The Dynamite Paradox: a super-weapon that barely wins

Give a child legal access to dynamite and Rock-Paper-Scissors changes less than you'd think. Hand it to only one child and their win rate climbs from a coin flip to 55.6% — barely better than random, even though the weapon of mass destruction can beat two of three opposing moves outright. And here's the twist that keeps strategists up at night: the dynamite-holder barely fires the stuff. They win by leaning on plain old Rock.

That's the counterintuitive core of Andrew Lohn's "Rock, Paper, Scissors, ... Dynamite" (Lohn, 2026), a game-theory paper from Georgetown's Center for Security and Emerging Technology. The author isn't actually interested in playground disputes. "Our interest is in understanding Dynamite the adjective," he writes — "as in 'that new AI model or joint strike fighter is dynamite.'" The toy is a lens for a serious, urgent problem: when a shockingly capable new technology arrives, when should we expect it to actually change who wins, and when should we expect it to quietly change nothing at all?

The answers are uncomfortable for the people developing and buying powerful new AI. A new capability can be genuinely disruptive without being valuable. It can be valuable while being used almost never. And it can render entire categories of work "strategically unplayable" — obsolete not because they're bad, but because the strategic math of the game quietly deletes them.

The Science

Game theory models competitions where each side has an arsenal of options, and every option beats some opposing options while losing to others. Rock beats Scissors, Scissors beats Paper, Paper beats Rock. When the game is fair and every option is equivalent, rational players mix their moves randomly at equal rates — 1/3 each in the classic three-move version.

Lohn's move is to inject a new, more capable option — Dynamite — and ask how the equilibrium shifts. Dynamite is versatile in the sense that matters: it defeats more opposing moves than any single original option. The analysis systematically varies three things: how many moves Dynamite beats (its capability), whether one or both competitors have it (access asymmetry), and whether the underlying game has three moves or many.

The simplest setup is a three-move game where only one player gets Dynamite that beats both Rock and Paper. The author derives the exact Nash equilibrium — the set of strategies where neither side can improve by changing alone — and computes the value the new move delivers.

But the paper's real interest is in the expanded games. In a "one-to-one" competition with $n$ moves, each move beats exactly one other, loses to one, and draws against the rest. There's also a "many-to-many" version like Rock-Paper-Scissors-Lizard-Spock, where each move beats two and loses to two. Lohn solves the one-to-one case in closed form)Skip and uses a fully worked example for the many-to-many case. The general result arrives as a tidy formula for the value of the new move,

$$v=\frac{2(m-k)}{km(m-k+2)},$$

where $m$ is the number of moves that remain strategically playable and $k$ captures how many opposing moves Dynamite fails to beat. This is the paper's engine: a single equation that explains why capability saturates, why value collapses, and why usage rates lie.

What They Found

The headline result from the three-move game: giving one player a Dynamite that beats two of three options raises their win probability from 50% to 55.6% — one extra win every nine rounds (Lohn, 2026). Not 90%, not even 70%. And crucially, the wins don't come from playing Dynamite. They come from the threat of it.

Here's the mechanism. The Dynamite-denied player, terrified of the high-capability move, over-adjusts: they throw Scissors far more often, because Scissors is the one move that beats Dynamite. But that's exactly the opening the Dynamite-holder exploits — not with Dynamite, but with Rock, which crushes Scissors. The Dynamite-holder's optimal play keeps their Dynamite usage unchanged from what a naive guess would suggest; they just throw more Rock. It's the basketball double-team in miniature: "make someone else beat us."

Even a world-beating Dynamite buys only a 5.6-point edge

Label	Value
Without Dynamite	50
With Dynamite (beats Rock & Paper)	55.6

The analogous dynamic plays out in sports where the star gets double-teamed — except the coach would be stunned at how little that star is actually worth. A dominant new capability, Lohn shows, is worth far less than its raw power suggests, because the opponent can just avoid the circumstances where it's strong.

That lesson gets sharper in larger competitions. In a one-to-one game with many moves, adding Dynamite produces a distinct category of obsolescence that Lohn calls "tactically useful, strategically unplayable." Some moves aren't dominated by Dynamite — they beat an opposing move that Dynamite also beats, and against Dynamite they draw or lose. Naively they look fine. But including them in your optimal strategy reduces your chance of winning. The math says to drop them anyway.

The number of moves that remain strategically useful grows only with the square root of the contest's size:

$$j=\sqrt{2k}.$$

So in a huge competition, Dynamite can render a substantial number of ostensibly useful options irrelevant. They're not weak; they're strategically redundant. The new move's value follows from fewer moves staying on the board.

