Let’s Make a (Iran) Deal

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Can a popular 1960s television game show help us understand Donald Trump’s decision-making process with regard to the war in Iran?

The answer is yes.

To understand why, we first need to understand how the game show worked. Using that as a model, we can apply it to Trump’s choices in Iran, see how he arrived at the current ceasefire and negotiation stage and consider what may come next.

The game show we’re considering was called Let’s Make a Deal. The host was Monty Hall, a Canadian-American talent who hosted the show from its debut in 1963 through 1976. The show was continued in many forms under different names all over the world, but the original format is what we want to study for geopolitical purposes.

The game consisted of a stage with three closed doors. Behind one door was a grand prize, such as an all-expenses-paid trip around the world. Behind another door was a modest prize, perhaps a TV set or kitchen appliance. The remaining door had a comedic “zonk” prize with little or no value. One of the famous zonk prizes was a live goat.

The number and order of the doors doesn’t matter mathematically, but for purposes of illustration, we can say that Door No. 1 has the grand prize, Door No. 2 has the zonk prize and Door No. 3 has the modest prize. The contestant does not know which door holds which prize.

The contestant was offered something of reasonable value but was allowed to “trade” that item for something hidden behind the doors. Most contestants would do the trade. Then they had to pick a door. Let’s say the contestant chooses Door No. 3.

Here’s where the game gets interesting.

Monty Hall, knowing where the prizes were, would walk up to the stage and open one of the doors the contestant did not choose. In our example, he would open Door No. 2 to reveal the zonk prize. He would then ask the contestant if she would like to change her mind. The contestant could switch from Door No. 3 to Door No. 1 or could stand pat with Door No. 3.

Most contestants would stick with Door No. 3. Their logic was that Door No. 3 originally had a one-third chance of being the grand prize. That’s the correct probability.

They would reason intuitively that Door No. 1 also had a one-third chance of being the grand prize. Since the odds were the same between Door No. 1 and Door No. 3 and since nothing had changed, there was no reason to switch doors.

If the contestant stuck with Door No. 3, that door would eventually be opened and the contestant might or might not win the grand prize.

The Math Most People Get Wrong

It’s counterintuitive, but the logic most contestants use is incorrect.

Door No. 3 still has a one-third chance of containing the grand prize. But Door No. 1 actually has a two-thirds chance.

A contestant given the situation described above should always switch doors. That doesn’t guarantee a win every time, but it does double the chances of winning.

Here’s why:

At the start of the game, Door No. 3 has a one-third chance of holding the grand prize. That means Doors No. 1 and No. 2 combined have a two-thirds chance.

The key insight is that Monty Hall is not opening a random door. He knows where the prizes are and deliberately reveals a losing door.

When Door No. 2 is opened and shown to contain the zonk prize, the two-thirds probability that originally belonged to Doors No. 1 and No. 2 does not disappear. Instead, it shifts entirely to Door No. 1.

Nothing has changed about Door No. 3. It still has a one-third chance of containing the grand prize.

But Door No. 1 now carries the full two-thirds probability that was previously shared between Doors No. 1 and No. 2.

That’s why switching doors improves your odds of winning.

This is a simple example of Bayes’ Theorem. You start with the best estimate you can make based on the information available. When new information arrives, you update your assessment.

Once Monty Hall reveals that Door No. 2 contains the zonk prize, the odds change. A rational contestant updates the probabilities and switches doors.

(By the way, when the Let’s Make a Deal solution was first published, thousands of readers — including many with PhDs — wrote in insisting there was no benefit to switching.

Experiments with pigeons showed the opposite. Pigeons almost always switch.)

Trump’s Three Doors

Interesting. But what does this have to do with Trump and the war in Iran?

It turns out that Trump has a Monty Hall problem of his own in terms of policy choices in the war.

The grand prize, from a practical standpoint, is a negotiated settlement. It doesn’t sound appealing, but it would end the fighting, reopen the Strait of Hormuz, help reunite MAGA and get Republicans focused on the midterm election.

The zonk prize is a continuation of the stalemate. This avoids fighting in the short run, but it keeps the Strait of Hormuz closed. The world was close to running out of energy and other strategic inputs, and major parts of the global industrial economy were coming close to shutting down. It was the worst possible outcome economically and politically.

The modest prize is escalation. It has a short-term feel-good aspect to it, but it doesn’t accomplish much in the long run without 600,000 boots on the ground. It might reopen the Strait of Hormuz, but at a high cost in lives and treasure.

We can think of retreat behind Door No. 1, stalemate behind Door No. 2 and escalation behind Door No. 3. Retreat has a political cost. Stalemate has an economic cost. Escalation has a cost measured in uncertainty and casualties.

The Zonk Prize Revealed

Trump was merely guessing as to which choice had the best outcome and which choice was the zonk prize.

Two weeks ago, Trump was leaning toward Door No. 3 without really knowing what he was doing or what the outcome might be. He was guessing.

At this point in the policy process, JD Vance and others explained to Trump that Door No. 2 was the zonk prize. In effect, he opened the door like Monty Hall.

Door No. 2 was never a good outcome. The result of running out of energy was always going to be catastrophic. It was just a matter of time and the time was near.

Now Trump was like the contestant in Let’s Make a Deal. He could stick to Door No. 3 or switch to Door No. 1.

His goal was to get the best possible outcome for the United States without really knowing how to achieve that. When he saw that stalemate was the zonk prize, the odds favored switching strategies to increase the odds of success.

And that’s what he did.

Why Trump Switched Strategies

Over the course of June 11 and 12, 2026, Trump first threatened to bomb Iran into reopening the Strait and then abruptly announced a planned memorandum of understanding (MOU) that would reopen the Strait by giving Iran most of what it was asking for and leaving critical issues to be negotiated over the next 60 days.

In effect, Trump switched from Door No. 3 to Door No. 1 to increase the chance of success.

It worked.

The odds of the Strait reopening went up significantly and, as of today, substantial tanker traffic is in fact moving through the Strait (although it’s a tenuous situation with Iran firing on an oil tanker in the Strait just yesterday). Economic catastrophe has been averted at the cost of some embarrassment for the United States.

But we still achieved the best possible outcome.

The Next Round of the Game

Of course, war and diplomacy are far more complex than Let’s Make a Deal. There are many mixed cases. Agreements like the MOU can be torn up and the war restarted.

Or the MOU negotiations can be used by both sides to restock depleted weapons systems in preparation for another round of fighting.

Trump has already said he will “bomb the hell out of” Iran if it doesn’t live up to his expectations under the MOU.

New doors and new choices keep emerging.

Still, models are a useful way to analyze complex problems when all the inputs are not known. Bayes Theorem, which is the model behind the Monty Hall problem, is a powerful tool that I used frequently in my work at CIA.

The lesson is straightforward: Start with the best assessment you can make. Then update that assessment when new information changes the odds.

Rather than throw up our hands at Trump’s apparent contradictions, we can view his decisions as responses to changing information and changing probabilities.

That approach won’t predict every outcome, but it can help us make more accurate forecasts than intuition alone.

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