"The Cat and the Canary" from Justice League Unlimited Season 1, Episode 14 (2005)

In this episode of Justice League Unlimited, Black Canary enlists Green Arrow’s help in busting open an illegal sports betting ring. What sport? Octagon-style metafighting. Run by Roulette, Meta-Brawl was a highly profitable operation where well-to-do types with a penchant for violence could watch superhuman gladiator matches and bet on the outcome. Much like being the sole movie theater in town, Meta-Brawl probably had near-monopoly power in setting admission fees. But being a smart businesswoman it is likely that Roulette charged a lower admission (something closer to the competitive price) and then ratcheted up her effective commission for those interested in gambling, thereby employing a two-part tariff to price discriminate.

The commission comes from Roulette’s function as a bookmaker. To illustrate how she made money on fights, imagine a bout between Atomic Skull and Wildcat. Assume that the two outcomes are Wildcat wins or Wildcat loses, with equal probability. If you were betting against a friend, the odds of each outcome would be 1-1 and a $100 stake would pay off $200. However, when placing bets at Roulette’s she would likely give each of you odds of 4-5, meaning for every $5 invested you stand to make a profit of $4 if your pick wins. This translates into a potential payout of $180 on a $100 investment. This is worse than even money, even though the odds of either fighter winning have remained at 50%.

In the above example the bookmaker’s “fair” book is 100% (50%+50%) but the actual book is 111.12% because 4-5 odds correspond to a probability of 55.56%. This extra 11.12% is called the overround. To ensure profits, Roulette would try to take bets in proportion to the underlying probabilities. In our simple case, with each fighter being equally likely to win, she would want all the money evenly split between the two.

To see her profits imagine she has 100 gamblers betting $100 on Atomic Skull, and the same action on Wildcat. She takes in $20,000 but only pays out $18,000 regardless of who wins. The remaining $2,000 is her profit, and represents 10% of total turnover. This 10% is called the Vig, or Roulette’s commission, for acting as an intermediary.

What if Wildcat, being the hometown hero, received a majority of the bets? Suppose 150 people put money on him and only 50 bet on Atomic Skull. If Roulette didn’t change the underlying odds she would now be at risk of losing money. Suppose Atomic Skull blasts Wildcat with a healthy dose of radioactivity, frying our hero’s organs. Roulette would only be paying out $9000 (return of $5000 investment + $4000 profit) and keeping $11,000. Great deal, right? But if Wildcat manages to dodge the energy blast and knock out Atomic Skull with an uppercut to the jawbone, you can bet Roulette will be feeling the pain vicariously. Now 150 people are each expecting to receive $180, or $27,000 total. She would be stuck $7000.

Being a genius at calculating odds we can assume Roulette has planned for this contingency. She would change her book by having 3-1 odds on Atomic Skull and 1-3 on Wildcat. She would again reduce these odds when taking bets to ensure that the actual book is over 100%. Now, as before, she will make money regardless of the outcome.

Being an illegal establishment there are a number of other strategies Roulette can employ to make additional profits. Let’s suspend our disbelief for a moment and suppose that she manages to capture Batman. The crowd would love nothing more than to see the Caped Crusader get pummeled, and might be more inclined to bet against him. Roulette can then offer worse odds to Batman’s opponent and likely make a killing. On the other hand there’s no better risk-mitigating strategy than cheating. Roulette could arrange for one of the fighters to take a fall and split the profits with him.

Either way, Meta-Brawl was a terrific business enterprise while it lasted.

The commission comes from Roulette’s function as a bookmaker. To illustrate how she made money on fights, imagine a bout between Atomic Skull and Wildcat. Assume that the two outcomes are Wildcat wins or Wildcat loses, with equal probability. If you were betting against a friend, the odds of each outcome would be 1-1 and a $100 stake would pay off $200. However, when placing bets at Roulette’s she would likely give each of you odds of 4-5, meaning for every $5 invested you stand to make a profit of $4 if your pick wins. This translates into a potential payout of $180 on a $100 investment. This is worse than even money, even though the odds of either fighter winning have remained at 50%.

In the above example the bookmaker’s “fair” book is 100% (50%+50%) but the actual book is 111.12% because 4-5 odds correspond to a probability of 55.56%. This extra 11.12% is called the overround. To ensure profits, Roulette would try to take bets in proportion to the underlying probabilities. In our simple case, with each fighter being equally likely to win, she would want all the money evenly split between the two.

To see her profits imagine she has 100 gamblers betting $100 on Atomic Skull, and the same action on Wildcat. She takes in $20,000 but only pays out $18,000 regardless of who wins. The remaining $2,000 is her profit, and represents 10% of total turnover. This 10% is called the Vig, or Roulette’s commission, for acting as an intermediary.

What if Wildcat, being the hometown hero, received a majority of the bets? Suppose 150 people put money on him and only 50 bet on Atomic Skull. If Roulette didn’t change the underlying odds she would now be at risk of losing money. Suppose Atomic Skull blasts Wildcat with a healthy dose of radioactivity, frying our hero’s organs. Roulette would only be paying out $9000 (return of $5000 investment + $4000 profit) and keeping $11,000. Great deal, right? But if Wildcat manages to dodge the energy blast and knock out Atomic Skull with an uppercut to the jawbone, you can bet Roulette will be feeling the pain vicariously. Now 150 people are each expecting to receive $180, or $27,000 total. She would be stuck $7000.

Being a genius at calculating odds we can assume Roulette has planned for this contingency. She would change her book by having 3-1 odds on Atomic Skull and 1-3 on Wildcat. She would again reduce these odds when taking bets to ensure that the actual book is over 100%. Now, as before, she will make money regardless of the outcome.

Being an illegal establishment there are a number of other strategies Roulette can employ to make additional profits. Let’s suspend our disbelief for a moment and suppose that she manages to capture Batman. The crowd would love nothing more than to see the Caped Crusader get pummeled, and might be more inclined to bet against him. Roulette can then offer worse odds to Batman’s opponent and likely make a killing. On the other hand there’s no better risk-mitigating strategy than cheating. Roulette could arrange for one of the fighters to take a fall and split the profits with him.

Either way, Meta-Brawl was a terrific business enterprise while it lasted.

## 10 comments:

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Nice read! but I have a small question on the betting system you just explained. How do Roulette determines/fix the betting ratio in the first place?

Syngergic:

This is where asymmetric information plays a big role. Roulette and her employees likely have more information about the fighters than the average gambler. They will have a much better idea of what the underlying true odds should be.

The actual odds that they offer will be based on the true odds, and if the market (being the gamblers) doesnt think this is mispriced then there should be action relative to these posted odds.

However, as market conditions change (someone decides to put a lot on an underdog), Roulette will have to change the offered odds.

Another interesting option, which isn't mentioned in the post, is laying off bets with other bookmakers who actually have better odds. This is a nice read, if this stuff interests you:

http://www.puntingace.com/bettingguide/bookmaking.htm

Thanks @E, sadly I couldn't look at the link you provided since it is blocked in the country where I stay. Thanks Again.

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