The algorithm, in full.

The science of it

Game theory is the mathematical study of strategic interaction — how rational (and boundedly rational) actors choose actions when the outcome for each depends on what the others do. It's not a metaphor. It's a body of formal results that has been refined for eighty years and used across economics, political science, evolutionary biology, cryptography, and military operations research.

GAMBIT doesn't invent the math. It packages a specific reasoning pipeline — identify the players → define their strategies → assess the payoffs → compute the equilibrium → update from live signals — into an engine that runs on any question you can frame as a yes/no outcome with an actor structure.

The foundational results we lean on

Nash equilibrium (Nash, 1950–1951). In any finite game where each player has a set of strategies, there exists at least one strategy profile such that no player can improve their expected payoff by unilaterally deviating. This is our "no free moves" anchor: if a player could get a better outcome by acting differently, and they know it, they will. Nash won the Nobel in 1994 for this work; the result is now taught in every serious game theory course. GAMBIT does not compute strict Nash equilibria for every scenario (real geopolitics has incomplete information, bounded rationality, and messy payoffs) — but the concept anchors our weighted pressure calculation.

Mixed strategies + minimax (von Neumann, 1928). John von Neumann proved that in any two-player zero-sum game with finite strategies, there is a mixed-strategy value that both players will converge to under rational play. This is why prediction markets don't clear at 100/0 for contested questions — well-informed actors on both sides bring the price to the equilibrium probability, and that price is the market's best estimate.

Bayesian updating (Bayes, 1763; Cox, 1946). The mathematically correct way to update a probability when new evidence arrives is Bayes' theorem: P(H|E) = P(E|H) · P(H) / P(E). GAMBIT's signals are Bayesian priors made explicit. Each signal has a multiplier that represents the likelihood ratio of that observation, given the target outcome vs. its complement. When multiple independent signals accumulate, they compound multiplicatively — which is why a market with three "up" signals moves more than one with a single "up" signal.

The Schelling point (Schelling, 1960). In "The Strategy of Conflict," Thomas Schelling argued that in games of coordination or conflict, players converge on focal points that are salient for reasons beyond pure logic — history, ritual, geographic features, round numbers. This is why market thresholds like "S&P 500 down 20%" or "Bitcoin at $200k" behave like magnets. GAMBIT respects these round-number thresholds in its base rates.

Repeated games + the folk theorem (Aumann, 1959; Friedman, 1971). When games are played repeatedly, cooperation becomes sustainable under conditions that a one-shot game would rule out. Most geopolitical scenarios are repeated games — Russia and the US, China and Taiwan, the Fed and markets — so the equilibrium looks different from a single-round analysis. Our cohesion parameter partly reflects how well a player can sustain the credible commitments that repeated interaction requires.

Prospect theory (Kahneman & Tversky, 1979). Real actors don't maximize expected utility — they're loss-averse, they weight probabilities non-linearly, and they treat gains and losses asymmetrically. This is why regime-survival threats (potential losses) drive so much of the pressure in geopolitical scenarios: the payoff matrix is not symmetric around the status quo.

Time-horizon compounding. If an event has probability p per year and years are approximately independent trials, then the probability of the event occurring at least once in t years is 1 − (1 − p)t. This is basic probability theory (a Bernoulli process), and it is why 10-year probabilities are meaningfully higher than 1-year probabilities even when nothing else changes. We use this formula directly.

What we are not claiming

• We do not claim to compute exact Nash equilibria. Real payoffs are unknowable to that precision.
• We do not claim these are the market-implied probabilities you'd find on Polymarket or Kalshi. Those are equilibrium prices — extremely useful, but reflecting trader positions, liquidity, and market frictions, not just the underlying strategic reality.
• We do not claim these probabilities are calibrated on a large historical sample. They are algorithmically derived from stated inputs. If our inputs (players, pressures, signals) are wrong, the outputs are wrong.
• We do not claim independence of events. In reality, tails are correlated (pandemics + wars + financial crises tend to co-occur). Our compounding formula is an upper bound on multi-year probabilities under strict independence.

Recommended reading

If you want to go deeper on the math + reasoning behind GAMBIT:

• Fudenberg, D. & Tirole, J. — Game Theory (MIT Press, 1991). The standard graduate textbook.
• Schelling, T. — The Strategy of Conflict (1960). Still the best book on strategic reasoning in conflict.
• Osborne, M. — An Introduction to Game Theory (Oxford, 2004). Cleaner undergraduate treatment.
• Tetlock, P. — Superforecasting (2015). Empirical work on what makes predictions accurate.
• Silver, N. — The Signal and the Noise (2012). Bayesian thinking applied to prediction.
• Aumann, R. — Nobel lecture, 2005. Repeated games + the game-theoretic view of international relations.
• Tetlock & Gardner — Good Judgment Project results. The empirical baseline for what humans can achieve in probabilistic forecasting.

