Drawing the Line Between Gambling and Finance: Part II—Insurance: Gambling on Catastrophe

Note:  This is the second article in a series looking at the legal connections between gambling and finance. The first article introduced the legal concept of aleatory contracts. Links to subsequent articles can be found at the conclusion of this article (when available).

* * * * *

Types of Insurance

Insurance is probably the most familiar and ubiquitous of the aleatory contracts. People face a variety of significant financial risks, such as house fires, car accidents, injuries and illnesses, or even the loss of income from the death of a family member. People can protect against these large, even catastrophic, financial losses by purchasing property insurance, casualty insurance, health and disability insurance, and life insurance, respectively.

Just about any risk can be insured, for a price. Most individuals rarely need anything more than “off the shelf” personal lines of insurance (e.g., homeowners’/renters’ insurance and auto insurance), along with health and life insurance. Businesses tend to carry “off the shelf” commercial lines of insurance, usually including at least a basic group of insurance coverages for commercial property, automobile, general liability, and workers’ compensation. Businesses also will take out additional insurance tailored to their particular business needs. Common commercial insurance coverages include aircraft, product liability, fidelity and surety, professional liability (a/k/a malpractice insurance), directors and officers, and inland marine policies (which ironically usually have nothing to do with either the ocean or soldiers).

Individuals or businesses having special risks not covered by a standard policy can obtain insurance by use of an endorsement or rider which expands coverage under a standard policy; this generally requires special underwriting review, additional premium, and special conditions or limitations on coverage. Particularly large or unusual risks often need to be insured via a special policy specifically written for the risk, often referred to as surplus lines insurance. Lloyd’s of London is famous for this type of specialty underwriting, often insuring singers’ voices or athletes’ bodies, as well as movie productions and rare art and jewelry. Insurers will write policies for events as silly as a hole-in-one at golf, or as difficult to predict as weather. For those individuals who are at risk (mostly teens in bad movies), there is even insurance available in the event the insured is abducted by aliens or turned into a vampire or werewolf.

Insurance as Wagering

An insurance contract essentially operates like a wager. The person purchasing insurance is betting a small amount of money (the “premium”) that a particular event will occur (e.g., his house burns down), in which case the insurance company will pay him the policy “benefit” (here, the value of his house. Given the asymmetrical financial arrangement—small premium, large potential benefit—how does the insurance company make money?

Insurance companies rely on two concepts to set the correct premium for a given insurance policy—underwriting and risk pooling. Underwriting looks at a variety of factors—e.g., geography, age, gender, type of business—which have been found to statistically correlate with the particular risk being insured, charging a greater premium for insuring more risky insureds. For example, a college-aged single male with multiple moving violations on his driving record is more risky to insure than a middle-aged married woman. Conversely, a middle-aged female smoker with diabetes would pay a higher life insurance premium than a healthy college-aged male. And some geographical regions will have a greater or lesser overall risk of car accidents or mortality.

In some respects, underwriting is analogous to a sports book operator setting a wagering line on a proposition ("prop") bet. Unlike traditional sports wagers on the winner of a game, the point spread, or point totals (over/under bets), prop bets are one-off wagers on individual occurrences in a game. For the recent Super Bowl, gamblers could bet on props such as the length of the national anthem, which player would score first, and which player would be named MVP. The research the sports books put into setting those odds at a level which would attract action while still giving the house a profit is essentially the process of underwriting.

Insurance Company as Casino

Still, even with underwriting, it is impossible to predict whether any particular individual risk will occur. In other words, while we know young men are more likely to be in car accidents and older smokers are more likely to die, we can’t predict which specific individuals will be in a car accident or die. Even if an insurer properly underwrites a particular risk, random chance may strike and require the insurer to pay off the policy benefit at a large loss.

Insurance companies avoid this risk by implementing risk pooling. Risk pooling harnesses the law of large numbers, which essentially states that over a large number of trials, a probabilistic outcome will approach its expected value. By writing thousands of similar insurance policies, an insurer can spread the risk of losses over the entire block of policies, and hope to experience losses commensurate with its underwriting assumptions.

In risk pooling, insurance companies operate in a fashion analogous to both pari-mutuel wagering books and standard casinos. In pari-mutuel betting, all wagers are pooled together and the house commission (a/k/a “vig”) is taken out. The remaining pooled funds are paid to winning bettors in a proportional manner. Insurance companies similarly pool premiums and pay off “winners” (those who have insurance claims due to an insured loss) with premiums from "losers" (ironically, those who did not suffer a insured loss). The insurance company keeps the remaining funds—known as “underwriting gain”—to cover expenses and for profit. [FN1]

The pari-mutuel wagering analogy breaks down to a degree, however, because a pari-mutuel book will never take a loss paying off winning wagers. An insurance company, by contrast, can have instances in which, for a particular policy year or for a particular block of policies, the paid claims exceed the premiums charged. This type of “underwriting loss” situation is actually rather common in the property insurance field, where one or several large-scale events—hurricanes on the Southern or Eastern coasts, tornadoes in the Midwest, fires or mudslides in California—cause both widespread and high-dollar losses. Insurance companies deal with short-term underwriting losses in several ways: viewing underwriting gain/loss over time (i.e., a block of policies may be unprofitable in individual years yet profitable over ten or twenty years), raising renewal and new issue premiums to recoup losses, and entering into reinsurance arrangements (discussed in Part III of this series).

Given the potential for underwriting loss over the short-term, the use of risk pooling in insurance has a stronger analogue in casino operations. On any given individual wager, the casino knows it has only a small statistical edge. The casino can’t predict which individual wagers will win or lose, or which individual gamblers will walk out with a profit or a loss. Further, casinos can experience short-term losses when a large single bet pays off (e.g., a slot jackpot), or when the casino experiences significant negative variance on wagers by high rollers (Vegas casino gaming revenues are notorious for significant swings from the performance of its high-stakes baccarat tables). But the casino does know that the more wagers it takes, the closer its profits will reflect its weighted average expectation for the built-in house advantage.

Like a casino, an insurance company is indifferent to whether any particular policyholder “wins” or “loses”. In fact, no insurer can predict which of its insureds will “win”—i.e., suffer a loss and be entitled to benefits in excess of the premium paid. The insurer operates by assuming that it has properly underwritten and priced the block of policies such that in the aggregate the total premiums charged will, over time, exceed the total benefits paid. The larger the risk pool, the closer the insurance company’s experience for the block of policies will track with its actuarial projections.

* * * * *

[FN1] An insurer also makes money on its investment portfolio. The funds ("reserves") held by the company to back its in-force insurance policies and expected claims are invested, predominately in high-grade bonds, along with some other types of permitted securities and assets (state insurance regulators monitor these investments closely for both risk and liquidity). The return on the investment portfolio is included in the setting of premium and expense charges for policies, keeping premiums and expense charges lower than would otherwise occur in a strict risk pooling arrangement. Income from the investment portfolio, rather than underwriting gain, has become the primary driver of profits in modern insurance.

