Oddhead Blog

The absurdity of gambling laws in the US leads to such silliness as:

• In 2007, Google, Microsoft, and Yahoo! paid millions in penalties for placing gambling ads, something they haven’t done since they were told to stop in 2004.
• Yahoo! can quote prices from intrade, but can’t link to intrade.
• Google can’t advertise for intrade/tradesports, but can place AdSense ads on intrade.com and tradesports.com. In other words, Google can’t sell eyeballs to gambling sites, but can sell eyeballs on gambling sites.

Mathematicians, third graders, and talkative defense department computers alike all know that there is an infallible way to play tic tac toe. A competent player can always force at least a tie against even the most savvy opponent.

In the July issue of Science, artificial intelligence researchers from the University of Alberta announced they had cracked the venerable game of checkers in the same way, identifying an infallible strategy that cannot lose.¹

It doesn’t matter if the strategy is unleashed against a bumbling novice or a flawless grandmaster, it can always eke out at least a tie if not a win. In other words, any player adopting the strategy (a computer, say) makes for the most flawlessy grandmasterest checkers player of all time, period.

The proof of correctness is a computational proof that took six years to complete and was twenty-seven years in the making.

Tic tac toe and checkers are examples of deterministic games that do not involve dice, cards, or any other randomizing element, and so “leave nothing to chance”. In principle, every deterministic game, including chess, has a best possible guaranteed outcome² and a strategy that will unfailingly obtain it. For chess, even though we know that an optimal strategy exists, the game is simply too complex for any kind of proof — by person or machine — to unearth it as of yet.

The UofA team’s accomplishment is significant, marking a major milestone in artificial intelligence research. Checkers is probably the first serious, popular game with a centuries-long history of human play to be solved, and certainly the most complex game solved to date.

Next stop: Poker

Meanwhile, the UofA’s poker research group is building Poki, a computer player for Texas Hold’em poker. Because shuffling adds an element of chance, poker cannot be solved for an infallible strategy in the same way as chess or checkers, but it can in principal still be solved for an expected-best strategy. Although no one is anywhere near solving poker, Poki is probably the world’s best poker bot. (A CMU team is also making great strides.)

Poki’s legitimate commercial incarnation is Poker Academy, a software poker tutor. An unauthorized hack of Poker Academy [original site taken down; see 2006 archive.org copy] may live an underground life as a mechanical shark in online poker rooms. (Poki’s creators have pledged not to use their bot online unidentified.)

Poker web sites take great pains to weed out bots — or at least take great pains to appear to be weeding out bots. Then again, some bot runners take great pains to avoid detection. This is a battle the poker web sites cannot possibly win.

That didn’t take long.

Betcha is (was) an honor-based peer-to-peer betting service based in Seattle. On July 9, the Washington State Gambling Commission swept into Betcha’s offices, Gestapo style, confiscating everything, right down to their Programming PHP manual. Founder Nick Jenkins is now staring straight in the face of our country’s unconscionable forfeiture laws: you know, the ones that give law enforcement the right to sell Nick’s stuff on eBay and keep the proceeds, without ever charging him with a crime.

The Seattle Post-Intelligencer reported on the raid. The vast majority of the commenters sided with Betcha, urging Washington State officials to find better uses for their time and tax money, lamenting Washington’s ever-growing “Nanny State” credentials, and decrying the seemingly corrupt and hypocritical gambling politics involved.

To Nick and other Betcha employees and investors: Thank you for taking this risk and putting your stake in the ground, even if the current outcome is not what you’d hoped for. I hope you have the wherewithal to see this through to your day in court so that, if nothing else, we can get some clarity in the law. Here’s to hoping you’ve simply lost a battle and not the war.

Readers: Go to Betcha’s site to sign up for email updates and find out how to help.

Betcha is bold. To say the least. The founder Nick Jenkins is either crazy, brilliant, or, like many founders, both. Betcha is a platform for peer to peer betting not unlike gottabet, betfair, or intrade. Except for two (intimately related) details: (1) all debts are on the honor system, and (2) it’s based in Seattle, WA, UIGEA. Betcha makes no bones about it ( no “wink wink” here): they expect users to bet on anything and everything including sports. But because coughing up is not strictly enforced, the site evades the letter of the gambling laws. To engender trust, Betcha verifies its users’ credit cards and tracks their reputation scores, but in the end all payments are voluntary. The site earns money via listing fees.

I can’t help but admire Jenkins and Co., and I hope their gambit succeeds: my heart is with them even if my head is a step behind. (For more legal discussion see Tom Bell and The Boston Globe.)

And as much as I like the concept, I do have to ding Betcha for one of the most convoluted, head-scratching explainers I’ve heard in a long time:

“As an open, honor-based betting platform, Betcha is like an auction site, Las Vegas, a marketplace of ideas, and The Golden Rule — all rolled into one. [1]

[1] “The Golden Rule” refers to the idea that you should do unto others as you’d have them do unto you. It is the fundamental principle behind most of the world’s major religions. And while we aren’t here to push religion on anyone, doing well by others is a principle we’d like to see more of.

