The Kelly Criterion in 3D - LessWrong

The Kelly Criterion is a gambling strategy which maximizes the logarithm of your expected wealth. The Kelly Criterion tells you what fraction f∗ of your bankroll to wager. It is a function of the net fractional odds[1] received b>0 and the probability of a win p∈(0,1). f∗=p(b+1)−1b Some properties are intuitively easy to understand. * The Kelly wager is positive iff the expected value bp−b(1−p) is positive. The Kelly wager is zero otherwise. * The Kelly wager is 1 for all p=1. (Ignore b=0.) * The Kelly wager is 0 for all b=0. (Ignore p=1.) What surprised me is that if you fix b and restrain p to the region of positive f∗ then f∗ is a linear function of p. This was not intuitive to me. I expected asymptotic behavior with the greatest df∗dp in a neighborhood of p=1. In other words, I expected the fractional wager to increase slowly at first and then increase faster as p approached 1. Actually, p is linear. Kelly wagers tend to be more aggressive then human intuitions. I knew this and I still underestimated the Kelly wager. I didn't mess this up in a high stakes situation where fear throws off my calculations. I didn't even mess this up in a real-world situation where uncertainty complicates things. I underestimated the Kelly wager on a purely conceptual level. I have written before about the utility of my fear heuristic. My fear heuristic might be helping to compensate for my Kelly miscalibration. RECALIBRATING I'm good at tolerating risk when it comes the small number of gigantic risky bets guiding my professional career. I'm also good at tolerating risk in the domain of painlessly small bets. (Not that there is much risk to tolerate in this latter case.) Judging by this post's analysis, I am awful at calibrating my risk tolerance for wagers between 0.05% and 1% of my net worth. Specifically, I am insufficiently risk tolerant. What makes this worse is that the region of 0.05% to 1% of my net worth is full of long tails. The wagers I'm skipping co

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Technological stagnation: Why I came around - LessWrong

“We wanted flying cars, instead we got 140 characters,” says Peter Thiel’s Founders Fund, expressing a sort of jaded disappointment with technological progress. (The fact that the 140 characters have become 280, a 100% increase, does not seem to have impressed him.) Thiel, along with economists such as Tyler Cowen (The Great Stagnation) and Robert Gordon (The Rise and Fall of American Growth), promotes a “stagnation hypothesis”: that there has been a significant slowdown in scientific, technological, and economic progress in recent decades—say, for a round number, since about 1970, or the last ~50 years. When I first heard the stagnation hypothesis, I was skeptical. The arguments weren’t convincing to me. But as I studied the history of progress (and looked at the numbers), I slowly came around, and now I’m fairly convinced. So convinced, in fact, that I now seem to be more pessimistic about ending stagnation than some of its original proponents. In this essay I’ll try to capture both why I was originally skeptical, and also why I changed my mind. If you have heard some of the same arguments that I did, and are skeptical for the same reasons, maybe my framing of the issue will help. STAGNATION IS RELATIVE To get one misconception out of the way first: “stagnation” does not mean zero progress. No one is claiming that. There wasn’t zero progress even before the Industrial Revolution (or the civilizations of Europe and Asia would have looked no different in 1700 than they did in the days of nomadic hunter-gatherers, tens of thousands of years ago). Stagnation just means slower progress. And not even slower than that pre-industrial era, but slower than, roughly, the late 1800s to mid-1900s, when growth rates are said to have peaked. Because of this, we can’t resolve the issue by pointing to isolated advances. The microwave, the air conditioner, the electronic pacemaker, a new cancer drug—these are great, but they don’t disprove stagnation. Stagnation is relative

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Bets, Bonds, and Kindergarteners - LessWrong

Bets and bonds are tools for handling different epistemic states and levels of trust. Which makes them a great fit for negotiating with small children! A few weeks ago Anna (4y) wanted to play with some packing material. It looked very messy to me, I didn't expect she would clean it up, and I didn't want to fight with her about cleaning it up. I considered saying no, but after thinking about how things like this are handled in the real world I had an idea. If you want to do a hazardous activity, and we think you might go bankrupt and not clean up, we make you post a bond. This money is held in escrow to fund the cleanup if you disappear. I explained how this worked, and she went and got a dollar: Then: When she was done playing, she cleaned it up without complaint and got her dollar back. If she hadn't cleaned it up, I would have, and kept the dollar. Some situations are more complicated, and call for bets. I wanted to go to a park, but Lily (6y) didn't want to go to that park because the last time we had been there there'd been lots of bees. I remembered that had been a summer with unusually many bees, and it no longer being that summer or, in fact, summer at all, I was not worried. Since I was so confident, I offered my $1 to her $0.10 that we would not run into bees at the park. This seemed fair to her, and when there were no bees she was happy to pay up. Over time, they've learned that my being willing to bet, especially at large odds, is pretty informative, and often all I need to do is offer. Lily was having a rough morning, crying by herself about a project not working out. I suggested some things that might be fun to do together, and she rejected them angrily. I told her that often when people are feeling that way, going outside can help a lot, and when she didn't seem to believe me I offered to bet. Once she heard the 10:1 odds I was offering her I think she just started expecting that I was right, and she decided we should go ride bikes. (She

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Anti-Aging: State of the Art - LessWrong

Aging is a problem that ought to be solved, and most Less Wrongers recognize this. However, few members of the community seem to be aware of the current state of the anti-aging field, and how close we are to developing effective anti-aging therapies. As a result, there is a much greater (and in my opinion, irrational) overemphasis on the Plan B of cryonics for life extension, rather than Plan A of solving aging. Both are important, but the latter is under-emphasised despite being a potentially more feasible strategy for life extension given the potentially high probability that cryonics will not work. Today, there are over 130 longevity biotechnology companies and over 50 anti-aging drugs in clinical trials in humans. The evidence is promising that in the next 5-10 years, we will start seeing robust evidence that aging can be therapeutically slowed or reversed in humans. Whether we live to see anti-aging therapies to keep us alive indefinitely (i.e. whether we make it to longevity escape velocity) depends on how much traction and funding the field gets in coming decades. In this post, I summarise the state of the art of the anti-aging field (also known as longevity biotechnology, rejuvenation biotechnology, translational biogerontology or geroscience). If you feel you already possess the necessary background on aging, feel free to skip to Part V. Part I: Why is Aging a problem? Aging is the biggest killer worldwide, and also the largest source of morbidity. Aging kills 100,000 people per day; more than twice the sum of all other causes of death. This equates to 37 million people - a population the size of Canada - dying per day of aging. In developed countries, 9 out of 10 deaths are due to aging. Aging also accounts for more than 30% of all disability-adjusted life years lost (DALYs); more than any other single cause. Deaths due to aging are not usually quick and painless, but preceded by 10-15 years of chronic illnesses such as cancer, type 2 diabetes and A

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