* * * * *

Additional articles in this series (links will be added as each section is posted):

Part I—Meet the Aleatory Contracts

Part III—The Reinsurer, the Bookmaker, the Poker Pro Staker

Part IV—Derivatives and Daily Fantasy Sports

Part V—Hedgers and the Law

Part VI—Speculators and the Law

Part VII—Risk Creation v. Risk Management

Drawing the Line Between Gambling and Finance: Part I—Meet the Aleatory Contracts

Randolph Duke: "Now, some of our clients are speculating that the price of gold will rise in the future. And we have other clients who are speculating that the price of gold will fall. They place their orders with us, and we buy or sell their gold for them."

Mortimer Duke: "Tell him the good part."

Randolph Duke: "The good part, William, is that, no matter whether our clients make money or lose money, Duke & Duke get the commissions."

Mortimer Duke: "Well? What do you think, Valentine?"

Billy Ray: "Sounds to me like you guys are a couple of bookies."

Randolph Duke: "I told you he'd understand."

~ "Trading Places"

Whenever talk turns to the legalization of online gambling or real-money daily fantasy sports leagues—issues confronting several state legislatures this year—one fairly common argument raised is that if we allow people to sit around in their underwear at home and day-trade stocks on E*Trade, we should let people sit around in their underwear at home and play fantasy sports or online poker. After all, isn’t the stock market just a big, legal casino?

Norman Chad, long time color commentator for ESPN’s broadcasts of the World Series of Poker, made this argument in a recent Washington Post column regarding real-money fantasy sports websites:

FANTASY SPORTS IS GAMBLING.

Now, I have nothing against gambling; I’m quite pro-gambling. I just hate it when people pretend something is not gambling. Poker players and sports bettors are labeled gamblers and often scorned by non-gamblers. Yet Wall Street – essentially the biggest casino in the nation, plus it’s kind of rigged – is not labeled gambling.

(People always worry about point-shaving in sports, when a player might throw a game to benefit bettors. How about insider trading? Heck, comparing point-shaving to insider trading is like comparing a rain shower to a monsoon. Hardly any game is ever fixed; by contrast, nefarious stock machinations occur on a daily basis.)

So, yes, stock trading is gambling and, yes, fantasy sports is gambling.

It’s not just daily fantasy sports. The argument regularly pops up whenever legalization of traditional sports betting or online poker is the topic du jour. And it’s hardly shocking that many professional daily fantasy sports and online poker players got their start in the world of finance.

So why are the trillions traded on Wall Street legal, while the billions bet online on sports, fantasy sports, or poker remain illicit? The answer is more complicated than might be imagined.

Aleatory Contracts

Gambling wagers closely resemble contracts such as insurance policies and financial securities because these transactions all fall within the same family of legal contracts—the aleatory contracts. The legal term “aleatory” derives from the Latin words aleator which means gambler, and alea, a dice game. “Aleatory”is defined as:

1: depending on an uncertain event or contingency as to both profit and loss

2: relating to luck and especially to bad luck

An aleatory contract, then, is “a contract whose execution or performance is contingent upon the occurrence of a particular event or contingency or an uncertain (random) event beyond the control of either party.” Any traditional gambling wager is clearly an aleatory contract—whether betting on a football game, a roll of the dice, or a hand of poker or blackjack, the outcome of the wager depends on the occurrence of a contingent or uncertain future event.

But the law also recognizes other types of aleatory contracts. For example, insurance is a classic aleatory contract in which a premium is paid in exchange for a promise of monetary benefits in the event of an uncertain (random) future loss (e.g., a house burns down). Similarly, many options, futures, and other financial derivatives are also aleatory contracts in which performance is tied to future conditions in the relevant financial market.

The underlying structure of each of the different classes of aleatory contracts is identical, though the terminology specific to each class of contracts may differ. But whether it is a gambling “wager” or an insurance “premium”, all of the aleatory contracts are based on the identical legal foundation: Party A pays $XX to Party B as consideration for Party B’s promise to pay $YY to Party A if a particular future contingent event occurs. So, from a purely analytical standpoint, there is no legal distinction between Party A paying Party B $5,000 in exchange for Party B’s promise to pay $100,000 to Party A twelve months in the future if:

1. Party A's house burns down or he dies (insurance); 
2. the price of corn rises or falls (futures); 
3. the price of Apple stock rises or falls (options);
4. interest rates rise or fall (swaps); or
5. the New York Jets win the Super Bowl (gambling).

Yet, of these examples, the first four contracts are generally legal (and regulated to varying degrees) throughout the United States, while the last contract is currently legal only in Nevada (and then only in a licensed sports book). If all of these contracts are functionally equivalent, why are some aleatory contracts legal and others illegal?

To answer that question, we first need to look at how the legal, non-gambling aleatory contracts function. In many cases, these contractual functions closely parallel certain aspects of gambling, both legal and illegal. Once the functions of the legal aleatory contracts have been examined, we can then look at how and why the law draws a distinction between gambling and other aleatory contracts.


Coming up (links will be added as each section is posted):

Part II—Insurance: Gambling on Catastrophe

Part III—The Reinsurer, the Bookmaker, the Poker Pro Staker

Part IV—Derivatives and Daily Fantasy Sports

Part V—Hedgers and the Law

Part VI—Speculators and the Law

Part VII—Risk Creation v. Risk Management

Making Poker Fun Again

"We have to find a way to make people realize [poker] has to be a social game. You have to allow certain things. In other words, if I ran this room [TI], which I don’t, it’d be, “phones off the table.” And I do it too when I’m playing. This is ridiculous. Because nobody talks anymore. And that’s why they don’t have fun."

~ TI poker dealer Dominick Muzio, interviewed for Rob's Vegas & Poker Blog

I caught the Vegas poker bug just over a decade ago, and since then have averaged five or six trips to Poker Mecca each year. I've seen a lot of poker rooms open (Venetian, Aria) and close (Paris, Hilton, Imperial Palace/Linq, Tropicana). Although the Vegas poker scene is still vibrant, there is no question the bloom is off the rose—fewer rooms, fewer games, more local grinders, fewer drunken tourists.

The decline, or perhaps the maturation, of the Vegas poker scene undoubtedly has had a number of contributing factors. Black Friday and the evaporation of online poker has meant fewer new players being introduced to the game. The recession certainly didn't help the poker industry. And younger people are flocking to Vegas, not to gamble, but to party all day, club all night.

Nobody can do anything to unwind Black Friday or create another poker boom. But based on my recent visits to Vegas, between poker players and poker rooms, it feels like the poker industry is shooting itself in the foot. Longtime Vegas poker dealer Dominick Muzio addresses this issue and hits on several key problems in a recent interview. I agree with many of his points, but want to add in a couple of additional thoughts.

