## Fred, Fran, and baby makes three

May 092008

Two mathematicians Fred and Fran were having a baby girl, their first child! They sought the perfect name, a name that would simultaneously reflect togetherness, relationships, and individuality in their burgeoning family. Day and night they debated, rejecting name after name. Finally, they had it! The perfect name!

They named her Erin.

Why?

[Yootleoffer: 1 Yootle for first correct response.]

• 2008/06/18 Addendum: Fred and Fran both study set theory.
• 2008/07/27 Addendum: It turns out I didn’t need the 6/18 hint-addendum: commenters had already chimed in with correct answers but, due to a combination of mechanical and pilot error, I didn’t realize it.

the winner is… John! His is the first correct response. Commenter d is also correct with a more succinct and mathematical explanation. Dennis is close but not quite complete. So I’ll award John 2 yootles, d 1 yootle, and Dennis 1/2 yootle. John and d please let me know your contact info to claim your bounty.

Dennis asks what a yootle is worth. A yootle is a quantified “thanks, I owe you one”. So it’s worth a return favor from me, someone who trusts me, someone who trust someone who trust me, etc.

Bonus challenge: come up with a family of four with the same property and reasonable names (necessarily of eight letters each).

• 2008/08/13 Addendum: The bonus round winner is… aj! He hacked up a script and discovered one of apparently many possible “perfectly” named families of four. Details are in the comments of this post. Thanks aj!

## Predictions: Apple bites, Google eats

Sep 142007

Happy 5768 everyone!

Time for some predictions.

1. Apple bites into PC pie. Apple Computer (remember them?) will attain at least 30% PC market share by 5772.

Probability: 40% ; Willing to stake: \$Y20

On the front lines, silver Powerbooks are infiltrating in droves. At techie conventions and computer science conferences, penetration has gone from almost zero to something approaching 1/3 by anecdotal evidence. Wandering about these venues, it’s not terribly uncommon to see a table of three or four who apparently all agree to think different. At Yahoo!, more and more of Jobs’s ministers are simply preaching to the converted. In our Yahoo! Research New York office, for example, laps are topped at least two to one with half-eaten half-glowing apples. Even tech celeb Marc Andreessen has returned to the fold.

But can the Apple bug jump from geeks to grandmas? (Well, my daughters’ grandma is already infected.) I’m guessing so. After all, these same alphadopters led the way to mp3s, Google, Wikipedia, Slashdot, blogs, Firefox, Digg, and Homestar Runner, unlocking remarkable truths along the way like “web search can be monetized”, “Really Simple trumps Really Smart”, and “give up now, Friendster has already won”. (Oops.)

Why is there an Apple renaissance on the desktop? A big reason is that the OS’s natural monopoly is not so natural anymore. Today, the browser is the most important piece of software on your computer, and a viable cross-platform browser (Firefox) exists that almost every web site designs to. A second reason: it turns out that Intel chips are faster and better than PowerPC chips after all, despite decades of vehement Apple fanboy arguments to the contrary. Third, Apple’s built-in iLife software suite really is astonishingly useful and well designed and speaks to the new killer apps of the desktop: pictures, music, video, web, and email. A final reason is, well, Apple is cool, and technology is at least as much about fashion as function, or at least more than geeks would like to admit.

Disagreers can accept my yootleoffer or put your play money where your mouth is on related bets at PPX and Inkling.

(Side note: My take on Apple’s fumbled iPhone price cut: I believe that Apple reacted in fear of the looming gPhone. However, if history is a guide, that fear may be an exaggerated fear of the unknown.)

Probability: 60% ; Willing to stake: \$Y20

Google is the king of selling advertisements. So they must believe that advertising is effective, right? Then why doesn’t Google advertise for itself? (I’m not counting recruiting ads.) I’m guessing the reason is that they don’t have to. As a media darling, they get more than enough free press to catalyze their already monstrous word of mouth. I expect that as the glow wears off, as some of the not not evil jabs — deserved or not — start to stick, and as they settle into Big Company mode, you will start to see Google spots on TV and elsewhere.

2007/09/19 Update: Maverick blogger, Maverick owner, Yahoo! benefactor, and uber alphadopter Mark Cuban is dancing with the Steves.

2010 Update: I was right, just 1.5 years too early. In other words, I was wrong.

## Challenge: Low variance craps strategy

Mar 032007

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:

 The Challenge: Suppose that I walk into a casino with \$200. I arrive at a craps table that has a \$5 minimum bet and allows 2X odds. I’m looking for a strategy that: Has at least some chance of making a profit (otherwise, why bother?), and Maximizes the expected amount of time (number of dice rolls) that my \$200 will last.

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!