Random walk theory and Monte Carlo simulations work in prediction markets. Even when you don't know the underlying probability distribution of price changes. Most questions that determine profitability depend only on drift and variance. Not the specific distribution. Fair value. Risk of ruin. Sizing. Timing. Volatility. Decay of edge. All of these. Here's how to use random walks and Monte Carlo to win in Kalshi-style binary markets.
Critical distinction. You operate in uncertainty, not risk. Risk means you know the distribution. You know the probabilities. Uncertainty means you don't. In prediction markets, you never will. Not without material non-public insider information. That's illegal under CFTC regulations. Banned by Kalshi. Random walks and Monte Carlo let you navigate uncertainty. To win.
The core insight: you never know the distribution
You never know the true distribution of price moves on Kalshi. Price changes come from news. Liquidity. Order flow. They're not Gaussian. Not stationary. They jump. Discontinuously.
Legal constraint:
The only way to know the true probability distribution would be through material non-public insider information. This is illegal under CFTC regulations and explicitly banned by Kalshi. Trading on insider information violates securities laws and can result in criminal prosecution.
Therefore, you operate in uncertainty, not risk. You work with estimates, not known probabilities.
But that isn't a problem. You don't need the distribution to get real edge. Random walk tools work anyway because:
All you need is:
- Price follows a martingale (fair-game property)
- Drift comes only from mispricing or edge
- Variance determines risk of getting blown out before settlement
Price on Kalshi is literally a bounded random walk
With constraints:
Bounded state space
Price S ∈ [0, 1]. Contracts are bounded between $0 and $1. This creates natural constraints on the random walk.
Driftless under no-information
Without informational edge, price follows a martingale. The expected future price conditional on current information equals today's price.
Variance driven by liquidity
Volatility comes from order flow and liquidity, not from fundamental uncertainty. Low liquidity markets have higher variance.
Mean-reverting from order flow
Order flow imbalances create temporary mispricings. These tend to mean-revert as liquidity providers and traders rebalance positions. Producing predictable volatility patterns.
This structure alone lets you reason about expected PnL. Worst-case drawdown. Path to expiration. How mispricings evolve over time. Why mispricings self-correct. No distribution needed.
Warning: tail risk and fat tails
Price movements in prediction markets have fat tails. Extreme events happen more frequently than Gaussian models predict. A single news event can cause discontinuous jumps. A classification error can. A market structure failure can. Standard variance estimates miss these.
Variance estimates from historical data underestimate tail risk. Always size positions conservatively. The worst-case scenario is worse than your variance calculations suggest.
Optional stopping theorem: why timing doesn't give you edge
If price is a martingale, the expected future price conditional on current information is today's price. Therefore:
Timing the market produces no edge, unless:
- You have better information
- You know the market is structurally biased
- You know something about flow/liquidity dynamics
- You know the crowd is systematically wrong
This is why your edge in markets like RANKLIST is informational. Not structural. The random walk tells you this. Don't rely on timing. Your advantage is in belief vs. market-implied probability. Size positions appropriately. Don't try to trade around noise.
Variance scaling: how big your position can be
You don't need the distribution. You only need volatility. If price executes a random walk with daily standard deviation σ, then:
Where:
- σ=daily standard deviation (volatility)
- T=time to expiration
This is how you choose sizing. When betting on a slow-settling market:
Example: You buy a 65¢ contract. Based on an actual 80 to 85% belief. You need to survive price wandering. To maybe 60¢. Or 55¢. Before resolution.
You don't need the full distribution of price moves. √T scaling tells you how ugly the path can get. Kelly fraction scales inversely with this variance.
Drift shows up only when the market is wrong
If your belief p ≠ price S, then the contract has drift equal to:
Where:
- p=your true probability estimate
- S=current market price
You can treat the contract price as a random walk with small upward drift if you are long and your belief > price. The magnitude of the drift relative to volatility determines:
How fast price converges
Larger drift relative to variance means faster convergence toward your estimated probability.
