Arbitrage Betting, Chinese Businessmen & Real-Life Freerolls

When the downsides are very minimal or zero, you should be more concerned with taking lots of chances–running lots of “experiments”–than being “right” with the risks you decide to take.

About Lucky Maverick

About Jonathan Bales

You might think that blogging about probability, game theory, and expected value wouldn’t be much of a panty-dropper, and you’d be correct. Literally haven’t met or even heard from a single woman from this fucking newsletter.

I still like to start off each post with something about myself I know the opposite sex would find irresistible, just in case. So, ladies…

I had a dream about sports betting arbitrage the other night.

I know, I know. Women go crazy for arbs.

And before you even say it, I know what you’re gonna ask:

“But did your dream recognize arbitrage as nothing more than negative synthetic hold, not a guarantee that both sides of a bet are +EV?”

Yes, actually, as a matter of fact it did.

The dream got me thinking about real-life “arbitrage” situations, and how we might apply the concept of asymmetrical payoffs in sports betting or other markets to day-to-day decisions. This post will take a look at:

• Why you shouldn’t blindly bet arbitrage situations

• Why searching for arbs is still of importance

• Focusing on payoffs more than accuracy

• How to identify real-life arbitrage/freerolls/+EV bets

Synthetic Hold

Arbitrage betting is the act of taking advantage of differences in pricing in a market to guarantee a risk-free profit. This applies to effectively any market, and sports betting is no different.

In sports markets, bookmakers offer odds that reflect their estimate of the probability of an event occurring. Even money represents 50/50 odds, +200 (bet $100 to profit $200) equates to 33% implied odds, and so on.

Sportsbooks leave themselves wiggle room on these odds, typically offering -110 on a standard “coin flip” bet, i.e. you must bet $110 to win $100. If the odds are 50% or close to it, the sportsbook will eventually make money from the difference in what they charge versus what you get paid if you win.

This is called the hold. Every bet at a sportsbook has a hold percentage you must overcome in order to make money. To beat a standard -110 bet, for example, you need to win roughly 52.4% of bets.

That’s more difficult than it sounds, but the good news for sports bettors is they don’t need to just blindly bet at one sportsbook. For most bets, there are odds flying around all over the market, in constant flux as bets come in and information comes out.

For the bettor, the hold that really matters is synthetic hold. You can think of synthetic hold as the percentage that a theoretical sportsbook would take if it only offered the best price on every bet from every sportsbook you use.

Let’s say DraftKings is offering a Chiefs/Bills game at -110 on both sides. You also bet at FanDuel, Fanatics, BetMGM, and other books, and notice that DraftKings has the best price on the Chiefs at -110, but the Bills are -105 at Fanatics. The hold at DraftKings is 4.55%, but the synthetic hold–the hold offered by your theoretical book that only offers the best prices–is only 3.48%.

The reason that synthetic hold is so important is that, the lower it goes, the higher the odds that you’ll make a profitable bet solely by chance. If you imagine a scenario in which you can get -101 on each side of a bet–0.5% synthetic hold–even the slightest bit of good information could overcome the hold to get you on the profitable side.

Arbitrage As Negative Synthetic Hold

Sometimes, the synthetic hold turns negative. This is an arbitrage situation, and although they’re not all over the place, they’re not incredibly scarce, either. This is particularly true in smaller markets or niche sports where odds fluctuate far more than popular markets with a lot of action.

If you can find both sides of a bet offered at +101, for example, you can bet $100 on each to return a total of $201–a total of $200 bet, $201 returned, and a profit of $1 or 0.5%. This might seem trivial, but we’re talking about effectively overnight risk-free profit. At +105 on both sides, the return is 2.5%.

The important point I want to make is that moving from 0% to negative hold–an arbitrage–simply means that you can profit by betting on both sides of a bet, not that both sides of the bet are long-term profitable on their own.

If we take this to a logical extreme, you can see why betting both sides of an arb often breaks down. Would you rather have a guaranteed $1 or flip a coin for $100? Obviously the latter option, with $50 of EV.

When an arb has a very small negative synthetic hold–let’s take the same example of +101 on both sides of a bet–the odds of both bets being +EV is extremely small: effectively the same as if the bet is exactly 50/50. If both sides of a bet are +110, on the other hand, the true odds are much more likely to fall between that range, making both sides good.

An arbitrage opportunity allows for the possibility that both sides of a bet are profitable, but it far from guarantees it. Your willingness to actually bet on both sides should be a function of the spread between the odds on each side and your confidence in knowing which side is actually good.

When an arb’s negative synthetic hold is minimal, which is the case most of the time, one side of the bet is still likely to be bad. If you can identify it with any regularity, you’re better off betting only one side and forgoing the guaranteed profit.

