Sobriety and Probability Theory
Sobriety and Probability Theory
What's the "expected value" of drinking a beer?
Let me warn you from the outset: This is likely the most esoteric essay I’ve ever written about sobriety. As always, I’ll do my best to explain my thoughts clearly and concisely, but this edition of the newsletter might be a little bit more difficult to follow than most of them.
With that said, the concepts I’m going to describe can provide a great way to think about alcoholism and sobriety. So, I hope you’ll stick with me, but if you’re looking for some lighter reading, maybe give the newsletter archive a glance instead.
Expected Value
Expected value is a concept in probability theory. I have to admit, however, that I first came across back when I was in college and playing way too much poker.
In short, expected value is the average of all possible outcomes of a random event.
For example, imagine we were betting on the outcome of a coin flip. Heads, you win $1. Tails, I win $1.
From your perspective, there are two possible outcomes, each with equal probability: you win $1 or lose $1. On average, you break even. Therefore, the expected value of the coin flip is $0.
No, imagine that we change the payouts. Heads, you still win $1. Tails, you lose $100. On average, you’re now losing $49.50 on each flip. ($1 - $100 is -$99, and -$99/2 is -$49.50).
Your odds of winning the coin flip are the same in both examples (50/50). In the first example, however, the coin flip is a neutral bet, while in the second, the coin flip is an absolutely terrible bet.
The key difference is that in the second bet, the consequences of losing far outweigh the benefits of winning. You’re risking a loss of $100 for a win of just $1. It’s easy to see that it’s a terrible move. (Even if the odds of winning were 50 to 1 in your favor, the bet would still have a net loss.)
Expected value is an important concept in probability theory, and we can see from the example above why it’s also useful for gamblers. But what is its relevance to sobriety?
The Odds of a Relapse
Expected value is a great way to think about many types of decision-making, even when the results aren’t so obviously quantifiable.
Whenever we evaluate a decision with multiple potential outcomes, we have to ask ourselves two questions:
What are the odds that each outcome will happen?
How good or bad is each outcome?
Humans aren’t always great at seeing how these questions overlap. For example, millions of people play the lottery when the jackpot gets large, without ever thinking about just how astronomically low their odds of winning are.
The flip side is that sometimes we make decisions that seem low risk, but are still a terrible idea because of how devastating the consequences would be if things go wrong.
Since getting sober, I’ve had to ask myself many times whether a particular action might put my sobriety at risk.
Can I walk down the liquor aisle at the grocery store without being tempted to buy something?
Can I go to a party where everyone is drinking except for me?
Can I drink non-alcoholic beers that taste just like the real thing?
The first question I have to consider is how likely it is that each of these actions would lead to a relapse. 50/50? 10% chance? 1% chance?
For most of us, we can intuitively see that 50/50 odds of a relapse, or even a 10% chance, are risks that we shouldn’t take. However, it gets harder to see the danger when the odds drop to 1%.
That sounds relatively safe. 1% isn’t a high number. We take bigger risks than that every day.
However, the next question I ask myself is what would happen if I relapsed? The answer to that is that it would ruin my life.
I know from experience that it’s all too easy for me to fall back into addiction. The first time I tried to quit drinking, I relapsed after a few months and kept drinking for another seven years!
Those are truly terrible consequences. I’d destroy my finances, my health, my friendships. I’m not exaggerating when I say that a relapse could easily lead to my death.
When I take those consequences into account, I can see that even an action that has just a 1% chance of leading to a relapse isn’t worth taking.
When we think about the steps that recovering addicts take to protect their sobriety, it can sometimes feel like overkill.
However, when we think about the consequences of a relapse, we can see why those steps make sense.
I’m not saying that any given action is categorically right or wrong. Some former drinkers can easily go to a party without risking their sobriety, others can’t. The important point is that we need to carefully consider just how risky each action is, and just how badly things could turn out if we do end up drinking.
If you’ve made it this far, I appreciate you sticking with this slightly offbeat take on sobriety. Next week, I’ll get back on track with something a little more normal!
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