption are router-competititve. And compared to the price of NAT, this thing is a bargain! The way I picture it, you would need to add an 802.11AC radio to the USB3, and then you'd be set.

The thing that I'm hoping for is that this was a panic buy because somebody at Facebook got spooked that a killer rival VR social app might render FB gradually irrelevant. So the purchase was a defensive move only, to make sure that they leading VR hardware comes from their own house and can't be used to undercut them. I think it's quite possible they didn't have any concrete social VR application in mind. This would not be a strange move for a rich and paranoid company. I'll call this the "playing defense" scenario.

If FB really is just playing defense, then maybe they'll invest in Oculus to make sure it's the VR standard, but they won't really profane it with stupid Facebook shit, because they don't really know how to do that anyway, apart from maybe some app that nobody will really use (except maybe webcam girls).

Of course, if they really are playing defense and they realize that VR isn't really a treat to their market, maybe they will cut funding from Oculus and let the project rot on the vine. That's a real danger, and it would set back the field for a while.

On the other hand, maybe Facebook knows exactly what they want to do with Oculus, and they are about to bend the project to their evil will. Whatever that would be, I'm sure I would think it's an abomination. This is why the gaming community reacted to badly to the announcement. But even if this is true, it might not be a total catastrophe. The important question is whether the technical issues that make VR so hard (latency, pixel persistence, motion tracking, etc.) will be getting a lot of attention, or a little. If it is a lot, then even if the final product is larded up with stupid Facebook crap, a hack will exist to remove it, thus producing an excellent VR headset. I just wonder how much FB is willing to invest in fundamental VR research and hardware improvement. Hopefully they won't neglect this side of things.

The niche of 3D printers is with geeks who want to make stuff, but are uncomfortable around dremel tools, files, saws, sandpaper, clamps and glue. However, they are comfortable with software, know how to install quirky drivers, etc., so they feel like with a 3D printer, they become empowered make stuff without having any idea how to make stuff.

But you know, for the price of even a crappy 3D printer, you can put together a pretty impressive collection of real tools and materials. Just check eBay. Yes, your first projects will be crap, but as you get better, the work will get really fun, and you will be doing something new with your brain, which feels good. So figure out what you can't buy but need to have, and ask yourself whether it could be made of wood, paper machee, machined from brass, or made in a sand mold from aluminum (which you later finish). In many cases, the results will be better and cheaper if you don't make it in a 3D printer.

I recently sat through The Desolation of Smaug and now I have no appetite whatsoever to watch another Peter Jackson movie. It all started so promising The Fellowship of the Ring, but now his movies have more shark-jumping than Tolkien.

I assume that this is really the core of the idea - that the move would raise coal prices enough to stimulate more investment in renewables. I'm not saying it's a good idea, or even a better idea than investing this $50B directly into renewables, but I imagine that this is what they must have been thinking.

But the point is, the remaining 90% of the coal would be left in the ground, where it is not going to hurt anybody. This isn't about punishing coal miners or even mining companies. This is supposed to be about protecting the Earth's atmosphere and climate.

When we hear these impressive bandwidth numbers, usually a prophecy that "the future is on the cloud" is not far behind. Once our connection to the server is faster, we will get everything we could want without doing any of the computing on site. But people forget that a very low latency is also very important to the cloud experience, and there is very little that we can do about latency. At some point, we just run into fundamental laws of nature. I have a feeling that in my lifetime, consumers will basically stop caring about the width of their pipe (for most, it will be wide enough), and prefer the ISPs that give them the best ping. People who are thinking a few tech generations in the future would do well to keep this in mind, I think.

They already sold a trailer of weed to Canadian prison guards and smuggled weed into the US using a "drone" model train. This is exactly the sort of thing they would do! Bubbles buys a quadrocopter to play with, Julian figures out how to use it for selling drugs, Ricky crashes it, Trevor and Corey take the blame.