The five-step method

Every GAMBIT market answers one question: given the current strategic landscape, what's the probability of this outcome within a given time horizon? We answer it in five steps.

1. Identify the players. The 3–5 real actors whose decisions determine the outcome. States, factions, institutions, market participants, stochastic forces.
2. Define grand strategies. Each player's long-run objective and revealed preference — what they actually want, not what they say.
3. Establish action sets. The realistic moves available to each side and the cost/benefit of each.
4. Evaluate constraints + payoffs. How internal cohesion, resource limits, and external pressures alter each player's cost of failure or success.
5. Compute the equilibrium. The Nash-adjacent probability of the target outcome, weighted by player power and updated with live signals.

The probability engine

The core formula is short. Given a scenario with players i, signals j, and time horizon t years:

— Weighted pressure —
P̄ = Σᵢ ( pressureᵢ × powerᵢ ) ÷ Σᵢ powerᵢ

— Annual probability —
pannual = clamp(  b × 2P̄ × ∏j mⱼ ,  0.002,  0.85)

— Time-horizon compounding —
P(event | t) = 1 − ( 1 − pannual ) t

— Confidence band —
CI( t ) = ± ( 0.06 + 0.03 √t )

where b = historical base rate · mⱼ = signal multiplier · P̄ ∈ [−1, +1]

Step 1 — Base rate

The historical annual rate for this class of event. For "US recession," it's roughly 14–16% based on 70+ years of NBER data. For "US ground invasion of Iran," it's about 2%. Base rates are the anchor — they prevent our reasoning from wandering too far from what history shows.

Step 2 — Player pressure

Each player has a pressure score from -1 (strongly opposes the outcome) to +1 (strongly pushes toward it). We weight by power (their ability to affect the outcome) and sum. The result is a single weightedPressure number that becomes an exponent: pressure of +1 roughly doubles the base rate; pressure of -1 roughly halves it.

Step 3 — Signals

Each market has 3–5 live signals — current-state observations that shift the base rate up or down. Each signal has a multiplier like 1.3× (raises probability) or 0.85× (lowers it). Signals are Bayesian priors made explicit.

Step 4 — Annual probability

Multiply the base rate by the pressure multiplier and signal multiplier. Clamp between 0.2% and 85% — we don't output certainties.

Step 5 — Time-horizon compounding

If the annual probability is p_annual, the probability of the event occurring at least once in t years is 1 - (1 - p_annual)t. This is a fundamental identity — it's why 10-year horizons show much higher probabilities than 1-year, even when nothing else changes.

Step 6 — Confidence bands

Our 95% band widens with the square root of the time horizon. A 6-month estimate is tight; a 10-year estimate is loose. This isn't just modeling humility — it reflects the real property that longer horizons compound structural uncertainty.

What we softened — and why

Real game theory papers can produce point estimates that feel more confident than they should. GAMBIT deliberately softens in three places:

1. No point estimates. Only bands.

Every output includes a lower and upper bound. If we say 28% [17% – 39%], that's a claim about our reasoning, not the future. The wider the band, the less confident the model.

2. Nash-adjacent, not Nash-strict.

We don't require players to be fully rational or have complete information. The cohesion parameter captures how well a player can execute their optimal strategy. A fragmented actor with high pressure and low cohesion contributes less than the pressure alone would suggest.

3. Signals are humble.

No single signal moves the probability by more than about 40%. This prevents any one "hot take" from dominating. Signals need to accumulate to move the answer materially.

Where the model breaks

Honest failure modes:

• Black swans. By definition, GAMBIT can't model events with no historical prior. When something genuinely new happens, our base rates lag.
• Regime changes. If the underlying game changes — new institutions, new technologies, new coalitions — historical rates from the old regime overstate stability.
• Correlated tails. Multiple simultaneous shocks (pandemic + war + financial crisis) violate our independence assumption. Reality has more correlated tails than any tractable model.
• Player misidentification. If we've defined the wrong actors, the whole model is off. Every market's player list is a modeling choice, and we show it explicitly so you can argue with it.

Data sources

Every market cites its primary sources at the bottom of the analysis modal. Categories:

Every market is hand-modeled — no scraping, no automated fitting. That's the point. GAMBIT is a reasoning tool. The algorithm makes reasoning explicit, replicable, and criticizable.