The Kelly Criterion for Prediction Markets: A Complete Guide to Optimal Bet Sizing

TL;DR: The Kelly Criterion is a 70-year-old formula that tells you exactly how much of your bankroll to bet when you have an edge. For prediction markets, it simplifies to: bet fraction = (your probability − market price) ÷ (1 − market price). Full Kelly maximizes long-run growth but creates brutal drawdowns. Use half Kelly or quarter Kelly in practice. Every serious prediction market agent implements some variant of this formula in its position sizing layer. If you learn one piece of math for trading prediction markets, make it this one.

Why Most Prediction Market Traders Go Broke

In 2019, researchers Victor Haghani and Richard Dewey ran an experiment. They gave 61 participants — finance professionals, quantitative traders, economists — a bankroll of $25 and let them bet on a biased coin. The coin landed on the profitable side 60% of the time. A clear, known, verified edge.

The optimal strategy? Bet 20% of your bankroll on every flip.

The results were brutal. 28% of participants went bust. The average payout was just $91 out of a theoretical optimum of over $10,000. Only 21% hit the maximum. Eighteen people bet their entire bankroll on a single flip.

These were finance professionals. They had a known edge. And most of them destroyed their bankrolls anyway.

The lesson: having an edge is not enough. The size of your bet determines whether your edge compounds into wealth or blows up your account. This is the problem the Kelly Criterion solves, and it is the single most important concept in bankroll management for prediction markets, sportsbooks, and any repeated betting scenario.

The Kelly Criterion: Origin Story

In 1956, John Larry Kelly Jr. — a physicist at Bell Labs — published a paper called “A New Interpretation of Information Rate” in the Bell System Technical Journal. Kelly framed the problem as a gambler receiving tips over a noisy telephone wire from a confederate at a horse track. The question: given imperfect information about outcomes, what fraction of your bankroll should you wager to maximize the long-term growth rate of your wealth?

The answer became the Kelly Criterion. It is mathematically equivalent to maximizing the expected logarithm of wealth — the strategy that compounds capital fastest over infinite repeated bets.

The formula’s practical use was demonstrated almost immediately. Edward O. Thorp, a mathematics professor, used Kelly-based strategies to beat blackjack and later applied the same framework to the stock market through his hedge fund Princeton Newport Partners. In the 2000s, Kelly-style analysis became mainstream in investment theory. Warren Buffett and Bill Gross have both been associated with Kelly-influenced capital allocation methods.

Now, in 2026, the Kelly Criterion sits at the core of how autonomous prediction market agents manage their bankrolls. IOSG Ventures identified it as the foundational position management framework for prediction market agents in their March 2026 research report. Every agent architecture that handles real money — from Olas Polystrat to open-source Poly-Trader bots — implements some version of Kelly in its strategy layer.

The Formula: Two Versions You Need

Version 1: The Classic Kelly Formula (Sportsbooks & General Betting)

For a bet where you either win or lose your entire stake:

f* = (bp - q) / b

Where:

• f* = optimal fraction of bankroll to bet
• b = net odds received on the bet (decimal odds minus 1; e.g., a bet paying 3-to-1 means b = 3)
• p = probability of winning (your estimate)
• q = probability of losing (q = 1 − p)

Worked example — sportsbook bet:

You find an NFL moneyline on BetOnline at +200 (decimal 3.0). Your model gives the underdog a 40% chance of winning.

• b = 2 (the net payout: you risk $1, you get $2 profit if you win)
• p = 0.40
• q = 0.60

f* = (2 × 0.40 − 0.60) / 2 = (0.80 − 0.60) / 2 = 0.10

Kelly says bet 10% of your bankroll.

If your probability estimate were 30% instead of 40%, Kelly would give:

f* = (2 × 0.30 − 0.70) / 2 = (0.60 − 0.70) / 2 = −0.05

Negative result. Kelly says don’t bet. Expected value is negative. Walk away.

Version 2: The Prediction Market Kelly Formula (Polymarket, Kalshi)

Prediction markets use binary contracts that pay $1.00 if the outcome occurs and $0.00 if it doesn’t. The contract price is the market-implied probability. This simplifies the Kelly formula considerably:

f* = (p − market_price) / (1 − market_price)

Where:

• f* = optimal fraction of bankroll to bet on YES
• p = your estimated true probability
• market_price = current price of the YES contract

This works because in a prediction market, the net odds b = (1 − market_price) / market_price, and substituting into the classic formula yields this simplified version.