A counter-Dynamite halves the champion's edge — value collapses fast

Label	Value
Value (7 moves, extensive Dynamite)	0.029
Value (opponent gets limited Dynamite)	0.022
Value falls quadratically in escaped moves	0

Two things blunt Dynamite's value in big contests. First, capability saturates. Dynamite's value rises only up to a point as it defeats more and more moves; beyond that point, those extra moves were never going to be played anyway, so beating them does nothing. Second — and this is brutal — value falls quadratically with the number of moves Dynamite fails to beat:

$$v\approx 2k^{-2}.$$

The more avenues of escape the opponent has, the faster Dynamite's worth evaporates/client.

Then there's the usage paradox. In the expanded games, the high-capability move is played rarely in the optimal strategy — often nearly the least-used move on the board, its usage falling as $\frac{2}{k^{3/2}}$ in large contests. The move that supposedly defines the game sits almost untouched. Its entire value is in how it bends the opponent's strategy toward vulnerability.

The paper's final example layers asymmetry on asymmetry: a seven-move game where one player has "extensive" Dynamite (beats three moves) and the other has "limited" Dynamite (beats two). The surprising result is that the weaker limited Dynamite can be worth more relative to its power than the extensive one. Providing the weaker player a limited Dynamite can make moves unplayable for both sides that the extensive Dynamite alone didn't touch — deploying distinct moves for each player, even though their Dynamites defeat overlapping sets of options. In the worked example, the extended player's value drops from 1/35 to 1/45 merely because the opponent gained a lesser counter-weapon.

Why This Changes Things

This is a paper that weaponizes a children's game to upend how we think about investing in, pricing, and fearing powerful AI. The implications land in four distinct places.

First, capability is not value. Lohn's central warning is that a new technology can be dramatically more capable without being dramatically more valuable. In the asymmetric three-move game, a Dynamite that beats two-thirds of the universe of opposing moves buys a 5.6 percentage point edge. "That small win percentage decreases further in competitions with more than three moves," he notes. Anyone who assumes raw power translates into competitive dominance is reading the wrong equation.

Second, usage rates lie. This is the paper's most pointed practical jab. "Organizations may need some other methods or simple models to understand, assess, and assign the value of AI," Lohn writes. An AI tool that reshapes an entire competitive landscape could be invoked almost never — because its value is strategic, not operational. This has direct pricing implications: an AI company that charges per use will starve even while delivering enormous value, because the customer's optimal strategy is to use it sparingly as a threat, and lean on cheaper, older tools to actually win.

Third, obsolescence is subtler than we think. Lohn maps out three distinct ways a move dies. A move can be weakly dominated — strictly outclassed by the new arrival. It can be strategically unplayable — not outclassed by Dynamite directly, but removed because including it weakens your equilibrium. And many moves survive despite looking redundant because the moves that would beat them were also deleted from the game. "That suggests that AI might make more tools or tasks obsolete than might be anticipated while allowing others to remain useful (or even increase in usefulness) despite appearing redundant." For a workforce worried about AI, the paper's message is double-edged: whole categories of work can vanish without being obviously bad at anything, while other roles survive and even grow in importance precisely because they were made redundant-looking.

Fourth, there's an asymmetry of response. Because dynamical value comes from forcing an opponent to over-adapt, the defender facing a powerful new move isn't helpless — they can blunt it by keeping their own option space broad. The quadratic collapse in equation 3 is essentially a strategic defense: the more moving parts you keep on the board, the faster a single super-weapon's value decays.

What's Next

Lohn is honest about what the model can and can't do. "Models are necessarily oversimplifications that can be 'intellectually useful, but only at the most elementary level,'" he concedes, quoting an earlier skeptic. Rock-Paper-Scissors captures the strategic structure of capability, but real competitions have moving targets — technologies improve, opponents learn, circumstances change mid-game.

illustrates how the threat of a single super-move reshapes an entire opponent strategy: blue bars (the Dynamite-holder's wins) exceed red bars (losses) against every move the denied player can throw, and the green bars show how the denied player must spread their play to survive.

and

show how even a weaker opponent's limited Dynamite reconfigures both players' equilibria, deleting moves neither side could have predicted.

The forward-looking significance is that this toy model gives decision makers a language for a failure mode they keep walking into. When a new AI system lands in a company, a military, or a market, the rational first question isn't "What can it do?" — it's "What strategic environment is it entering, and how will everyone else adjust to it?" A model that can only deliver 5.6 points of win probability from a world-beating weapon is a reminder that in any competition, your success is bounded by your adversary's freedom to avoid your strength.

What the paper opens up next is a research program: how do these equilibria change when the game has more richness — when moves can be combined, when capability can be grown mid-contest, when players don't have perfect information about each other's arsenals? Each generalization is a step from the schoolyard toward the boardroom.

The deepest takeaway is almost philosophical. Dynamite didn't win the game — it changed the rules of what winning looks like, then stood back and let Rock do the work. The most disruptive technology may be the one that never gets used, because its real product is a new geometry of every other option around it.