Oddhead Blog

This is the first of a series of challenge posts. I’ll pose a problem in the hopes of convincing the wise Internauts to come forth with solutions. I intend the problems to be do-able rather than mind boggling: simply intriguing problems that I’d love to know the answer to but haven’t found the time yet to work through. Think of it as Web 2.0 enlightenment mixed with good old fashioned laziness. Or think of it as Yahoo! Answers, blog edition.

Don’t expect to go unrewarded for your efforts! I’ll pay ten yootles, plus an optional and unspecified tip, to the respondent with the best solution. What can you do with these yootles? Well, to make a long story short, you can spend them with me, people who trust me, people who trust people who trust me, etc. (In lieu of a formal microformat specification for yootles offers, for now I’ll simply use the keyword/tag “yootleoffer” to identify opportunities to earn yootles, in the spirit of “freedbacking”.)

So, on with the challenge! I just returned from a pit stop in Las Vegas, so this one is weighing on my mind. I’d like to see an analysis of strategies for playing craps that take into account the variance of the bettor’s wealth, not just the expectation.

Every idiot knows the best strategy to minimize the casino’s edge in craps: bet the pass line and load up on the maximum odds possible. The odds bet in craps is one of the only fair bets in the casino, so the more you load up on odds, the closer the casino’s edge is to zero. But despite the fact that craps is one of the fairest games on the casino floor, it’s also one of the highest variance games, meaning that your money can easily swing wildly up or down in a manner of minutes. So on a fixed budget, craps can be exceedingly dangerous. What I’m looking for is one or more strategies that have lower variance, and are thus less risky.

So that this challenge is not vague and open ended, let me boil this overall goal down into something fairly specific:

I prefer if you ignore the center bets in your analysis. Bonus points if you examine what happens with different budgets, table limits, and/or allowed odds. Another way to motivate this is as follows: I have a small fixed budget but want to hang around a high-limit table for as long as possible, because I get a better atmosphere, more drinks, and a glimpse of life as a high roller.

As an example, here is a strategy that appears to have very low variance: On the come out roll, bet on both the pass line and the don’t pass line. If the shooter rolls 2, 3, 7, or 11 you break even. If the shooter rolls 4, 5, 6, 8, 9, or 10, you’re also guaranteed to eventually break even. The only time you lose money is when the shooter rolls a 12 on a come out roll, in which case you lose your pass line bet and keep your don’t pass bet (i.e., you lose half your total stake). There’s only one problem with this strategy: it’s moronic. You have absolutely no possibility of winning: you can only either break even or lose. One thing you might add to this strategy to satisfy condition (1) is to take or give odds whenever the shooter establishes a point. Will this strategy make my $200 last longer on average than playing the pass line only?

For bonus points, I’d love to see a graph plotting a number of different strategies along the efficient frontier, trading off casino edge and variance. Another bonus point question: In terms of variance, is it better to place a single pass line bet with large odds, or is it better to place a number of come bets all with smaller odds?

To submit your answer to this challenge, post a comment with a link to your solution. If you can dig up the answer somewhere on the web, more power to you. If you can prove something analytically, I bow to you. Otherwise, I expect this to require some simple Monte Carlo simulation. Followed of course by some Monte Carlo verification. Have fun!

Addendum: The winner is … Fools Gold!

Here is a fluffy post for a fluffy (but important) topic: the economics of attention.

Yahoo! is in the business of monetizing attention: that’s essentially what advertising is all about. We (Yahoo!) attract users’ attention by providing content, usually free, then diverting some of that attention to our paying advertisers. Increasingly users’ attention is one of the most valuable commodities in the world. This trend will only accelerate as energy becomes cheaper and more abundant, and thus everything we derive from energy (that is, everything) becomes cheaper and more abundant, on our way to a post-scarcity society, where attention is nearly the only constrained resource.

Today, users generally accept content and entertainment in return for their attention, though likely in the future users will be more savvy in directly monetizing their own attention. I’ve heard a number of companies and organizations large and small discuss direct user compensation. Beyond advertising, the economics of attention is important for the future of communication in general.

I haven’t found much academic writing on the topic, though I haven’t looked thoroughly. John Hagel’s piece “The Economics of Attention” is a good start, and he looks to have compiled some nice resources on the topic, though I haven’t yet investigated closely.

An organization that has garnered some attention of their own (of the Web 2.0 buzz variety) is Attention Trust. I find the description on their own website vague and impenetrable. The best explainer on Attention Trust I could find is PC4Media’s, though questions remain. The basic concept is simple enough: users should be empowered to control and monetize their own attention, including the output of their attention (e.g., their click trails, personal data, etc.). Just how Attention Trust plans to hand this power to the people seems to be the hand-wavy part of their story.

Another interesting company in this space is Root Markets, whose business is to connect both sides of the attention market in an attempt to commoditize attention. Their first product is much more specific than that: an exchange for mortgage leads.

If the absence of formal models of the economics of attention is real — and not simply a matter of my own ignorance — than it may be that some economist can make a career by truly tackling the topic in a precise and thorough way.