Path risk
How likely you are to be proven right before getting stopped out by temporary adverse price movements.
This is exactly why positions with large informational drift (p − S) and small variance are good trades: the signal >> noise, allowing for larger position sizes.
Computing ruin probability without distribution
If you size 20% of net worth into a trade, random walk math gives you:
Where:
- drift=p − S (your edge)
- X=percentage drawdown threshold
- variance=empirically estimated from historical movements
This does not require you to know the noise distribution. Only variance. Variance can be estimated from historical Kalshi movements. But historical variance underestimates tail risk.
Run this on your trades. Estimate worst-case temporary drawdowns before expiration. Size positions appropriately.
But recognize this. These are estimates under uncertainty. Not precise calculations. Historical variance doesn't capture regime changes. Structural shifts. Tail events that haven't occurred yet. Always add a margin of safety. Beyond what variance calculations suggest.
Order flow and mean reversion
You don't need the distribution. The structural mechanics matter:
Order flow imbalances
When one side of the order book gets heavy, price moves. These imbalances tend to correct. Price mean-reverts.
Predictable volatility patterns
Order flow creates volatility patterns. Short-term reversals. Trading opportunities.
Better entry timing
Understanding mean reversion helps you time entries. Buy on temporary overshoots.
More aggressive sizing
When you see flow-driven overshoots, size more aggressively. Mean reversion helps.
None of this requires distribution knowledge. The structure forces the walk to behave in bounded, mean-reverting ways.
The biggest use: understanding path dependency
You often ask things like:
How much could this wander against me?
Is there a risk of getting blown out?
Could a classification failure cause volatility spikes late?
Random walk math answers that with just:
- Drift (your edge: p − S)
- Variance (volatility)
- Time to expiry
- Bounds (0 to 1)
Distribution-free.
That's why even a wildly mispriced Kalshi market tends to "drift" toward the correct probability over time, but still takes inefficient, noisy paths that matter for bankroll variance. This is exactly what you're optimizing when you talk Kelly sizing.
Critical caveat: path dependency and tail events
Drift suggests convergence. But the path matters enormously. A single tail event can wipe out your position. A classification error. A market structure failure. Unexpected news. Any of these can cause a discontinuous jump. Before convergence occurs.
The random walk framework helps you understand expected paths. But it doesn't protect you from tail events. You must size positions to survive variance. And the possibility of extreme jumps. Historical data doesn't capture these.
Master path risk and position sizing
Understanding random walks and Monte Carlo simulations helps you size positions, estimate path risk, and avoid getting stopped out before your edge materializes. Get early access to tools that use Monte Carlo methods to calculate optimal position sizes and manage risk across your prediction market portfolio.
Summary: what random walks give you
You don't know the distribution of price moves on Kalshi. You never will. Not without illegal insider information. Random walks still give you:
Path risk estimates
"How much the price can wander before expiration."
Key insights:
- Expected maximum temporary drawdown ≈ O(σ√T)
- Helps you size positions to survive adverse paths
- No distribution needed. Only variance. But recognize tail risk.
Sizing logic (Kelly / fractional Kelly)
"Using variance scaling to determine optimal position size."
Key insights:
- Kelly fraction scales inversely with variance
- Larger variance → smaller position size
- Works without knowing exact distribution, but add margin of safety for tail risk
When informational edge dominates noise
"If drift >> σ/√T, you can size much bigger."
Key insights:
- Large drift relative to variance = high signal-to-noise
- Allows for more aggressive position sizing
- Small variance markets are better for large positions
Understanding why timing doesn't give additional EV
"Optional stopping theorem: martingales have no timing edge."
Key insights:
- Expected future price = current price (conditional on information)
- Timing only helps if you have better information
- Focus on sizing, not timing
Understanding volatility bursts around news
"Bounded random walk with jumps explains price spikes."
Key insights:
- News creates discontinuous jumps in price
- Bounded between 0 and 1 creates natural constraints
- Mean reversion after news-driven moves
Mispricing decay over time
"Even without a distribution, drift forces convergence."