In recent years, many poker rooms are catering to players by adding cell phone charger outlets, offering free WiFi, and generally eliminating most restrictions against use of cell phones and tablets at the poker table. These changes are generally a good thing. Players can make plans, keep up with friends and family, or take care of routine work emails between hands. Heck, I've even negotiated a couple of multi-million dollar settlements while playing at Aria.

But, like all good things, some poker players have found a way to abuse this accommodation of electronic devices. During my last trip to Vegas in late December, I played at several tables in three different rooms (Aria, Ceasars Palace, and Planet Hollywood) where one or more players were watching movies or TV shows on their phones or tablets. In three different games I played in, there was at least one player (each an obvious local grinder) who would have a tablet out with large, noise-canceling headphones. Each of these players was completely oblivious to the action, and had to be nudged by the dealer every time the action was on them preflop. Even when they played a hand, the headphones never came off, often slowing the game further when they missed verbal declarations of bet sizes or other action. These players could hardly have been less engaged in the game. And from looking around the rooms, these players are surprisingly common and apparently tolerated by poker dealers and management.

Poker rooms also continue to ruin the poker environment with poorly conceived promotions. The biggest, busiest, most successful rooms (e.g., Aria, Venetian, Bellagio) seem not to need promotions beyond generous hourly comps and a reasonable rake. But some of the smaller rooms still take a jackpot drop to fund promotions. And, as long the promotion is a high hand jackpot or something similar, these promotions really are fairly innocuous, and may even achieve their purpose of making Joe Tourist excited about the game.

The problem is that some rooms are still using promotion dollars to chase "regulars" who far too often are more interested in the promotion than in the game itself. During my December visit, I decided to check out the recently renovated and relocated poker room at Caesars Palace. Now, the room has greatly improved in two respects. First, the rake has been dropped from $5+$1 to $4+$1, comparable to many of the mid-sized rooms on the Strip. Second, the new location adjacent to the sports book and in the middle of the casino floor offers better visibility for casual, "walk-by" players.

Unfortunately, Caesars was running a promotion in December which involved several weekly drawings and a monthly main drawing. Eligibility was based on playing a minimum number of hours for each week and for the month, and also required the player to be present at the time of the drawing. Essentially, the promotion was targeted at local players who were much more likely to qualify for and be present for the drawings than were tourists. The result was a predictable mess. Every table I played at had at least four or five players who were constantly checking to see if they had enough hours to qualify for the drawings. These players rarely played a hand preflop, and postflop there was little action unless two players hit the flop hard. The room was chock-full of nits who were reading magazines, drinking comped drinks, and checking their phones; basically doing anything except playing poker. Thrill a minute, I tell you.

It seems like many poker room managers and serious poker players don't grasp the concept that live poker—at least low-stakes poker—is really about entertainment. I'm not saying every game needs to involve drunken Brits tackling players or a Sherminator look-alike. But when Joe Tourist sits down with a few hundred dollars in his pocket, he would like to win money, but mostly he wants to enjoy himself for a few hours—have a few beers, share a few laughs, get a few stories to take back home. A table filled with local nits grinding hours, folding every hand, watching a movie, paying no attention to the game, and interacting mostly in grunts is pretty much the opposite of what casual players want to see. Sure, Joe Tourist may stick around and lose a buy-in to the game. But a casual player who is not enjoying himself won't pull out a second buy-in, or come back the next day. Treating low-stakes poker like a boring day job—even if is exactly that—is a terrible business decision.

Setting the Line for Sports Betting Revenue

EXECUTIVE SUMMARY

Recently, the sports betting legalization movement has gotten some welcome traction, with legislatures in several states taking a fresh look at the issue, and the commissioners of the professional sports leagues showing signs of increasing comfort with the legalization concept. In much of the media coverage of the issue, sports betting advocates use a financial pitch touting the massive revenue streams that could be realized from regulating the currently illicit sports betting market. Most of these financial projections seemed rather large, often claiming hundreds of billions of dollars in wagers would generate hundreds of millions in tax revenues. With the recent New Jersey online gaming boondoggle—where actual online gaming revenues have fallen woefully short of the projections touted by legalization supporters—I set out to research a short post analyzing the assumptions behind the sports legalization effort. As will come as no surprise to my dozen or so regular readers, my research resulted in a much longer piece.

In Part A—Introduction, I review a few examples of the common revenue projections touted by sports betting advocates. In Part B—Guesstimating the Illegal Sports Betting Market, I look at the common projections of the scope of the current illegal sports betting market and discover the most widely cited estimates are essentially bogus. In Part C—Conflating Amounts Wagered with Gaming Revenues and Tax Revenues, I analyze the common mathematical errors riddling many sports betting revenue projections, errors which generally result in a significant overestimate of potential revenue streams.

In Part D—Estimating the Potential Size of the Legal Sports Betting Market, I take a stab at generating my own back-of-the-envelope, wild-ass guess at the potential size of a legalized sports betting economy, and provide a couple of handy-dandy interactive spreadsheets so readers can generate and bedazzle their own revenue estimates. One interesting conclusion is that data from Nevada, currently the nation's only mature and saturated sports betting market, suggests that estimates for sports betting revenues in New Jersey and nationally may be wildly overstated (spoiler alert): "Applying the Nevada ratio to these historical revenue numbers would suggest New Jersey might reasonably expect somewhere between $59.8 million and $107.2 million in annual sports book revenues, which translates into $4.8 million to $8.6 million in additional annual tax revenues (applying the current 8% gaming tax rate)." Finally, in Part E—Market Issues: Expansion, Conversion, and Competition, I explore a few factors which further complicate any attempt to estimate the potential revenue streams from legalization of sports betting.

I enjoy placing the occasional recreational sports wager, usually in Vegas, sometimes with a friend, and occasionally through more traditional back channels. I am firmly in the Legalize-Regulate-Tax camp. But if sports betting legalization is going to be sold as a revenue generator, we owe it to the public to use solid data where available, and to appropriately flag and hedge estimates and assumptions which lack rigorous underlying research. Let's sell sports betting legalization on its merits, not like a bunch of carnival hucksters.

* * * * *

A.  Introduction

As the movement to legalize sports betting on a national basis gains momentum, an increasing number of public figures are finding ways to voice their support. NBA commissioner Adam Silver has led the charge, penning a New York Times op-ed piece and sitting for a prominent ESPN: The Magazine interview to advocate for a "realistic" debate about legalizing and regulating sports betting. The new MLB commissioner, Rob Manfred, similarly seems open to a discussion of legalized sports betting.