Worked example — Polymarket:

Market: “Fed cuts rates in March?” priced at $0.30 (30% implied probability). Your macro model estimates 40% true probability.

f* = (0.40 − 0.30) / (1 − 0.30) = 0.10 / 0.70 = 0.143

Kelly recommends putting 14.3% of your bankroll into YES shares at $0.30.

Worked example — Kalshi:

Market: “BTC above $86k by end of month?” priced at $0.77 (77% implied). Your model says 85%.

f* = (0.85 − 0.77) / (1 − 0.77) = 0.08 / 0.23 = 0.348

Kelly recommends 34.8% of your bankroll. That sounds aggressive — and it is. Here is where things get dangerous.

Why Full Kelly Will Wreck You: The Case for Fractional Kelly

Full Kelly maximizes the theoretical long-run growth rate. But “long-run” means infinite repetitions, and the path to that theoretical optimum is vicious.

The cold math of full Kelly:

• There is a 33% probability of halving your bankroll before doubling it
• There is a 1/n probability of seeing your bankroll reduced to 1/n of its peak at some point
• Drawdowns of 50-80% are not anomalies — they are expected features of the distribution

Full Kelly also assumes something that is never true in practice: that your probability estimates are perfectly accurate.

In the Polymarket BTC example above, Kelly recommended 34.8% of bankroll based on an 85% probability estimate. What if the true probability is actually 78% — just a 7-percentage-point miss?

f* = (0.78 − 0.77) / (1 − 0.77) = 0.01 / 0.23 = 0.043

The recommended bet drops from 34.8% to 4.3% of bankroll. A small estimation error produces an 8x swing in position size. At higher contract prices (the $0.75+ zone), the margin between a good bet and a terrible bet is razor-thin.

This is why professionals use fractional Kelly:

Half Kelly retains roughly 75% of the long-run growth rate while dramatically reducing the probability and severity of drawdowns. Quarter Kelly is even more conservative — appropriate when your probability estimates are uncertain or you are trading in thin markets where slippage affects execution.

The practical recommendation for most prediction market traders and agents: start with quarter Kelly, graduate to half Kelly as you validate your edge through tracked results over 100+ bets.

Kelly on Prediction Markets: The Price Zone Problem

One thing unique to prediction markets that traditional Kelly discussions miss: the contract price itself determines your risk-reward profile in a way that creates distinct danger zones.

Price zone asymmetry:

In the $0.75+ zone, you are risking $0.75+ to win $0.25 or less. The market price needs to be significantly wrong for a positive Kelly fraction, and even slight probability overestimation flips the sign. This is where prediction market traders most commonly blow up — buying “safe” high-probability contracts with massive position sizes.

The rule: reduce your Kelly fraction as contract prices increase. Half Kelly below $0.50. Quarter Kelly above $0.70. No directional bets above $0.85 unless you have genuinely asymmetric information.

How AI Agents Implement Kelly

Autonomous prediction market agents don’t just use Kelly as a calculator — it sits at the core of their decision architecture. The typical agent stack processes bets through a pipeline:

1. Intelligence Layer → Probability Estimate

The agent’s LLM or statistical model analyzes available data — news feeds, on-chain data, historical patterns, sentiment — and produces a probability estimate p for a given market outcome. This is the input that makes or breaks the Kelly calculation.

Different agents approach this differently:

• LLM-based agents (like those using Claude or GPT-4) generate probability estimates through reasoning over news and context
• Ensemble agents (like Polyseer) combine multiple models — Bayesian updating, sentiment analysis, LLM reasoning — and use the weighted consensus as p
• Statistical agents use historical base rates, regression models, and market microstructure data

2. Strategy Layer → Kelly Position Sizing

Given the probability estimate and current market price, the agent calculates the Kelly fraction. In production, this looks something like:

def kelly_fraction(estimated_prob: float, market_price: float, kelly_mult: float = 0.25) -> float:
    """
    Calculate fractional Kelly bet size for a prediction market.

