Yeah, I think that a smartwatch along the lines that you describe would be a plausible consumer product. For me, limited battery life would be the killer, but that might have solutions. One that I would like to see is ePaper for the display, which would also help with outdoor readability. On a watch, you could experiment with color schemes that are not your Kindle classic black text on white background. With a good designer, an ePaper smartwatch could look a lot like a Swiss fancy watch, but pack all sorts of functionality inside. (I've been convinced for years that the "bigger and fatter" trend in men's watches is a scheme designed to pave the way for wrist computers.)
I think a lot will depend on whether they can design a non-obtrusive charging method. My idea is to make a little inductive platform that you keep in your bathroom, which is the resting place for the watch as you shower. When you are done with your shower and put the watch back on, it has a guaranteed week of normal-use battery life. (Not that users would only shower once a week, but sometimes they won't shower at home and they shouldn't have to worry about watch death.)
The people most likely to make it through any kind of collapse are ones who can organize or join a social network that functions despite the new challenges. They would willingly watch the backs of their friends and receive the same benefit from them. They would shut up and work on the projects of the group, even if they suspected a "more optimal" strategy was available.
The first people to starve or die from infections would be the individualists who think that as soon as things get tough, they have to retreat to bunkers with their guns. People with social skills, people who are easy to like, people who are good with kids, people who evoke sympathy from others, people who are hard-working, open and jovial - they would be the ones that are in the best position to benefit from the cooperation that will become necessary when things get tough.
The way I see it, the fact that we can survive without the explicit beneficence of others is probably the biggest luxury of our age. We work for money, trade money for necessities and comforts, and this works fine even in the complete absence of exchanging favors. But this kind of lifestyle is a complete anomaly in human history. Actually, even now, the majority of the Earth's people do not live this way. This kind of informal social reciprocity is what we would need to return to. We would become tribal again. On Slashdot, people are under the illusion that the individualism of late-industrial society can somehow survive its collapse. That would be a fatal mistake. The right strategy is to give up a great deal of our autonomy for the sake of being useful to others. What you're ultimately doing after you subordinate yourself to the group will probably not involve much of what you learned in your jobs and hobbies. A lot of it will involve digging, carrying, sawing, gathering and socializing. Grit and attitude are far more valuable for these necessary things than skill and knowledge. Even complete non-experts with the right work ethic will contribute a great deal to their collective group, because of the sheer amount of extra work that will be necessary in a post-collapse society.
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?
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 =
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 =
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
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!
If you have a procedure with 10 parameters, you probably missed some.