One of the primary arguments used by sports betting advocates is that legalization will lead to a gusher of tax revenues for cash-strapped state governments. In that vein, Florida sports talk show host and writer David Moulton penned an article in the News-Press asserting that legalization of sports betting would raise, "conservatively", $750 million in annual state tax revenues for Florida. In New Jersey, state officials have touted annual tax revenue projections ranging from $100 million to $120 million, and up to $166 million. Certainly these are eye-popping figures which might persuade skeptical voters to take a flyer on sports betting.

The problem with the tax revenue argument for gaming is that it is easy to promise revenues, but hard to deliver. New Jersey Governor Chris Christie famously promised new tax revenues of $200 million in the first year of legalized online gaming. As has been well-documented, actual revenues fell more than $150 million short of projections. Even worse, gaming industry analysts have revised their best-case long-term revenue projections to fall significantly below the projections used by online gaming advocates to support their case for legalization.

The New Jersey online gaming revenue debacle is a cautionary tale as the sports betting legalization debate heats up. Yet sports betting advocates repeatedly cite financial figures which are confusing at best and misleading at worst. How can we present the public with more accurate revenue estimates?


B.  Guesstimating the Illegal Sports Betting Market

Sports betting advocates fail to distinguish between estimates of illegal wagering activity and the potential casino revenue and tax revenue streams which might be realized if that illegal wagering were instead captured via a regulated sports betting regime. There are actually two separate errors in play here: a) accurately estimating the size of the illicit sports betting market, and b) determining how much of the illicit market could be converted to the regulated market. For the moment, let's focus on estimating the size of the current illegal sports betting market.

Sports betting advocates often tout figures such as the American Gaming Association's estimate that Americans illegally wagered $3.8 billion on this year's Super Bowl (a figure widely adopted by the general media). Or, there's the common assertion that Americans illegally wager up to $400 billion per year on sports. The problem with these estimates is that the figures are presented without any supporting data or underlying assumptions. As my high school math teacher might say, the groups touting these estimates never "show us their work".

Let's take a look at that $400 billion estimate for the amount Americans supposedly wager illegally each year on sports. That figure seems to be a rounding up of an estimate of an annual illegal sports betting market of $80 billion to $380 billion as reported in the 1999 final report of the National Gambling Impact Study Commission (NGISC), generated at the request of Congress. Sure, the data might be a little dated, and the figures are less robust than claimed, but it's still a pretty solid number, right?

Actually, wrong. The NGISC report is pretty easy to find, and sure enough, right there on Page 2-14, the report states: "Estimates of the scope of illegal sports betting in the United States range anywhere from $80 billion to $380 billion annually, making sports betting the most widespread and popular form of gambling in America." The problem arises when you look at the footnotes for that assertion. The NGISC report cites as support for this estimate a Las Vegas Review-Journal newspaper article on a proposed college sports betting ban. Try looking for that article, and the trail grows cold. However, Jordan Weissmann at Slate was enterprising enough to run that footnote to ground. Weissmann discovered that the Las Vegas Review-Journal article in question relied upon estimates given by various individuals to the NGISC during its hearings, with the $380 million figure apparently "pull[ed] out of thin air" by one of the commissioners. Thus was born a supposedly reliable statistic repeatedly cited as authoritative in support of a wide range of important policy decisions. In reality, the $380 billion statistic is, at best, a scientific wild-ass guess ("SWAG").


C.  Conflating Amounts Wagered with Gaming Revenues and Tax Revenues

Another common tactic used by sports betting advocates is to throw out a figure for the amount being wagered on sports betting without clarifying that the amount cited is not the same as the actual revenue being generated for the casino industry, nor is it the amount of tax revenue realized from the casino revenues. Although the gross amount wagered (referred to as the "handle") is usually a huge, attention-grabbing figure, the reality is that the amount retained by the sports book as operating revenue (the "hold") is only a small fraction of the handle. Yet it is the hold that matters most when making policy decisions regarding sports betting.

The David Moulton News-Press op-ed noted earlier makes a particularly egregious hash of this issue. Moulton asserts that the state of Florida will retain 10% of the handle as tax revenues. Moulton's claim is based on the 10% commission (a/k/a "vigorish" or "vig") traditionally imposed by bookmakers on sports wagers. Moulton makes two egregious, fundamental errors here.

First, Moulton fails to recognize what any casual sports bettor knows—sports books refund the commission on all winning wagers and only keep the commission on losing wagers. Sports books want to operate much like a stockbroker and match buyers and sellers (winners and losers), taking a commission along the way for a small but steady piece of the action. Lines on games are set and adjusted to keep the action on both sides as even as possible, minimizing risk to the sports book of being overly exposed to heavy action. Traditional straight bets like point spread and totals (over/under) bets do usually require the bettor to lay 11/10 odds (i.e., bet $11 to win $10, or $110 to win $100), giving the sports book a house edge of roughly 4.76% on the wager (not the 10% edge claimed by Moulton). Other common bets like moneyline wagers will have a similar house edge around 5%, while more exotic wagers like parlays, teasers, futures, and props may have a house edge exceeding 30% (which is why sports books drool when a sucker approaches the counter with a parlay wager).

To get a feel for a reasonable expected hold for traditional sports books, it's easiest to simply see how Nevada sports books have historically performed. Taking the Nevada statewide sports book revenue statistics for the past five years, individual sports bets averaged a hold of 4.9%, parlays averaged a hold of 31.2%, and sports books overall averaged a hold of 5.4%.

Nevada sports book revenues 2010-2014 (all dollars in thousands (add 000)).

Data source: Nevada Gaming Control Board "Gaming Revenue Reports"

Full spreadsheet with individual year data available via web and Google Docs.

UPDATE (28 June 2015):  Via Billy Polcha, Nevada gaming revenue data
for 1984-2014 have been compiled in a user-friendly format 
by the UNLV Center for Gaming Research. 

If one dives into the year-by-year data, the individual sports bets will fluctuate from the expected 4.76% hold depending on sport and how well favorites perform. It is well-known that most sports bettors (so-called "squares") are less sophisticated and will tend to bet on favorites and overs, so sports books often hedge their lines in those directions, padding their edge slightly on those bets. Parlay bets have a house edge of 25%-35%, but the handle on those bets is small relative to individual bets (because of the higher payouts, parlay bettors generally bet smaller amounts). Still, parlay bets consistently add 50 to 60 basis points (0.5% to 0.6%) to the overall house hold each year.

Based on Nevada's actual data, it appears a reasonable assumption that the typical sports betting hold is around 5.5% of the handle. So, just like that, nearly half of Moulton's projected tax revenues evaporate.

But Moulton has made another egregious error—conflating the casino hold (gross gaming revenues) with tax revenues. Assuming the State of Florida is offering sports betting through casinos and racetracks (as is the case in Nevada and is being proposed in New Jersey), the hold from sports wagers represents the gross revenue stream for the casinos and racetracks. The sports books need to pay overhead and expenses, and make a reasonable profit from the hold in order to operate. Actual tax revenues would only be a percentage of the hold.