    Args:
        estimated_prob: Agent's estimated true probability (0-1)
        market_price: Current contract price on the market (0-1)
        kelly_mult: Kelly multiplier (0.25 = quarter Kelly, 0.5 = half Kelly)

    Returns:
        Fraction of bankroll to allocate (0 if no edge)
    """
    if estimated_prob <= market_price:
        return 0.0  # No edge — don't bet

    full_kelly = (estimated_prob - market_price) / (1 - market_price)

    # Apply fractional Kelly
    fraction = full_kelly * kelly_mult

    # Hard cap: never risk more than 5% on a single position
    return min(fraction, 0.05)

Note the hard cap at 5%. This is a guardrail that overrides Kelly’s recommendation when the formula suggests aggressive positions. The Poly-Trader open-source bot defaults to a 5% maximum per bet regardless of Kelly output. Olas Polystrat uses hardcoded spending limits enforced at the wallet level via Safe smart contract accounts.

3. Wallet Layer → Execution with Guardrails

The wallet layer (Layer 2 in the AgentBets stack) enforces spending controls that act as a backstop against Kelly miscalculations:

• Session caps: Maximum total spend per trading session (e.g., $500/session via Coinbase Agentic Wallets)
• Per-trade limits: No single bet above a fixed dollar amount
• Drawdown kill switch: Agent pauses automatically if portfolio drops below a threshold
• Allowlisted contracts: Agent can only interact with approved prediction market contracts

These wallet-level controls are critical because the Kelly formula is only as good as the probability estimate feeding it. A hallucinating LLM that overestimates its edge by 10 percentage points will generate dangerously oversized Kelly fractions. The wallet guardrails prevent a bad intelligence-layer output from draining the bankroll.

For a deep dive on wallet security for prediction market agents, see the Agent Wallet Security Guide.

Multi-Market Kelly: Portfolio-Level Sizing

Real prediction market agents don’t bet on one market at a time. They scan hundreds of markets across Polymarket, Kalshi, and sportsbooks simultaneously. This introduces the multi-market Kelly problem: how do you size positions across multiple independent (or correlated) bets?

Independent markets — the simple case:

If markets are genuinely independent (e.g., “Fed cuts rates in March” and “Lakers win NBA championship”), you can calculate Kelly fractions separately for each. But you need to ensure that your total capital allocation doesn’t exceed 100% of your bankroll. The standard approach:

1. Calculate Kelly fractions for each market with an identified edge
2. Sum all fractions
3. If the sum exceeds your risk budget (e.g., 40% total exposure), scale all positions down proportionally

Correlated markets — the hard case:

Many prediction markets are correlated. “Democrats win the Senate” and “Democrats win the White House” share underlying factors. Betting full Kelly on both independently double-counts your risk. Agents handling correlated markets must model the correlation structure and reduce position sizes accordingly. This is where multi-market Kelly becomes a genuine portfolio optimization problem and where quantitative agents have a structural advantage over manual traders.

Capital lockup — the prediction market twist:

Unlike sportsbooks where your bet settles in hours, prediction market contracts can lock capital for weeks or months. A $1,000 position in a market settling in June 2026 is capital that cannot be deployed elsewhere. The effective Kelly fraction should be adjusted downward for long-dated markets to account for the opportunity cost of locked capital.

Kelly vs. Alternatives: What Else Exists

Kelly is the theoretically optimal bet sizing strategy for maximizing long-run compound growth. But “theoretically optimal” comes with asterisks. Here is how it compares to alternatives that agents and traders actually use.

Flat betting (fixed unit size):

Bet the same dollar amount on every trade regardless of edge. Simple, robust to estimation errors, but leaves money on the table. A 15% edge and a 2% edge receive identical sizing. Appropriate for traders who cannot reliably estimate probabilities but can identify positive-EV situations.

Confidence-tiered sizing:

IOSG Ventures’ March 2026 research on prediction market agents recommends this approach over pure Kelly for most agent implementations. Instead of a continuous Kelly fraction, the agent categorizes opportunities into 3-5 confidence tiers, each with a fixed position size and an absolute cap. Low confidence gets 1% of bankroll. Medium gets 2%. High gets 3-4%. Maximum position never exceeds 5% regardless of how large Kelly says the edge is.

The advantage: this approach doesn’t require precise probability estimates. It only requires ranking opportunities by relative confidence — something LLMs and ensemble models do more reliably than producing exact probability numbers.

