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Expected Value Is a Lie When You Only Get One Toss

Alan Mourgues
November 30, 2025

Consider this challenge.

You have to choose one of these two games:

Game 1

Toss a coin:

  1. Heads: I give you $1m (win)
  2. Tails: You walk away with nothing (lose)

Game 2

Toss a coin:

  1. Heads: You get $5m (win)
  2. Tails: You lose $3m (lose)

Let’s break this down.

Game 1 is a no-brainer.

Zero downside. Pure optionality. You'd take this every single time.

But life doesn’t hand out upside without downside, does it?

You already know this… risk and reward are joined at the hip. No pain, no gain.

Now, Game 2?

Let’s see. A quick expected value calculation gives you:

Expected value = +$1m, which is much better than Game 1’s +$0.5m.

So clearly, Game 2 is the “rational” choice… right?

Wrong.

Here’s the key issue: it’s a long-run concept… it applies only when you can repeat the game many times.

In a single coin toss, “50% chance” doesn’t mean anything practical.

You don’t experience the average.

You either win once or lose once, and losing $3m is very real. Most people can’t afford the second outcome even once. It can be ruinous.

So choosing Game 2 isn’t “wrong”… what’s wrong is believing the expected value guarantees anything.

In a one-shot scenario, the decision comes down to two things:

That’s it.

Now consider Game 3

Game 2, but repeated 1,000 times.

This is where everything changes.

A single toss can kill you. A thousand tosses? Much harder.

Once you can repeat the coin toss thousands of times, now probability starts working in your favour:

Net: ≈ +$1 billion, and the odds of being down after 1,000 flips are practically zero.

This is the entire business model behind casinos and insurance companies. They don’t gamble.

They force games into the repeatable regime where the edge compounds.

So to make money, you have to become the casino; you either win more on your wins,

or you win more often than you lose.

Now let’s bring this back to Oil & Gas.

Exploration Drilling Is Game 2… Not Game 3

An exploration prospect may look like this:

You run the math in Excel and the economics are great. A stunning slide deck. Board nodding. Everyone happy.

But here’s the catch:

An exploration well is not a repeatable game for most companies.

You don’t get to drill 1,000 exploration wells. You don’t get to let the law of large numbers iron out your variance.

You might only drill one, or two, or five in your entire corporate life.

That means each exploration well behaves exactly like a single coin toss:

A spreadsheet “portfolio” of 50 prospects with positive EV is great in theory, but only exists in the model.

If you can’t actually drill 50 wells, the portfolio logic collapses.

Who Really Gets to Play Game 3?

There are companies in this industry that genuinely get to play the long game.

The supermajors (Exxon, Shell, TotalEnergies, Chevron, BP, Petrobras, CNOOC) operate on a completely different plane.

They drill hundreds of wells a decade. And when you drill that many wells, a dry hole isn’t a catastrophe. It’s Tuesday.

Five, ten, 20 dry wells? They’ll survive that too.

Why? Because somewhere in that long chain of attempts sits a Guyana-scale discovery… something so large it pays back every previous failure with change left over.

For them, exploration genuinely is a repeatable game. They have enough tosses of the coin for probabilities to play out.

Everyone Else Is Playing Game 2 While Pretending It’s Game 3

But step outside the world of the giants, and the picture changes dramatically.

They’re still playing Game 2. One toss at a time. One well at a time. One $30–50 million decision that can make or break the entire company.

The variance that supermajors can shrug off is the same variance that can wipe out a smaller player before the expected value even has a chance to show up.

It’s not that the geology is wrong. It’s that the structure of the game is wrong.

The Real Winning Strategy

Savvy exploration strategists understand this instinctively.

The don’t just chase prospects… they become the casino, by spreading risk, splitting costs, sharing wells, stringing projects together, and bringing in partners who can carry the worst of the downside.

They create optionality. They buy themselves more tosses of the coin, so probabilities can play out and the real-life portfolio start to resemble the model spreadsheet.

Bottom Line

In the end, the prospect is never the real asset.

The real asset is your ability to stay alive long enough for probability to matter.

Because even the best expected value in the world is worthless if you go bust on the first or second toss.

Survive the variance, and the upside eventually shows up.

Fail to survive, and the math never gets its turn.

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Alan Mourgues is a Petroleum Reservoir Engineering Consultant with 25 years of international experience. He is the founder of CrowdField — the go-to hub for Oil & Gas subsurface professionals to upskill, freelance, and monetize their expertise. CrowdField brings together a global community through: i) Freelance marketplace for niche talent and task-based solutions; ii) Digital Store & Vault of engineering tools, workflows, and resources; iii) AI Hub showcasing startups, workflows, and use cases; iv) Learning resources including webinars, blogs, and curated datasets. Alan’s mission is to empower professionals to turn knowledge into income and future-proof their careers as the energy transition unfolds.

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