So, the actual tax revenues depend on what gaming tax rate is applied to the hold, a rate which is likely to vary widely by state. In Nevada, the top marginal tax rate for gross gaming revenues is currently 6.75% (with additional local, county, and state assessments which may add up to an additional 1% to the effective tax rate). In New Jersey, the top marginal tax rate for gross gaming revenues is currently 8.0% (with an additional 1.25% community investment assessment). In Florida, the the top marginal tax rate for slot machine revenues is currently 35% (the state has a compact with the Seminole tribe permitting the tribe exclusive rights to offer certain table games in exchange for a flat annual payment).

It is not clear, however, that Florida would apply its high slot revenue tax rate (35%) to sports book revenues as sports books are more expensive to operate. As one casino industry study noted, there is a direct correlation between lower gaming taxes and higher employment rates in the casino industry. Further, the study notes that many states have adopted lower tax rates for table game revenues in recognition that table games have higher overhead and expenses than do slot machines. The study suggests (p. 29) that 40% of gross revenues is the maximum tax rate for table games to operate profitably. One would suspect that sports books have even greater expenses relative to revenues than table games and cannot operate profitably at such a high tax rate.

So let's do the math. Moulton used an assumption—frankly, a decidedly unscientific wild-ass guesstimate—of $7.5 billion in sports betting handle, and projected tax revenues for the state of Florida of $750 million (10% of the handle). In reality, even if Florida were to have $7.5 billion in handle, the resulting gross revenues would be roughly $412.5 million (assuming a 5.5% hold), with maximum tax revenues of $144.4 million (applying the current 35% tax rate). In other words, even using Moulton's gross gaming handle assumption, and even applying the current 35% tax rate, the actual projected tax revenues for Florida are less than 20% of what Moulton promised. 

It's hard to tell if Moulton is merely cosmically awful at math, too lazy to do basic research about sports betting, or intentionally fudging the numbers with some sleight of hand to create a more palatable illusion of the benefits of sports betting legalization. Whatever the case, Moulton's revenue projections are likely wildly overstated. Still, even $415 million or so in annual gross gaming revenues can create a lot of jobs and economic development. And another $145 million or so in annual tax revenues is nothing to sneeze at, even if it is a rounding error in relation to Florida's $77 billion state budget.

Although not as laughably wrong as Moulton, other sports betting advocates often make similar errors in calculating gaming revenue and tax revenue projections off of gross wagering data. For example, one news story from New Jersey reported that one study projected "sports betting would be a $6.7 billion industry in New Jersey, bringing in $166.2 million in tax revenue." But the numbers don't add up. Assuming $6.7 billion refers to the gross amount wagered (the handle), casino gross revenues would be roughly $368.5 million (assuming 5.5% hold). For the $166.2 million tax revenue projection to hold up, a tax rate of 45% would have to be applied to the gross revenues, rather than New Jersey's current 8% tax rate (which would result in only $29.5 million in tax revenue). Clearly something doesn't add up here.

Or, for another example of overreach by sports betting advocates, New Jersey state senator Ray Lesniak, a vocal advocate for sports betting legalization, has reportedly claimed that sports betting could bring in more than $100 million per year in tax revenue for the state. But simple reverse-calculation shows that $100 million in tax revenue necessarily implies gross casino revenues (hold) of $1.25 billion (assuming 8% tax rate), and gross amounts wagered (handle) of $22.7 billion (or roughly six times Nevada's 2014 sports betting handle) (assuming 5.5% hold). If the $166.2 million tax revenue handle estimate noted above is reverse-calculated, the predicate numbers are $2.1 billion in gross casino revenues (hold) and gross amounts wagered (handle) of $37.8 billion (roughly ten times Nevada's 2014 sports betting handle). These figures may be defensible, but considering New Jersey only has roughly three times the population of Nevada, it is clear these tax revenue projections are incredibly optimistic.

As noted earlier, sports betting financial projections are going to carry a large degree of uncertainty. But if legislators and ultimately voters are to weigh the costs and benefits of sports betting legalization, it would be helpful if the financial projections weren't riddled with obvious and avoidable errors.


D.  Estimating the Potential Size of the Legal Sports Betting Market

In the absence of quality market research (based on scientifically and statistically sound sampling and modeling techniques), is there any way to derive a useful, or at least better informed, estimate of the potential size of the American sports betting market?

Moulton attempts to buttress his estimates of the Florida sports betting market by reference to the amount of sports bets handled by a local bookie. In fairness to Moulton, other sports betting advocates occasionally make the same argument. But the problem with this approach is that there is no way to scale one bookie's business into meaningful statistics for a state or the entire country. The density of bookies in a given community, the number of customers per bookie, the average amount bet by each customer, and other important details will inevitably either vary so widely or be so opaque to verification as to render it impossible to draw any meaningful conclusions beyond the individual bookie's business. As the old saying goes, the plural of "anecdote" is not "data".

1.  Extrapolating from known data (Nevada)

One potential approach to estimating sports betting revenues would be to extrapolate from known data. Unfortunately, with Nevada as the sole data point, extrapolation is likely subject to a high degree of variance. For starters, Nevada is the sole location in the United States offering a full slate of sports betting, and is a mature industry established for several decades. Tourists are a major part of the gaming economy, and are probably much more likely to be inclined to wager on sports than average Americans. Nevada also draws heavily from the wealthy population of neighboring California, skewing direct demographic comparisons to other states. Further, Nevada's major population centers are heavily saturated with casinos, not to mention statewide mobile sports betting, making it more likely legal sports betting has displaced a high percentage of illegal sports betting options (e.g., offshore internet sites and traditional bookies). At best, Nevada can be viewed as a best-case upper boundary on sports gaming revenues in other states (i.e., if a state like New Jersey has roughly three times the population of Nevada, it is unlikely New Jersey will exceed three times the gross sports betting revenues of Nevada, at least in the short-term).

Nevada had gross sports wagers (handle) of $3.9 billion in 2014, and in view of trends over the past five years, can reasonably be projected to exceed $4.0 billion in 2015. Extrapolating to New Jersey, to meet the projections of $100 million in annual tax revenues, if the state had gross sports wagers of $12 billion (three times Nevada, proportionate to population), the state would need to double its gaming tax rate to 16%. Conversely, the state could hold its tax rate at 8% and double the sports wager volume to $24 billion (six times Nevada). The assumption New Jersey will generate six times the gross sports betting handle of Nevada seems somewhat far-fetched, even if New Jersey is the only legal East Coast sports betting venue. [FN1].

Gaming revenue and tax revenue table (all dollars in thousands (add 000)).