Inverted risk approach:

Start with the maximum amount you’re willing to lose on a single trade, then work backward to determine position size. If your maximum acceptable loss is $100 and the contract price is $0.30, your maximum position is $100 / $0.30 = 333 shares. This approach is entirely risk-defined and ignores edge estimation altogether.

The 2026 Landscape: Kelly in the Age of Prediction Market Agents

Prediction markets processed over $44 billion in trading volume in 2025 — a 400%+ increase from 2024. By February 2026, Kalshi’s weekly volume surpassed Polymarket’s, approaching 50% market share. The infrastructure for autonomous agents to trade these markets is maturing rapidly.

Olas Polystrat launched in February 2026 as the first consumer-grade autonomous trading agent for Polymarket. Users define strategies in natural language, and the agent identifies probability deviations in markets settling within four days. Risk management uses self-custodied Safe accounts with hardcoded position limits — a practical implementation of the constrained Kelly philosophy.

Poly-Trader and similar open-source bots implement Kelly directly: an AI module estimates probabilities, a decision module calculates Kelly fractions, and an execution module places trades via the Polymarket Agents SDK. The default settings use quarter Kelly (MAX_BET_PERCENTAGE=0.05, MIN_EDGE_PERCENTAGE=0.15) — conservative guardrails that prevent overbetting on thin edges.

The convergence of prediction markets and sportsbooks creates new Kelly optimization challenges. DraftKings Predictions, Kalshi sports contracts, and traditional sportsbooks now offer overlapping markets on the same sporting events. An agent running cross-platform arbitrage needs a unified Kelly framework that accounts for correlated exposures across all platforms. The Sports Betting vs Prediction Markets guide covers how these industries are merging and what it means for agent infrastructure.

AI agents have a structural advantage in Kelly implementation: they don’t panic. A human trader watching a 40% drawdown (well within full-Kelly’s expected range) will often abandon the strategy and start making emotional sizing decisions. An agent with proper guardrails continues executing its fractional Kelly allocation mechanically. Over hundreds of bets, this discipline is the difference between compounding returns and going bust.

Practical Implementation: Your Kelly Checklist

If you are building a prediction market agent or trading manually, here is the implementation path:

Step 1 — Establish your probability estimation method. Kelly is useless without a probability input. Build or adopt a model (LLM-based, statistical, or ensemble) and track its calibration over at least 50 resolved markets before using it to size real bets.

Step 2 — Start with quarter Kelly. Use kelly_mult = 0.25. This gives you a buffer against estimation errors while still scaling bets with edge. Graduate to half Kelly only after 100+ bets with verified positive results.

Step 3 — Set hard position caps. No single bet should exceed 5% of your bankroll, no matter what Kelly says. For contract prices above $0.70, reduce the cap to 2-3%.

Step 4 — Enforce session limits at the wallet level. If you are running an autonomous agent, use Coinbase Agentic Wallets or Safe multisig to enforce maximum spend per session. The wallet should be the last line of defense against a misbehaving intelligence layer.

Step 5 — Track everything. Log every bet: market, estimated probability, market price, Kelly fraction, actual position size, outcome. After 100+ bets, compare your estimated probabilities against actual outcomes to measure calibration. If your estimates are consistently biased, adjust your Kelly multiplier downward.

Step 6 — Respect the formula’s constraints. If Kelly says don’t bet (f* ≤ 0), don’t bet. If Kelly says bet small, bet small. The formula is telling you something about the relationship between your edge and the risk. The most common mistake is overriding Kelly with gut instinct when it recommends a smaller bet than you “feel” is right.

What’s Next

The Kelly Criterion is the mathematical foundation. To build a complete prediction market trading or agent system, you need:

• Probability estimation: See the Agent Intelligence Guide for LLM-based analysis, Bayesian updating, and ensemble methods
• Wallet infrastructure: The Agent Wallet Comparison covers how to set up spending controls for autonomous agents
• Market execution: The Prediction Market API Reference documents the Polymarket CLOB and Kalshi API endpoints for placing trades
• Cross-platform arbitrage: The Cross-Market Arbitrage Guide covers how to detect and execute opportunities across sportsbooks and prediction markets
• The full stack: The Agent Betting Stack explains how Identity, Wallet, Trading, and Intelligence layers fit together

Browse the AgentBets marketplace for prediction market agents that implement Kelly-based bankroll management, or explore the tool directory for calculators and APIs.