Market Analysis · 3 min read

Santa Doesn't Fly Blind: How Binary Markets Hide Continuous Beliefs

Binary Contracts, Continuous Beliefs

Prediction markets look binary.

Yes or no. Above or below. Happens or doesn't.

But that's just a contract wrapper.

Before resolution, prices move continuously—drifting, adjusting, absorbing information—until they eventually collapse into a single, objective truth. What looks like a binary outcome is actually a probabilistic belief updating over time.

Santa doesn't fly blind on Christmas Eve.

He has Rudolph.

In markets, we have Monte Carlo simulations.

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The Binary Illusion

A Kalshi or Polymarket contract resolves to one number. But before that moment, prices reflect a spectrum of beliefs.

A YES price at 65¢ doesn't mean "this will happen."

It means: given what we know right now, the market thinks this happens ~65% of the time.

That distinction matters because binary markets don't reward being close—they reward being right about frequency.

The future isn't a point estimate. It's a distribution.

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TSA Average Check-ins: Our Santa's Reindeer Case Study

We chose the TSA weekly average market because it exposes this mismatch cleanly:

• Data is public and daily
• Seasonality is explicit (Christmas Eve & Day matter)
• The contract aggregates seven noisy days into one number

Intuition struggles here. Distributions don't.

Instead of asking "will TSA be above X?", a better question is:

If we replay this week many times, what range of outcomes shows up most often?

That's exactly the kind of foggy weather that Monte Carlo's "red nose" can help us navigate through.

Historical TSA daily checkpoint throughput for the Christmas week (Dec 22–28) across 2022–2024. The bottom row shows the simple weekly average for each year, highlighting both the consistent day-of-week holiday pattern and the upward shift in overall travel levels over time.

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Rudolph (Monte Carlo) Enters

Monte Carlo isn't about predicting the future.

It's about enumerating many plausible ones, given what we know.

In this case, we simulated thousands of Christmas weeks by combining:

Structure: The actual day-by-day pattern from last Christmas

Level: Current 2025 travel activity (anchored to recent TSA prints)

Noise: Real holiday-week deviations from prior years

Each simulation respects the calendar, today's travel levels, and the fact that holiday travel is messy.

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Reading the Distribution, Not the Headline

Once you see the distribution, the market stops feeling binary.

You can see:

• Where outcomes cluster


• Where probabilities thin out


• How much weight lives in the tails

Positions then become a consequence of structure, not conviction.

As daily TSA data prints, uncertainty collapses one day at a time—the fog lifts, the distribution tightens, and beliefs update.

That's how probabilistic markets actually work.

Distribution of simulated TSA weekly average check-ins for Dec 22–28, 2025, generated via 10,000 Monte Carlo runs. Each bar represents the frequency of simulated weekly averages falling within a given range; red vertical lines mark Kalshi contract thresholds, with annotations showing the modeled probability that the weekly average exceeds each level.

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The Bigger Picture

This isn't really about TSA.

Any market that compresses noisy inputs into a single outcome—weather, macro prints, earnings averages—behaves similarly.

Binary markets resolve to truth.

But they arrive there continuously.

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Notes & Disclosures

Written by Mr. Froxter
Follow on X: @MrFroxter

This article was originally written for FlowFrame. All rights reserved.

At the time of writing, the author holds a position in the Kalshi market discussed.

This article is for informational purposes only and does not constitute financial advice.

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