Pillar
In prediction markets the cleanest edge is structural, not predictive: exploit incoherent prices via geometry, size for error, price for execution.
The cleanest prediction-market edge is geometric, not predictive. Learn convex sets, polytopes, separating hyperplanes, conjugates, and why KL beats Euclidean, and the arbitrage machinery stops looking like a wall.
A bracket has 9.2 quintillion outcomes and you can describe the legal ones with about 200 rules. Read them as assert statements, hand the solver a direction, and it returns one valid outcome at a time.
Frank-Wolfe projects onto a shape with a quintillion corners by adding one corner per step, about a hundred total, with a gap number that certifies how much profit you might still be missing.
The clean arbitrage solver crashes near 99 cents because the log gradient blows up at the boundary. The barrier fix shrinks the shape off 0 and 1, converging slower but actually finishing.
A prediction-market price is the capital-weighted consensus, not a probability fact. Coherent prices can still be wrong, but before betting your view, pass the Brier Skill Score gate: beat the market on your own logged forecasts or stop.
Bayes turns news into an edge, but the whole trade hangs on the likelihood ratio you estimate. Update in log-odds, tie it to the maker's softmax, and gate every belief on three tests: better, earlier, calibrated. Then shrink.
Kelly gives the growth-optimal bet size, outputs "no trade" when the edge is too thin, and punishes overbetting with ruin while underbetting only costs growth. Bet small, often, and never the negative-f* trades.
Kelly grows your account; it doesn't keep you alive. Add a simulated drawdown budget, a CVaR tail cap that VaR hides, and a portfolio QP that prices the correlated blowup you didn't see.
A guaranteed arbitrage is fiction until both legs fill. Sequential fills move the book against you, you pay the VWAP not the quote, and below five cents slippage and gas eat the edge. Copying an arb just makes you exit liquidity.
A limit order that fills in seconds is bad news: fast fills are adversely selected. Take liquidity only for arbs and large edges, provide it for small ones, and set your spread equal to your uncertainty about the true probability.
Winning a prediction-market bet does not make it a good trade. Grade the decision before resolution against five invariants: named edge, bounded downside, real-liquidity execution, error-aware sizing, and robustness to competition.
Prediction-market losses cluster into six anti-patterns: belief without calibration, arbitrage without execution, Kelly without error bounds, correlation blindness, backtest-equals-live, and no named edge. Each is a skipped step you can catch before you lose.
Nine sources of edge in prediction markets, ranked cleanest to dirtiest: structural, execution, microstructure, temporal, informational, regime, portfolio, adversarial, operational. Forecasting is fifth and the most dangerous to size.
The cleanest edge is not always yours. Match the source to your resources: small accounts trade informational and regime, large accounts with infrastructure run structural and execution, and specialists play to their skill.
Two prediction markets can each sum to a fair dollar and still be jointly riggable. The reason is geometry: logic deletes impossible outcomes, and the prices can land outside what's left.
Prices that don't sum to a dollar are a guaranteed trade, not a rounding error. De Finetti proved it in 1937, and Polymarket's speed-first design guarantees the mispricings keep coming.
Every arbitrage question reduces to one: is the price inside the marginal polytope or outside it. Inside means no trade; outside, the wall separating you from the shape is your portfolio.
The best arbitrage trade is the closest fair price to the unfair one. One projection returns the trade, the profit, and the target prices at once, measured with KL divergence, not a straight ruler.
A structural arb that printed in October can be worthless by February with no change to the math. Regimes, the term structure of strategy, and crowding decide who actually gets paid, and usually it is not you.
Five state-election arbs feel diversified until a national shock sinks all five at once. Linear correlation hides that; tail dependence exposes it. Use a Student-t copula and size for the 25-to-1 day.
Wire your solver to your order router and one crash takes down both. Separate detection from execution behind a trade-proposal interface, stack three layers on three clocks, and let a fast scanner trigger the slow solver only where it pays.
Let five agents touch the wallet and they overspend, stack correlated risk, and breach the tail budget. A single allocator funds proposals by one optimization, and hard risk governors override it to keep you solvent.
A single P&L number hides four systems and a lot of luck. Grade execution with eta, attribute profit by edge source, split regret into detection, computation, execution, and sizing, and you finally know whether it was skill, structure, or luck.
Softmax is the Polymarket price formula. Work one trade to the cent, see why the maker's loss is capped, why the liquidity parameter b sets price impact, and why arbitrage distance is measured in KL, not Euclidean.
Polymarket could kill structural arbitrage but won't: coherent pricing means an NP-hard solve per trade. It chose speed, pays arbitrageurs roughly 20 percent of fees, and the edge regenerates on every trade forever.
Kelly's formula is identical in a prediction market and a prop challenge, but one optimizes long-run growth and the other a first-passage race to a target before an absorbing trapdoor. Opposite geometry, opposite sizes.
The CVaR-constrained portfolio QP that sizes Polymarket election arbs is the same machine that sizes a futures book. Different loss shapes, one tail metric, one fix for the correlation that spikes in a crisis.
Fill quality, the maker's profit equation, and the markout test move from a Polymarket CLOB to an FX or futures book unchanged. The payoff structure differs; adverse selection is adverse selection.
Fill quality is the midpoint minus your execution price over the spread, measured after the fill. Market orders average -0.72, fast limits -0.31, slow limits +0.43. Speed and fill quality move opposite.
A prediction market resolves to 0 or 1 on a fixed date, and that wall flips the strategy. More than 30 days out prices trend, so momentum pays. Inside 7 days prices overreact to noise, so reversion pays.
Prediction-market prices cluster near 0 and 1, and that is exactly where the log-scoring arbitrage math breaks. Worse, it can fail silently: no crash, just a wrong trade with a confident profit number.
Five "diversified" state-election arb positions share one national driver. Correlation 0.75 hides tail dependence 0.90, so a single shock turns a ±$0.10 book into a -$2.50 loss: a 25:1 ratio, not 5:1.