Interactive spreadsheet available via Google Docs; download spreadsheet
(second tab) into Excel or your own Google sheet to use interactive feature.

One other way to potentially extrapolate meaningful data from Nevada is to look at the ratio of sports betting revenue to overall casino revenue. It's no surprise to anyone familiar with the casino industry that slot machines and table games are the primary gaming revenue drivers. Looking back at the 2014 year-end data for Nevada, the state's casinos had total slot revenues of $6.7 billion, and total table game revenues of $4.2 billion. Sports book revenues, however, were "merely" $227 million. Running the math, sports book revenues represented roughly 2.02% of total gaming revenues (slot, table game, and sports book revenues combined). And again, Nevada is a mature, highly saturated gaming market.

The Nevada sports betting ratio provides us a second useful upper boundary for checking the validity of sports betting revenue estimates. For example, New Jersey gaming revenues were $2.9 billion in 2013, down from a peak of $5.2 billion in 2006. Applying the Nevada ratio to these historical revenue numbers would suggest New Jersey might reasonably expect somewhere between $59.8 million and $107.2 million in annual sports book revenues, which translates into $4.8 million to $8.6 million in additional annual tax revenues (applying the current 8% gaming tax rate). 

On a national basis, the calculation is more complicated because many states have gaming markets which are substantially less mature and less saturated than Nevada and New Jersey. The AGA reports national gaming revenues of $37.34 billion in 2012, nearly equaling the historical revenue high point of $37.52 billion in 2007. Let's assume total gaming revenues increase by roughly 20% by the end of 2015, for total national gaming revenues of roughly $45 billion. Applying the Nevada ratio would suggest we might reasonably expect roughly $930 million in annual national sports book revenues, which translates into annual tax revenues of roughly $139 million (at a 15% tax rate) to $325 million (at a 35% tax rate).

Despite its small population, Nevada accounts for more than one-quarter of national gaming revenues ($10.70 billion of the $37.34 billion in national gaming revenues in 2012). No state has ever outperformed Nevada in gaming revenues in absolute terms, let alone on a population proportional basis. If sports betting advocates want to float sports betting revenue estimates for their state which are greater than Nevada's historical sports betting revenues, it's a fair question to those advocates why they think their state will outperform Nevada in sports betting revenues when they have never done so with respect to other casino gaming revenues.

2.  Extrapolating from demographic data

Acknowledging the limitations of extrapolating from Nevada to other states, is there any way to estimate national figures for sports betting revenues based on something other than a just a wild-ass guess pulled from thin air? One way economists or actuaries might approach the problem would be to estimate gambling habits by demographic group and extrapolate against known populations. Of course, no such rigorous study has been conducted to date. So we are left to attempt what might be best described as a slightly scientific wild-ass guess analysis.

First off, it's important to note that sports betting is an overwhelmingly male-oriented endeavor (one sports book operator in Delaware estimates men are over 90% of his clientele). Next, it's safe to say that there is a significant segment of the male population who either do not gamble at all, or do not gamble on sports. So, let's work with an assumption that roughly 1-in-8 (12.5%) men gamble on sports, along with a small percentage of women. Next, let's assume most men who gamble on sports wager around $5,000 per year on sports (essentially $100-$200 per week during football season, and $1,000 or so during the NCAA basketball tournament), with a smaller group of men being more regular, hardcore sports gamblers who wager greater amounts. We will also reduce the average bet size for the youngest population, commensurate with their lower average earnings. These assumptions (using 2013 Census data) result in gaming revenues and tax revenues as set forth in the following table:

Interactive spreadsheet available via Google Docs; download spreadsheet

into Excel or your own Google sheet to use interactive feature.

Essentially, the use of the above set of assumptions results in total national sports wagers (handle) of $215 billion, with gross casino revenues (hold) of $11.8 billion, and tax revenues of $1.7 billion to $3.5 million (assuming a tax rate of 15% to 30% of gross gaming revenues). Note that these assumptions result in an estimate that there are roughly 16 million potential sports bettors nationally, each wagering (not losing—just placing total bets) roughly $13,500 per year on average (the Totals row contains the weighted average for wagers placed given the initial assumptions used). If the estimates of total sports bettors or average wager seem high or low, one must question the validity of the underlying assumptions. Frankly, considering this estimate is an order of magnitude (roughly 12 times) larger than the national projections based on the Nevada ratio, this estimate most likely overstates the potential gaming revenues to a significant degree. Certainly the oft-cited $380 billion illegal sports betting market statistic looks increasingly dubious even under this more optimistic analysis.

Of course, the above set of assumptions were conjured out of the ether, with only the flimsiest of tethers to reality. If one downloads and plays with the spreadsheet, it quickly becomes obvious that the bottom line handle, hold, and tax figures are highly sensitive to the initial assumptions used. But without more rigorous data from scientifically validated surveys, these kinds of guesstimates are about as good as we can get, which means every estimate of gaming revenues and tax revenues from sports betting legalization has to be accompanied by large asterisk noting a significant margin of error.


E.  Market Issues:  Expansion, Conversion, and Competition

As if the difficulty of estimating the potential sports betting market size weren't already difficult enough, there are a number of issues which further complicate the process.

First, there is the issue of market expansion. There is likely a decent group of potential sports bettors who are currently not betting because they lack a connection to an illegal gambling option or choose not to use such a gambling option. Legalization of sports gambling would give these individuals an outlet to pursue sports gambling, expanding the sports betting market.

Next, there is the issue of market conversion. There is unquestionably a thriving illicit sports gambling market being utilized by sports gamblers in those states without a legal sports gambling option (essentially everywhere except Nevada, for sports gamblers who either live in or can easily travel to Nevada). The interesting question is how much of the illicit market will migrate to the legal market once sports betting is legalized in additional states. Although the legal market would superficially seem to offer significant advantages for sports gamblers, that assumption is not without major caveats.

Sports gamblers in recent years have become accustomed to immediate, around-the-clock, online access to sports betting. Some of this action is via direct wagering on offshore internet sports gambling sites, while much of the illicit action is mediated by local bookies who use offshore sites as a method for booking wagers. For example, a sports bettor might approach a bookie about betting on games. The bookie sets up an offshore account with a small deposit. The bookie makes the account available to the bettor, and they agree to a proportional betting scheme; e.g., $1 bet on the site equals $10 bet in real life. The bettor then makes small wagers online, which translate into larger real life bets with the bookie. Periodically, the bettor and bookie meet up to "square up" the account in real dollars.

Additionally, highly aggressive tax rates on sports book revenues are likely to be passed through to consumers in the form of higher commissions or surcharges. Further, legalized sports books will be forced to do tax reporting on larger bets and payouts. Sophisticated and higher volume sports bettors might well find that legalized sports betting is impossible to beat once higher taxes and commissions are taken into account, and will instead make the rational economic decision to continue utilizing illicit gaming channels.

