Dec 22, 2020
Dec 22, 2020

Asymmetry in outcomes: Success vs. failure in betting

What are asymmetric outcomes?

Why do we chase betting success?

Is it logical to play the lottery?

Risk of ruin and asymmetrical outcomes

Asymmetry in outcomes: Success vs. failure in betting

Asymmetric outcomes occur when the potential upside is much larger than the downside. So how do they work and why are they important in betting? Read on to find out.

What are asymmetric outcomes?

When the outcome of an event has two possibilities, an asymmetric outcome occurs when the potential upside (earning potential or return) is so much larger than the downside.

For example, a person attempting to make a viral video will generally either completely fail, causing the loss of the capital invested in creating the content, or succeed, achieving a massive return in revenue and social media following for the creator.

If the video fails to go viral the creator loses one unit of utility (the small cost of creating the video), if it succeeds then they gain a potentially limitless amount. There may be only a one in 1000 chance of the video succeeding but the upside of success outweighs the cost of failure by more than 1000.

In this case, even though the chance of success is tiny, it is still optimal for the creator to produce the content, since the payoff of one success far exceeds the cost of even a thousand failures. Author, trader, and statistician Nassim Taleb has covered the topic of asymmetric outcomes extensively:

“It is not how likely an event is to happen that matters, it is how much is made when it happens that should be the consideration. How frequent the profit is irrelevant; it is the magnitude of the outcome that counts.” – Nassim Taleb, Fooled by Randomness

Why do we chase betting success?

In some ways our content creator’s asymmetric outcome mirrors that of a prospective bettor. It is difficult to find a successful betting strategy or model, and time and resources (namely money) will be lost in pursuit of a viable approach.

However, the payoff of finding a sustainable edge, model, or strategy is huge – a potential income of a magnitude far greater than the cost of each failure combined. It’s arguably worth the small hits for the chance at the big breakthrough, which brings longer term betting success.

Longshots

A strategy that leans heavily on asymmetric outcomes is that of betting on longshots. By the very nature of betting on low probability bets, the bettor is looking to profit in a very similar way to the method Nassim Taleb describes.

Waiting for a sizeable edge to be borne out by a rare event occurring. This approach is not too dissimilar to the approach taken by some of those who shorted the sub-prime mortgage bubble. Taleb refers to these events as “black swans”.

Is it logical to play the lottery?

Lotteries are the ultimate longshot and a perfect example of a negative expected value bet. A rational bettor knows that buying a lottery ticket is a loss-making exercise. If 10 million €1 tickets are sold for a lottery with a single €8 million jackpot prize, then the expected return on each €1 spent on tickets is €0.8, and the expected loss is €0.2.

However, this equation does not consider the utility of each outcome to the participant. It is likely to be the case that €1 holds little to no utility to the participant, whereas €8 million is such a large amount of money it has almost unlimited utility to them.

Diminishing returns on large amounts of money is a widely studied phenomenon, so for some participants the €8 million will carry as much utility as €12 million euro.

Both are unimaginably large amounts of money to possess for most people, and provide such a huge utility upside that the €4 million difference is negligible. If the jackpot was actually €12 million (as it might as well be for such a participant) each ticket would have a positive expected return and it would be logical to play.

Lottery utility

Outcome

Probability

Return (Euro)

Utility change (Units)

Loss

99.9999%

-1

-0.000001

Win

0.00001%

+8,000,000

+100

As you can see from this theoretical example, the participant loses a negligible amount of utility for a loss of €1, an amount so small to be almost unnoticeable. However, a win confers an amount orders of magnitude larger. This is, of course, ignoring any utility gained from the enjoyment of playing the lottery itself. In pure monetary terms, playing the lottery doesn’t make sense, however from a utility point of view gambling on an extremely rare event can be surprisingly logical for the participant.

Risk of ruin and asymmetrical outcomes

In a situation where you are relying on a highly positive outcome from a series of low probability of success events, the most important thing for the bettor is to stay in the game.

This is partly why a suitable staking strategy is hugely important for successful bettors. Taleb gave an example of this by relaying advice he had received from a trader: “take all the risks you can, but make sure you’re in tomorrow”.

When attempting to come up with a profitable betting strategy, the most important thing for the bettor is to avoid is the risk of ruin.

Especially when working with volatile outcomes. Whether it’s betting on longshots or attempting to build a sustainable strategy, the bettor needs to position themselves in a way to benefit without the chance of being shut out of the game completely. With no capital there is no way of profiting when the rare event does occur.

So, buy a lottery ticket if you wish, but don’t empty your bank account on them.

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