Why You Should Still Look for Arbs

The reason you should still look for arbitrage opportunities is simple: they’re a proxy for EV. In identifying arbs, you’re looking for situations in which a quoted price is likely to be “off” from reality, just as with any other situation. It’s a very effective tool for quickly scanning robust markets and finding which odds are most likely to be wrong.

There’s nothing magical about a bet when both sides move to +101 as opposed to even money. One side is still likely to be profitable, and one is not. The only thing that changes as that spread increases–say to +105 on each side–is that your confidence in which side is actually good needs to increase in order to make it smart to not bet both sides. At, say, +120 on both sides, you’d need extraordinary confidence one side is much better than the other to only bet just one.

The overall process of identifying arbs is very useful, regardless of whether or not you bet both sides, because it’s the way you should go about analyzing bets anyway.

Freerolls

It’s become popular in the sports card collecting community to determine a card or collection’s sale price by flipping a coin. If a card’s “real” price is $400, the buyer and seller might flip a coin to determine if the final price should be $350 or $450, and neither would come out ahead in the long run. The variance around the price increases, but the EV is still $400.

There’s a hidden assumption in that logic, however: that both parties are acting ethically. And this is a giant assumption, as if one party plans to back out of the deal after losing the coin flip even part of the time, it completely throws off the math.

I recently saw a video of just this–a video I just spent 90 minutes searching for and still cannot find but I know a reader is going to know what I’m talking about and send it to me soon after I publish this article, at which point I will embed the video and delete this unnecessarily verbose explanation of why I’m about to describe a video readers cannot view.

In the video, the buyer offered to purchase a $40,000 card collection for $30,000 if he were to win a coin flip and $50,000 if he were to lose. This is a fair deal in theory, but not in practice, as the buyer lost the coin flip and immediately declared he’s not paying.

In this case, we’d say the seller got “freerolled.” The buyer unethically went into the deal knowing he’d either get a deal on the collection or back out at no cost, pushing all of the downside in the transition to the seller’s side. The seller shouldn’t have put himself in this position with someone he didn’t have trust in–even a small percentage chance of the buyer backing out after a loss equates to a -EV deal for the seller–and his naivety resulted in the opportunity for a freeroll.

Another example of a freeroll can be seen in the game credit card roulette. Popular in the gambling and finance communities, credit card roulette involves everyone chipping in a credit card at dinner or a night out and selecting one at random to pay the entire bill. The expected value of credit card roulette is neutral, assuming 1) everyone orders roughly the same amount over the long run, and 2) they don’t back out of the game as it progresses. If you knowingly and continually spend more than those around you or try to buy out of the game at a price that doesn’t reflect the current EV, that’s an unethical freeroll.

Not all freerolls are bad, of course. Some poker tournaments are freerolls, for example, offering prizes but requiring no entry fee, and it’s common for companies to run the equivalent of freerolls in order to attract business.

Freerolls are easy to spot in gambling situations, but your entire life is filled with them, just less obviously. Some are unethical, with people or businesses trying to exploit you, and some are not.

Arbitrage is the most obvious example of an ethical freeroll.

Although the sportsbooks might not agree, sports betting arbitrage is an ethical freeroll because you’re simply taking each book up on their offer to bet a specific team at a particular price. You’re not doing anything nefarious on either end of the bet; you’re just leveraging small volatility in the market’s pricing of an event to your advantage.

Many years ago, I performed what I’ll call “writing arbitrage,” which I discussed in my post Should You Work for Free?:

Internet content was becoming king and there were a bunch of sites that would pay freelance writers decent money to write short (and shit) articles. Remember eHow and About.com and those sites? Stuff like that.

They paid enough that I thought, “Man, this is too much money, I bet people would do it for less.” So they did do it for less, for me. I advertised my own company on Craigslist that paid writers very handsomely—and by that I mean about 50% of what I would be paid to write through another freelance publishing company at which they couldn’t be accepted—to create short articles, which I’d then publish under my name (with permission, of course…from the writers, not the company). $25 out, $50 in, and we’re off. That idea worked for a bit until the site contacted me wondering how I was writing 100 articles a day.

“I started drinking a new coffee,” I said. “And I’ve been experimenting with various writing styles, some very different than others.”

Okay, I’m going to call that one a “semi-ethical freeroll.” But a freeroll nonetheless.

Note that something isn’t a freeroll just in terms of money. You typically need to invest time and energy into identifying and leveraging freerolls, which could easily make them not worth the cost.