Given the realities of modern, online sports betting, there is a significant question as to how much illicit sports betting will migrate to legal options post-legalization. In a highly saturated gaming market like Nevada where both the brick-and-mortar casinos and mobile sports book options make sports betting convenient and ubiquitous, the conversion rate from illicit to legal sports betting will be a fairly high percentage. But in states where legal sports books are limited geographically and there is no online or mobile betting option, the conversion rate might be significantly lower. Certainly there is no basis to assume that all or even most currently illicit sports betting will necessarily move to legal options post-legalization.

Finally, there is the issue of market competition. Spurred in part by a UIGEA carveout, online fantasy sports competitions have boomed in the past decade. The relatively recent innovation of "daily fantasy sports" (DFS) contests on sites such as FanDuel and DraftKings has driven explosive financial growth in the fantasy sports market, with industry experts projecting revenues exceeding $2.5 billion by 2020. As Chris Grove of Online Daily Fantasy Report notes, the potential impact of DFS-style gaming on traditional casino gaming could be significant:

Social [gaming] and DFS don’t have to make a dollar to cost casinos a dollar of revenue.

Instead, they can (in theory) offer consumers an experience similar to gambling but at a lower cost. So the increasing popularity of DFS, for example, could have an outsized negative impact on casino revenues, one that isn’t properly communicated by the pure revenue number of the DFS industry.

It doesn't take a rocket scientist to project that DFS-style gaming is potentially a bigger threat to traditional sports betting than it is to, say, slots or blackjack. Currently, DFS holds two significant advantages over traditional brick and mortar sports betting—DFS is legal and DFS is mobile. People who are interested in sports betting (particularly younger people) may find that DFS satisfies their sports betting needs, and may well find the DFS experience superior to traditional sports betting.

Of course, it would be absurd to think DFS will single-handedly destroy traditional sports betting in the short-term. The markets for DFS and traditional sports betting may not overlap to a significant degree. DFS might actually expand the traditional sports betting market by creating new sports bettors. Brick and mortar casinos could also offer DFS wagering, as is currently permitted in New Jersey casinos. But fifty years ago, who would have anticipated the decline of the horse and dog racing industries, once the centerpiece of legalized gambling in most states, now mostly kept afloat via subsidies from other casino revenue streams? It would be folly not to at least consider the possible effects of DFS on traditional sports betting revenues.

The issue of market competition also applies in state-by-state analyses of the sports betting market. As an example, the New Jersey casino market has been decimated in recent years by expanded gaming competition in nearby markets. Even if New Jersey were to legalize sports betting, there is no guarantee neighboring states would not escalate the gaming wars and likewise legalize sports betting, siphoning off a huge chunk of New Jersey's anticipated sports betting revenues. Consequently, any state-specific sports betting revenue projections must be accompanied by significant caveats and qualifications regarding anticipated competition from nearby markets.


F.  Conclusion

So, after all of this jibber-jabber, how much casino and tax revenue can we reasonably expect to be generated by widespread legalization and taxation of sports betting?

Your guess is as good as mine.*

* But I'm betting the under.

-----------------------------------------------------------------------------------------

[FN1] Applied to Florida which has seven times the population of Nevada (and its own healthy tourism industry), the upper boundary for sports betting gross wagers (handle) is $28 billion, with gross gaming revenues (hold) of $1.54 billion, and annual tax revenues of $539 million (assuming a 35% tax rate). In other words, still well short of David Moulton's estimated $750 million in annual tax revenues.

Poker's Deus Ex Machina (Part II)—How a Computer Proved Poker Is a Game of Chance

AUTHOR'S NOTE: This post is the second of two related posts. Part I is HERE.

* * * * *

As discussed in my last post, the recent news that a team of researchers has "essentially weakly solved" heads-up limit hold' em poker (HULHE) should be considered significant support for the legal argument that poker is a "skill game"—i.e., a game where skill, rather than chance, is the "dominant factor" in the game. In fact, the Cepheus computer program's ability to play a non-exploitable, game theory optimal (GTO) strategy does advance the skill game argument by showing that the skill-chance analysis cannot be confined to a single hand, demonstrating the importance of making long-term strategic decisions (e.g., balancing ranges). Further, Cepheus proves that, at least for the HULHE variation of poker, a player can use a GTO strategy that is indifferent to the role of chance over the long-term (i.e., the strategy will not lose to a non-GTO strategy over a statistically significant number of hands).

So, has Cepheus resolved the skill game legal argument in favor of poker as a game of skill? Unfortunately, the opposite may well be the case. As one of Cepheus' researchers explained, an important implication of a GTO strategy is that it is designed to be impervious not only to the effects of chance, but also to any counter-strategy (emphasis added):

"Since poker is a symmetrical game, the end strategy which Cepheus plays is an unbeatable one. While chips can, of course, be won from Cepheus in the short term, there is no decision which can be made against it which will be a winner in the long term. If a perfect opponent, either human or computerized, were to play a semi-infinite number of hands against Cepheus the best possible result would be for them to break even. Any imperfect opponent, which unfortunately includes all human players, would make mistakes along the way and lose. That being said, what Cepheus cannot do is maximize its winnings against weak opponents, a skill [at] which humans excel. Cepheus is simply an invincible, immovable bunker, a Maginot Line that actually works."

Thus, if two players face each other and both play a GTO strategy, then neither player will be able to exploit the other player, neither player will have a strategic advantage, and the result of the game will be left entirely to chance. In other words, the fact HULHE has a GTO strategy necessarily implies that the game can be played in such a way that the sole determining factor in the outcome is the effect of chance (i.e., which player gets luckier).

Now the possibility of a GTO v. GTO showdown may appear only theoretical. But let's consider the opposite situation, where two HULHE novices are matched up. Assuming neither player has any knowledge of proper strategy, again the results of the match are determined solely by chance. Now, let's take the next leap—two equally experienced, talented players who try to exploit the other player's flaws. In order to exploit those flaws, each player will necessarily make flawed strategic decisions (i.e., deviate from GTO strategy). However, over time, the constant back-and-forth of play should result in a series of game adjustments by both players which leaves each of them playing a close approximation of GTO strategy, such that neither player has a significant strategic edge. Again, the long-term results of such an even-skill match would be governed mostly (predominantly) by chance.