Key insights:
- Mispricings drift toward correct probability
- Rate of convergence depends on drift/variance ratio
- Structure forces eventual correction
Monte Carlo simulations: winning through simulation
Monte Carlo methods let you simulate thousands of possible price paths. Without knowing the true distribution. You run random walk simulations. Use your estimated drift and variance. Understand what outcomes are likely. Position yourself to win.
How Monte Carlo works
Simulate price paths by sampling from your estimated drift and variance. Run 10,000+ simulations to see:
- Distribution of final prices at expiration
- Maximum drawdowns along each path
- Probability of hitting stop-loss levels
- Expected PnL across scenarios
Why Monte Carlo wins
Unlike analytical formulas, Monte Carlo captures:
- Path dependency. The order of events matters.
- Tail events. Extreme scenarios that formulas miss.
- Complex interactions between multiple positions
- Non-linear payoffs and boundary conditions
Monte Carlo example: sizing a position
You believe a contract trading at $0.65 should be $0.80. Run 10,000 Monte Carlo simulations:
- Each simulation: price follows random walk with drift = 0.15, variance from historical data
- Track maximum drawdown in each simulation before expiration
- Find position size where 95% of simulations avoid ruin
- Compare expected PnL vs. risk of ruin across different sizes
- Choose size that maximizes risk-adjusted returns
This gives you optimal sizing without knowing the true distribution. You're simulating uncertainty. To win.
Practical applications: what you can compute to win
Using random walks and Monte Carlo simulations, you can compute:
- Expected maximum temporary drawdown for your positions (via Monte Carlo)
- Optimal Kelly sizing for your bankroll given variance (simulate outcomes)
- Risk-of-ruin curves based on position size and drift (run 10,000+ simulations)
- Time-to-convergence estimates for mispricings (simulate price paths)
- Worst-case late-year volatility from classification errors (tail scenarios)
- Impact of 'market not reading the rules' drift (scenario analysis)
- Portfolio-level risk across correlated positions (multi-asset Monte Carlo)
All of these use random walk theory and Monte Carlo methods. You don't need the true distribution. Just drift and variance estimates. Run simulations. Understand what outcomes are likely. Position yourself to win.
Conclusion
Random walk theory and Monte Carlo simulations work in prediction markets. Even when you don't know the underlying probability distribution of price changes. You never will. Not without illegal insider information. The key insight. Most questions that determine profitability depend only on drift and variance. Not the specific distribution. Fair value. Risk of ruin. Sizing. Timing. Volatility. Decay of edge. All of these.
Price on Kalshi is a bounded random walk. Constraints: S ∈ [0, 1]. Driftless under no-information. Variance driven by liquidity. Mean-reverting when order flow imbalances correct. This structure alone lets you reason about expected PnL. Worst-case drawdown. Path to expiration. How mispricings evolve over time. All under uncertainty. Not known risk.
Use random walk theory and Monte Carlo simulations. Understand path dependency. Size positions based on variance scaling. Recognize when informational edge dominates noise. Avoid the trap of thinking timing gives you additional edge. The optional stopping theorem tells you this. Timing produces no edge. Not unless you have better information. Focus on sizing. Not timing. Run Monte Carlo simulations. See what outcomes are likely. Position yourself to win.
Remember this. You operate in uncertainty. Not risk. Historical variance underestimates tail risk. Fat tails mean extreme events happen more frequently than models predict. Always add a margin of safety. Beyond what variance calculations suggest. The worst-case scenario is worse than your estimates. Random walks and Monte Carlo simulations are tools. For navigating uncertainty. To win. They help you understand likely outcomes. Position yourself accordingly. But they're not guarantees.
Apply random walk theory to your trading
Understanding how random walks and Monte Carlo simulations apply to prediction markets helps you size positions correctly, estimate path risk, and avoid getting stopped out before your edge materializes. Join prediction market traders who are using Monte Carlo methods and sophisticated risk management tools to maximize long-term growth and win consistently.