You now have the Module 04 toolkit: axioms and Bayes, odds and EV, variance, Kelly sizing, Brier and log scoring, and joint thinking. Fallacies are why educated traders still torch bankrolls—they violate the math while feeling rational. This closing chapter ties Module 04 to earlier modules: markets aggregate beliefs, mechanisms punish some lies, and your brain still ships bugs.
Why fallacies matter
Prices can be efficient while you are wrong—or prices can be wrong because many traders share the same fallacy, amplified by information cascades. Naming the bug before you click is as important as the formula.
| Fallacy | Market symptom |
|---|---|
| Gambler’s fallacy | Fade streaks without model |
| Base rate neglect | Overreact to headline evidence |
| Conjunction error | Overpay parlay-like bundles |
| Hot hand | Chase momentum after noise |
| Hindsight bias | Fake great Brier scores |
Gambler’s fallacy
Belief: after several NO resolutions, YES is “due.” Truth: with independent trials and fixed p, past outcomes do not change future probability. A fair coin stays 50% each flip. The same Fed-cut contract drifting 40¢→25¢ without new data is not “due” to bounce unless your model rose for structural reasons—not because the tape lost five weeks.
Cascades look like streaks; distinguish social proof from physical due-ness.
Base rate neglect
Vivid evidence swamps how rare the event is. Bayes says posterior on H given evidence E is proportional to P(E | H) × P(H). If prior P(H) is tiny, strong P(E | H) may still leave posterior small.
Only 2% of similar bills pass committee historically; a whip count might move you 2% → 12%, not 2% → 70%. A market at 45¢ may be fallacy-driven or trading different resolution—read the rulebook. State base rate before evidence, update with likelihoods, compare posterior to c.
Conjunction fallacy
“A and B” feels more likely than “A alone” when the story is coherent. Math: P(A and B) ≤ min(P(A), P(B)) always. “Sweep IA, OH, and PA” is a conjunction bet—size as joint exposure, not three max-Kelly legs. Structural arbitrage profits when conjunction packages exceed tree logic.
Prosecutor’s fallacy
“If innocent, only 1% chance of this DNA match” is not “99% guilty.” Markets mirror: “if candidate wins, polls look like X” is P(polls | win), not P(win | polls). Confusing them inflates p, wrecks Brier, and oversizes Kelly.
Hot hand and momentum
Recent wins feel like a skill streak; rising YES feels like mandate to buy. Momentum is rational when informed flow follows real news; it is fallacy on thin AMM wiggle from five hundred dollars. Mid moved, not necessarily information.
Survivorship and hindsight
Leaderboards show survivors. After resolution, memory edits f toward 0 or 1—destroying calibration and inviting over-Kelly. Timestamped journals beat “I knew it.”
Cascade and base rate together
“Dark horse wins nomination” at 8¢. Cascade: everyone buys because tape is up. Base rate: historical long shots ≈ 3%. Your model after polls: 6%. At 8¢ you have no buy edge on YES (8% price > 6% belief); fading toward 5¢ needs limit discipline. Avoid “due” after a dip. The crowd may still be wrong—but your edge needs math, not a counter-story.
Fallacy firewall
Name the fallacy before submit. Write base rate and likelihood update. Check joint cluster for conjunction sizing. Compare p to c for EV; if the trade is story-only, pass. Halve Kelly on single-anecdote evidence. Score locked f with Brier and log. After a loss, review process, not outcome.
Before quoting “markets say X” in media, ask which contract, what liquidity, and whether the tree is coherent—not whether your fallacy filter is off.
Fallacy meets EV and Kelly
Positive EV built on a fallacious p is still gambling with extra steps. Kelly sizes a wrong p aggressively—the fastest path from “I read the article” to “I blew the bankroll.” Brier and log scores are the post-game audit that punishes the same bugs. Process: name fallacy → Bayes with base rate → joint cluster check → EV at ask → fractional Kelly → log f.
Availability and narrative
The most vivid story wins attention, not probability. A viral clip moves Polymarket before Kalshi; that is not automatically edge on the slower venue—it may be availability bias in your likelihood. Ask whether the clip changed P(E | H) or merely P(E) because everyone saw the same file.
Anchoring on the mid
Traders anchor on the first number they see—52¢ on TV—and treat moves as “cheap” or “rich” without a model. The market mid is a social anchor, not a prior. Bayes starts from a base rate or a pre-registered f, not from whatever flash on the chart.
Sunk cost and the fallacy family
Doubling size because “I already have so much in” is not a probability fallacy but behaves like one—you treat past loss as information about future p. The contract does not know your book. Re-run Bayes and EV from current beliefs and current ask only.
Module arc in one paragraph
Module 01 gave you prices as beliefs; Module 02 gave you friction; Module 03 gave you coherence enforced by others’ capital. Module 04 gave you the private toolkit—axioms, updates, EV, variance, Kelly, scores, joints, and cognitive guardrails. Module 05 puts the math inside explicit contract trees and product types.
Representative heuristic
“Looks like 2016” is not a likelihood. Similar vibes inflate p without data. Replace analogy with counted frequencies: how often did this pattern appear, and what happened next under this rule set? The base-rate chapter in Bayes is the antidote; fallacies are the disease.
Teaching others without tables
When you explain a market to a friend, lead with P and a sentence of resolution text, not a wall of cents. Fallacies spread in social settings faster than arbitrage corrects them—another reason thin markets can stay wrong until capital arrives.
Completing Module 04
You can translate prices to beliefs and EV, respect variance and size with fractional Kelly, audit beliefs with Brier and log scores, map portfolio risk with joints, and guard cognition against these traps.
What comes next
Next: Module 05 — Event Contracts & Product Structures begins with binary YES/NO mechanics in full product detail.