This implication for GTO strategy—that skilled players will eventually reach a close approximation of a GTO equilibrium strategy—is real and not theoretical. As was noted by Cepheus' researchers (emphasis added):

"So what does the availability of Cepheus’ data mean to limit hold’em play, particularly in the online environment where there are no effective checks against referencing Cepheus while play is ongoing? Not a great, deal unfortunately. While Cepheus would have undoubtedly had a detrimental and traumatic effect on a competitive online environment there is effectively no environment left to traumatize. Due to the rake, which is the share of the pot which the house claims as its fee, poker is a negative sum game. As the fundamental of heads up limit hold’em became better understood and the skill gap between competitors narrowed, many players found themselves in a position where they were able to beat their opponents but not both their opponents and the rake. More and more often, competition between players began to result in both players losing and the situation was exasperated [sic—exacerbated] by the decline of the online poker industry, which shifted a large portion of competitive play to lower stakes where the rake represents a larger percentage of a player’s potential winnings. Poker players, being rational people, did the only sane thing they could do, which was decline to play anyone who appeared to be of even remotely similar skill. At of the time of writing this article on a Saturday evening there are, on Pokerstars, the current market leader, thirty-five heads-up limit hold’em tables above the one dollar level where players are waiting for an opponent and one table at which two players are actually competing. Cepheus will undoubtedly prove a valuable sparring partner and research tool for casino players and enthusiasts looking to sharpen their skills, but the heyday of heads-up cash play has, unfortunately, already passed."

This concern about relative skill between players is common within the poker community. Online poker players have long engaged in the process of "bum hunting"—looking for games with known weak players to exploit. As poker professional Paul Ratchford explains:

"Poker is a zero sum game minus a cut that the house takes. So in an environment where all players are good and everybody plays game theory optimal poker EVERYBODY loses. The house takes money out of pots at an enormous rate especially at lower games. In fact, versus a bunch of skilled regulars (with zero recreational dollars in play) it may be impossible at a 6-max or full ring table for even some of the best in the world to win…. The bottom line is that if you are a professional poker player you need to be bum hunting / table selecting."

But the bum hunting problem is not limited to online play. Going back even to the early WSOP days, elite brick and mortar poker players like Doyle Brunson and Amarillo Slim would seek out games with easy marks like Archie Karas and Jimmy Chagra. More recently, high stakes professional poker players have pursued games with "whales" like Cirque du Soleil founder Guy Laliberté, baseball superstar Alex Rodriguez, and Texas banker Andy Beal (immortalized in the classic book, The Professor, the Banker, and the Suicide King: Inside the Richest Poker Game of All Time). Similarly, professional poker players Phil Ivey, Andrew Robl, Dan "Jugleman" Cates, and Tom Dwan have recently posted bail money or provided support to Paul and Darren Phua, individuals who reportedly control access to Macau's famed, whale-laden high stakes poker games. Back in Vegas, a number of poker pros jealously protect their whales from poaching by other pros:

"This game started about a week before the $1 million One Drop tournament and ran daily. Though a security guard kept gawkers and potential short-buys at bay, recognizable faces included One Drop Founder Guy Laliberte, Rick Salomon (the movie producer most famous for his Paris Hilton tape), and self-described model / actor / astronaut / asshole” Dan Bilzerian (@DanBilzerian). When this game runs, even the pros who play the regular 300-600 mix at Aria move elsewhere. 'Crazy' Mike Thorpe, who organizes many high-stakes mix games in town, says the regular 300-600 players at Aria, which include David 'Viffer' Peat and Ivey Room host Jean-Robert Bellande, have to move to Bellagio because Bobby Baldwin himself (Bobby’s Room namesake) would rather host his nosebleed no-limit game in The Ivey Room without pros."

Ironically, Bellande has himself been criticized by other poker players, including WSOP Main Event champion Greg Merson, for setting up high stakes poker games filled with whales, then excluding other poker pros from those games. Of course, this pattern of skilled "sharks" seeking out less talented "fish" to exploit isn't limited to high stakes play.

The irony of "bum hunting" or targeting "whales" and "fish" is that these weaker players generally play a highly flawed poker style that diverges markedly from GTO strategy. Although a GTO strategy would profit off these weak players over time, a non-GTO style will actually exploit weak players faster and for greater profit. So, in essence, poker's best players generally profit off of weaker players by utilizing a non-GTO strategy. Poker professional Paul Ratchford explains this irony (albeit in the context of no-limit hold 'em):

Maximum exploitive NLHE occurs when a player chooses the most exploitive line to maximize his/her expected value. Most players do not play balanced ranges and, therefore, we should seek to maximize our edge by playing appropriately unbalanced in response. In a Rock, Paper, Scissors example, where we know that our opponent will throw rock 100% of the time, we would simply use paper 100% of the time. Even if we knew that our opponent threw rock 40% of the time, 30% paper, and 30% scissors, the maximum exploitive play would still be paper 100%. In NLHE, if you play heads up versus an opponent who folds 100% of the time to three-bets, your response would be to reraise 100%. It is important to note that if you are playing against a GTO opponent, the maximum exploitive strategy will be GTO. The appropriate response to a perfectly balanced Rock, Paper, and Scissors range is to be perfectly balanced yourself.

Or, as Cepheus' own researchers admit, "what Cepheus cannot do is maximize its winnings against weak opponents, a skill [at] which humans excel."  In other words, maximizing profits in poker requires deviation from Cepheus-style GTO poker strategy.

The analytical takeaways from the discussion above can be distilled into these Poker Postulates:

• A poker player's relative skill advantage over his opponent matters more than his absolute skill level—i.e., "In the land of the blind, the one-eyed man is king."
• As the difference in skill between poker players increases, the effect of chance on game results decreases, but is never eliminated altogether.
• In poker games between players of substantially similar skill, results will be determined predominately by chance.
• In poker games between players of substantially dissimilar skill, results will be determined predominately by skill, even though over a short period of time chance may permit a lesser-skilled player to prevail.
• Skill in poker is more readily demonstrated by utilizing a non-GTO strategy to exploit weaker players than in utilizing a non-exploitable GTO strategy, at least insofar as success is measured by profits.

To be blunt, then, poker skill ultimately is not measured by how well a player selects starting hands, calculates pot and implied odds, or balances ranges. Likewise, poker skill is not measured by degree of similarity to or deviation from a GTO strategy. Rather, poker skill predominately turns on game selection; that is, being able to get into a game with weaker opponents whose flawed strategies can be exploited via a non-GTO strategy.

Returning, then, to the skill game legal argument, the clear implication of the Cepheus GTO strategy research is that poker advocates are left defending the awkward proposition that poker "skill" has little to do with game-related strategy and mostly means "preying on weak players" (or bum hunting, or fleecing fish—pick your own metaphor). Presented in this context, poker players begin to look less like mathematical savants and more like casino operators luring patrons to a -EV table game. In fact, for many poker players, their odds of winning money would actually be enhanced dramatically if they gave up poker for a seat at a house-run table game.

Is it any wonder the law treats poker the same as Mississippi Stud or Let It Ride?

“The creatures outside looked from pig to man, and from man to pig, and from pig to man again; but already it was impossible to say which was which.”

~~ George Orwell, Animal Farm