Ride-sharing giant Uber Technologies Inc. (UBER) caught a nice tailwind recently after announcing that Dallas riders can now book Avride robotaxis through its platform. It's the kind of autonomous mobility news that gets investors excited. Over the past five sessions, Uber stock has climbed 4%. Still, zoom out a bit and the picture looks less rosy—shares remain down roughly 10% since early October.

The broader tech sector jitters haven't helped. You know the drill: bubble fears, recession whispers (even though recession risks have actually subsided), and consumers feeling pessimistic about the economy. When people feel broke, ordering rides—which isn't exactly the budget transportation option—might not top their priority list. These are real headwinds worth considering.

But here's what actually matters for near-term options traders: Can any of the fundamental catalysts supporting Uber stock translate into probabilistically high directional outcomes? That's the question worth digging into. And to answer it, we need to get creative with how we understand where prices are likely to cluster.

Thinking About Risk Like Cannonballs

Bear with me on this conceptual exercise. Imagine you could break apart Uber's price action and convert each piece into a projectile—say, a cannonball. Fire these cannonballs into an open field. After hundreds of discharges, there should be a point where the projectiles feature the tightest grouping. In mathematical terms, that's called probability density.

But we're not just interested in where all the cannonballs land. We want to know the grouping of a specific set of cannonballs—the signal we're isolating. If this particular set features different groupings compared to the aggregate, we might have stumbled onto a structural arbitrage. Translation: Most of the market expects one outcome, but you've calculated a different one.

This cannonball exercise requires serious math—what I call trinitarian geometry. It combines probability theory (Kolmogorov), behavioral state transitions (Markov), and calculus (kernel density estimations). Sounds intimidating, but it really just boils down to understanding the likelihood of a directional outcome materializing in a chaotic, non-linear world. And once you grasp the concept, it opens up an entirely new dimension of insight.

What makes this powerful is that we can now identify and analyze the shape of risk. That changes everything.

What the Numbers Tell Us About Uber

Using this trinitarian geometry approach, the forward 10-week returns of Uber stock will likely range between $89 and $95.20, assuming an anchor price of $90.34. Price clustering would most likely occur around $91.

That's the aggregate view—all trials since Uber's initial public offering. But we're hunting for a specific signal: the 4-6-D sequence. In the trailing 10 weeks, Uber printed four up weeks and six down weeks, with an overall downward slope. Under this particular circumstance, the forward 10-week returns would likely range between $88 and $95.20, with price clustering predominant at $91.50.

Honestly, a half-percent positive variance isn't exactly something to write home about. But what's genuinely fascinating is the shape of the risk curve.

Starting from $92 onward, for every dollar the price increases, the drop-off in probability density accelerates at a super-linear rate. Between $92 and $93, probability density declines by approximately 31.25%. Between $93 and $94, the erosion jumps to about 77.73%. From $94 to $95, the decline hits 98%. That's a dramatic fall-off.

However—and this is the interesting part—the shape of risk bulges outwardly at the belly. The curve almost resembles a shark fin. This geometric shape suggests we could be a bit more speculative with our options strategy.

Two Strategies Worth Considering

If we only had the basic clustering data, the conservative play would be a 90.00/92.50 bull call spread expiring January 16, 2026. This trade would require Uber stock to rise through the second-leg strike of $92.50 at expiration, which is contextually realistic. The maximum payout is 85.19%—decent, but we can do better.

For traders willing to push a bit harder, the 90/95 bull spread, also expiring January 16, presents an intriguing proposition. The breakeven price sits at $92.25, which is practically right at the point where probability density is about to drop off severely.

Think about what this means: You're buying call premiums associated with the realistic side of the distributional risk curve—the slices likely to materialize. Simultaneously, you're selling the portion of the risk curve that's least likely to happen.

Sure, Uber stock would need to rise through the $95 target at expiration to trigger the maximum payout of over 122%. That's admittedly ambitious. But here's the beauty: Uber's curvature bulge gives us a fighting chance for a substantial payout while also limiting the opportunity cost if the stock climbs above $95.

Nothing prevents Uber from exceeding that level, but the empirical data shows it's less probable. We wouldn't have this knowledge without calculating the shape of risk. That's why understanding these geometric patterns matters so much—it transforms how we think about positioning trades.

The traditional approach to options trading often relies on gut instinct or simplistic probability assumptions. But when you can visualize and quantify the actual shape of risk, you gain an edge. You can see where the market is overpricing unlikely outcomes and where it's underpricing realistic scenarios. That's the arbitrage opportunity hiding in plain sight.

For Uber right now, the math supports a more aggressive stance than you might initially assume. The shark fin shape of the risk curve—with its bulging belly and sharp drop-off—creates a favorable setup for traders willing to push their strike prices a bit higher. It's not reckless speculation; it's calculated aggression based on probability density analysis.

Of course, all of this assumes you're comfortable with the inherent risks of options trading and that your analysis of Uber's fundamentals aligns with a bullish near-term outlook. The robotaxi news provides a catalyst, and if autonomous mobility adoption accelerates, Uber could surprise to the upside. But you're also betting against negative consumer sentiment and lingering tech sector anxiety.

The point isn't that this trade is guaranteed to work—no trade ever is. The point is that by understanding the geometry of risk, you can structure positions that align with probabilistic outcomes rather than just hoping for the best. And in options trading, that kind of mathematical foundation can make all the difference between random speculation and informed strategy.