My aunt is a coupon-cutting freak, for example, and can easily turn a $150 grocery bill into $100. The only cost? Twenty hours of her time and a kitchen filled with barely edible foods that were on sale.

Real-Life Asymmetries and Chinese Businessmen

Remember, in betting, synthetic hold represents the probability of you being on the profitable side of a bet by chance. As it decreases, your odds rise. When it goes negative, your odds are 100%.

In real-life, you can think of synthetic hold as the risk you’re taking on with each decision and the odds you’ll be harmed by making a bad choice. When the risk is high, you need disproportionately high confidence you’re on the right side. When it’s low, you can take more chances, similar to what investors do when interest rates are low.

Unlike in sports betting, though, real-life payouts are typically not fixed. The upside and downside scenarios in certain areas are massive. This means that when “real-life hold” goes to zero or negative–when you’re effectively paid to take chances–you should go crazy firing off bets.

There’s a five-part article series called the paradox of Chinese businessmen that I really like. In it, Cedric Chin writes:

First, (I learned) that the most successful Chinese businessmen were often the least educated ones. Second, that Chinese businessmen as a group were more superstitious than most, but that this didn’t seem to have much of an effect on their ability to run their businesses! And finally, that the vast majority of Chinese business people did not think too far ahead. They optimised locally, and by keeping close tabs on the bottom line, shut down lines of business that weren’t performing as well.

Chinese business is sort of the antithesis to business school. Instead of being rooted in theory, Chinese businesses (and much of Eastern philosophies and ways of living) are rooted in pragmatism.

What’s true is what works.

There are a couple immediate ramifications I can see from this perspective. The first is that payoffs matter more than accuracy. The second related point is that “wrong” beliefs/actions can stick around if they cause no harm. Like the tailbone or the appendix, there are a lot of seemingly vestigial Eastern practices that likely don’t “work,” but like being superstitious for the businessman, it doesn’t matter because they cause no harm.

I bring this up because when you look at something like Eastern herbal remedies, you’re kind of seeing a situation with little, zero, or negative “synthetic hold.” That is, the downsides of being wrong are effectively removed. When you take something like green tea extract or turmeric–or perhaps get acupuncture–you’re effectively getting a freeroll. Maybe it will work for you, and maybe not, but you’re highly unlikely to be harmed.

You can acquire life freerolls/arbitrages by applying this same mindset. In the field of health/wellness, for example, you might perform low-risk wellness experiments on yourself, looking for a combination of a solid base of evidence of efficacy with minimal side effects/downsides.

In doing this myself, I’ve landed on supplements like creatine, magnesium, and theanine–all of which I take daily–that have significantly improved my overall quality of life. Creatine, for example, is arguably the most studied supplement ever due to a lot of myths that arose when it became popular among bodybuilders; the evidence is extremely strong for creatine’s effectiveness in enhancing not only exercise performance, but also cognitive and mental health, while being extremely well tolerated.

Some other supplements that I’ve found effectively act as a health freeroll: glycine, taurine, NAC, apigenin, garlic extract, and many others.

Other Real-Life Arbs/“Freerolls”

When you think less in terms of being “right” and more in terms of the payoffs when you’re right/wrong, you notice a lot more interesting real-life freerolls. Some examples:

• Walk while on calls/meetings; you forget that you’re moving and can rack up steps without it being horribly boring.

• Negotiate through questions; ask relevant questions rather than counter to get information on motivations and possibly get the other side to negotiate against themselves.

• Choose the best long-term solution when decision paths have similar short-term returns; you’re freerolling your future upside.

• Do favors; while there is some time/energy commitment, you also can get something out of it–even if the favor is never reciprocated–in feeling good about yourself…and there’s the potential from benefiting from future goodwill.

• Fade consensus opinions when the cost is low/zero; if you’re right (think early Bitcoin), you’ll be asymmetrically rewarded. Being wrong very early isn’t very costly.

• Send cold emails offering value to those you’d like to work with/for; there is a small time cost, but the downside is just getting ignored while there’s a small probability for big upside.

• Talk less, listen more; there’s very few downsides to speaking up “too little”–very often it’s even beneficial in terms of how you’re viewed–and the upside is your words carry more weight when you do use them.

• Use emotional freerolls; bet against the team you want to win when it’s +EV, accept the worst possible outcomes as your fate, etc.

Just as reducing synthetic hold decreases the probability of being wrong by chance, focusing on payoffs instead of accuracy improves your odds of finding real-life freerolls where you can truly generate value from nothing.

When the downsides are very minimal or zero, you should be more concerned with taking lots of chances–running lots of “experiments”–than being “right” with the risks you decide to take.

About Lucky Maverick

About Jonathan Bales