Whaa? Four (weak) analogies plus a long-winded footnote? C’mon, Betcha, please KISS.

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!

In the wake of US authorities arresting two executives of prominent European online gambling companies, and the surprise passage of the Unlawful Internet Gambling Enforcement Act of 2006, the shares of publicly-traded online gambling firms with large US exposure are down 50% or more. Now these companies are selling off their US operations for as little as $1. And it’s not just offshore gambling execs and shareholders who are worried. Many people are lamenting the seemingly dulled prospects of operating real-money prediction markets in in the United States.

In the previous post, I discussed what is legal in the US and what is not. In this post, I’d like to explore the pros and cons of different strategies for carving out a legal niche for prediction markets.

My personal opinion, and likely the opinion of many readers, is that gambling should be legal in the US as a matter of personal freedom, and that the US should follow the lead of the UK in legalizing, regulating, and taxing online gambling. However, as a practical matter we cannot hope for anything close to blanket legalization anytime in the foreseeable future. Here are four less sweeping approaches to drawing the legal boundaries, some more realistic than others.

1. Economic Purpose Vs. Entertainment
   Robert Hahn and Paul Tetlock have written an excellent op ed in the New York Times calling for special legal distinction for prediction markets apart from gambling laws. They propose an “economic purpose test”, which would legalize prediction markets that have some economic value: either value as an instrument for hedging risk, or “information” value as a predictor of outcomes of significant economic consequence. Hahn and Tetlock argue that presidential betting would pass their economic purpose test, and that sports betting would not pass their test. However, one can argue that sports teams, local sports bars, and even city governments could use sports betting markets to hedge risk. I believe that, as a practical matter, sports betting would simply have to be called out as an exception in any such test.
2. Skill-Based Vs. Chance-Based
   One argument is to draw the legal lines to outlaw pure chance-based games with a proven mathematical house edge that cannot be overcome. Roulette, craps, lotteries, and other common casino games fall into this category. The flipside would be to argue that any game that might allow a mathematical edge to a player with superior information or superior strategy should be allowed. Sports betting, poker, and, of course, prediction markets fall into this category. There is some precedent for allowing skill-based “gambling” games in many US states, as discussed in the previous post.
3. Exchanges Vs. Bookies
   Another argument is to distinguish the new betting exchanges from more traditional bookies. Betting exchanges, like BetFair and TradeSports, simply provide a central marketplace for people to trade bets with one another. They collect transaction fees, but their profit does not depend at all on which side of a bet wins or loses. In contrast, bookies can end up with imbalanced exposure and may stand to gain or lose depending on the outcome of the bet. Also, bookies effectively enforce an artificially large bid-ask spread (often operationalized as a “vig” or tax on winnings) to ensure their profitability, while exchanges do not. Executives at TradeSports argue that these distinctions put them in safer legal territory than more typical online gamling operations. I’m not sure that US prosecutors would agree. The argument can sound like Napster’s argument that they were not directly responsible for users of their service who were violating the law.
4. Investment Caps or Investor Qualifications
   One might argue that by enforcing strict investment limits, say $500 per person, the risk to problem gamblers is sufficiently minimized. This is part of the “no action” agreement between the Commodity Futures Trading Commission (CFTC) and the Iowa Electronic Markets. An almost opposite approach, but with similar motivation, is to limit participation to individuals with a very large net worth (e.g., millions of dollars). This is the legal cover that many hedge funds use: the supposition is that these individuals “know what they’re doing”, understand the risks, and have enough money to survive the inevitable ups and downs. The CFTC weilds a lighter regulatory hand on exchanges that cater only to the super rich.

In my opinion, although all the above arguments make some sense, the only one with any chance of actually gaining ground in the current legal and political environment is the first one (the “economic purpose test”), perhaps with the additional cover of a low investment cap and special exceptions ruling out sports betting and other stigmatized topics. Many people in the US, including lawmakers, still harbor outdated notions that gambling is a religious sin or has the taint of organized crime. If prediction market advocates want to make progress toward legalization, I believe they will have to distance themselves from gambling and sports betting. Although there is no logical distinction between betting on sports and trading contingent contracts, there is a very real social, political, and legal distinction. Though it can seem unpalatable to support gray and illogical distinctions, the unfortunate reality is that gray and illogical distinctions are the only ones with any practical chance of becoming law.

The gambling laws in the United States, as in many other countries, are a hodgepodge of inconsistent and hypocritical provisions. First, most of the laws are at the state level, not the federal level, so a true understanding requires familiarity with fifty different sets of rules. But even at the federal level, the picture is murky, convoluted, and full of seemingly nonsensical exceptions.

So what is currently legal?

Here are some forms of gambling that are legal in the US:

• Betting on horse races
• Betting on Jai Alai in Florida
• Betting on other sports (e.g., professional football, college basketball, …) in Nevada
• Betting on roulette, craps, slot machines, and other “unwinnable” casino games in Nevada, Atlantic City, riverboat casinos, Detroit, American Indian reservations, and other specially designated places
• Betting in state-run lotteries (which, incidentally, usually have a much larger “house edge” than any casino game)
• Betting in “skill-based money tournaments” in most states (see below)
• Betting in financial markets: Betting on stocks, options, futures, derivatives, “hedgelets”, and other financial instruments officially sanctioned by either the Commodity Futures Trading Commission (CFTC) or the Securities and Exchange Commission (SEC)
• Betting on presidential elections in the Iowa Electronic Markets
• Betting for insurance purposes: Betting on death, injury, theft, etc.

Yet casino gambling and sports betting are illegal in most of the country, and gambling on the Internet is illegal — well, sort of. MSNBC has an “oldie but goodie” special report on online gambling, which includes an article about the murky legal waters of online gambling.

The central question — whether Internet gambling is legal, illegal or exists in a legal nether world where no rules apply — is as gray as lawyers can make it.

(Aside: The same special report also includes articles on the rise of betting exchanges, and opportunities for arbitrage.)

Examples: Companies surviving on the edge

Here are some examples of US-based companies that are successfully navigating the murky legal waters. Some of these companies’ operations seem to teeter on the edge of what the gambling laws say is legal and what is not.

The Ticket Reserve and YooNew both allow sports fans to purchase tickets to important playoff games (e.g., the US NFL Super Bowl) contingent on their favorite team making it to the game. So, for example, a “Steelers Super Bowl ticket forward” entitles its owner to a ticket to the Super Bowl if and only if the Steelers are one of the two final teams that play in the Super Bowl, but is worthless if the Steelers do not make it to the Super Bowl. This is a brilliant idea: most fans value attending a big playoff game much more highly if their favorite team is playing in the game. Once a “ticket forward” is purchased, it can be sold via an exchange back to another fan at a profit or loss. The price of a “Steelers Super Bowl ticket forward” of course is intimately related to the odds of the Steelers making it to the Super Bowl, so in theory a gambler can use the TicketReserve or YooNew as an alternate betting exchange, without any intention of keeping the ticket and going to the game. These two companies have very carefully and (so far) successfully distanced themselves from the stigma and legal headaches of US gambling laws. Still, they are sufficient close to “the edge” that I doubt many large companies would take such a risk; both The Ticket Reserve and YooNew are small startups. (Aside: rumor has it that YooNew uses Robin Hanson’s logarithmic market scoring rule market maker for pricing.)

WorldWinner is another company that has successfully navigated the legal boundaries. WorldWinner was originally a US-based company, now owned by the international company Fun Technologies, and at least at one point was featured on Yahoo! Games (Internet Archive of Y!Games circa 2004). WorldWinner collects entry fees from players and pays out money to winners of various tournament-style games, including some clearly designed to resemble common casino games, like “Catch-21″ (resembles blackjack) and “Royal Flush” (resembles poker). So how do they operate legally in the US? They work hard to be able to claim that their games are games of skill, not games of chance or luck. Most US states allow these “skill-based money tournaments”, but not all. Another interesting special case are companies that insure challenge prizes like those often featured at halftime of major sporting events.

HedgeStreet is one of the few companies that has trudged down the lengthy, costly, and arduous path of obtaining official sanction from the US Commodity Futures Trading Commission (CFTC). This is the safest route for any new prediction market company, as a CFTC license immediately overrides the fifty states’ varied and convoluted gambling laws. But HedgeStreet often seems to emphasize speculation as opposed to hedging in their advertisements, information collateral, and choice of contracts (e.g., short-term instead of long-term housing prices). Reportedly InTrade (the non-sports arm of TradeSports) is attempting to go down the same path toward CFTC approval. I wonder if the new anti-gambling climate will adversely effect their chances of approval. The Iowa Electronic Markets have a “no action” letter from the CFTC allowing them to operate, but that is a special case unlikely to be repeated having to do with the university’s academic status and a $500 max investment limit. US-based Cantor Fitzgerald is the parent company of UK spread betting firm Cantor Index (which in turn owns the play-money Hollywood Stock Exchange). The main difference (legally speaking) between Cantor Index, BetFair, and TradeSports, is that while Cantor Index and BetFair appear to take pains to lock out US-based bettors, TradeSports seems to specifically target the US audience by listing US-centric contracts and actively seeking exposure in US press outlets. Certainly there are other companies I’ve missed that are interesting test cases for US gambling laws.

What’s the lesson? Although the waters are murky, there are some innovative companies that are so far successfully staying on the good side of the myriad prosecutors, regulators, and lawmakers putting up barriers. Let’s encourage and support these companies, and thank them for blazing trails for the rest of us. At the same time, let’s push for clearer, saner, and less restrictive laws. More on this last point in the next post.