Kelly Criterion on Polymarket: Optimal Bet Sizing Guide
The mathematically optimal formula for sizing Polymarket positions — adapted for binary prediction markets, explained with worked examples and practical rules.
Contents
What Is the Kelly Criterion?
The Kelly Criterion, developed by John L. Kelly Jr. at Bell Labs in 1956, is a formula for determining the optimal fraction of your bankroll to bet on any given opportunity. "Optimal" here means maximising the long-run geometric growth rate of your bankroll — not maximising the return on any single bet.
The key insight: betting too little leaves money on the table; betting too much — even on a +EV bet — can cause ruin via variance. Kelly finds the exact fraction that maximises compounding over time. It is provably the best long-run strategy for a series of bets with known edge, making it the gold standard for systematic Polymarket traders.
Two things Kelly does not do: guarantee you won't lose money on any individual bet, and require you to perfectly know your edge in advance. The practical challenge of Kelly is that it is highly sensitive to your probability estimate — which is why most professional bettors use a fractional version rather than full Kelly.
The Kelly Formula for Polymarket
Polymarket is a binary market — each bet resolves to either $1.00 (YES wins) or $0.00 (NO wins). This simplifies the Kelly formula considerably compared to multi-outcome bets.
f* = (P − q) / (1 − q)
For a NO position:
f* = ((1−P) − q_no) / (1 − q_no)
Where:
- f* = optimal fraction of bankroll to bet
- P = your true probability estimate that YES resolves
- q = current market price for YES (in dollars per share, 0–1)
- q_no = cost per NO share = (1 − YES price)
The Simplified Version
Because Polymarket prices ARE probabilities (shares pay exactly $1), the formula collapses to a clean expression:
This is equivalent to: edge divided by odds. Your edge is (P − price). Your odds are (1 − price) — the amount you profit per dollar correctly bet. Kelly says bet the ratio of these two quantities.
Intuitive Check
If P = price (no edge), Kelly recommends f* = 0 — don't bet. If P = 1.0 (certainty), Kelly recommends f* = 1.0 — bet everything. Both extreme cases make intuitive sense, validating the formula.
Worked Examples
Example 1 — Standard Political Market
Market: "Will the Senate confirm Nominee X?" — price: 45¢ YES. Your estimate: 65% true probability.
f* = (0.65 − 0.45) / (1 − 0.45) = 0.20 / 0.55 = 36.4% of bankroll (full Kelly)
Half-Kelly: 18.2% | Quarter-Kelly: 9.1%
On a $1,000 Polymarket bankroll, full Kelly = $364 stake. Most traders would use $91–$182 (quarter to half Kelly) on this position.
Example 2 — BTC Price Target Market
Market: "Will BTC exceed $120K by August?" — price: 22¢ YES. Your model estimates 38% probability based on implied volatility.
f* = (0.38 − 0.22) / (1 − 0.22) = 0.16 / 0.78 = 20.5% of bankroll (full Kelly)
Half-Kelly: 10.3% — still meaningful. This market has decent edge but high uncertainty, making half-Kelly appropriate.
Example 3 — Near-Zero Edge (Should Not Bet)
Market: "Will Party X win the midterm majority?" — price: 52¢. Your estimate: 55%.
f* = (0.55 − 0.52) / (1 − 0.52) = 0.03 / 0.48 = 6.25% of bankroll
Even full Kelly only suggests 6.25%, signalling this is a thin edge. After accounting for estimation uncertainty (your 55% estimate could easily be 51–59%), the true expected Kelly fraction might be near zero. Pass or micro-bet only.
Example 4 — Very High Probability Market
Market: "Will the US have a president on Jan 20?" — price: 97¢. Your estimate: 99.5%.
f* = (0.995 − 0.97) / (1 − 0.97) = 0.025 / 0.03 = 83% of bankroll
Kelly recommends a large fraction — but notice the reward is tiny (3¢ per share). On $1,000 bankroll with 83% Kelly = $830 staked to win $25.60 max. Many traders avoid near-certainty markets because the Kelly fraction is high but the absolute return is trivial and liquidity is poor.
Why Half-Kelly Is Better in Practice
Full Kelly maximises expected log wealth — but only when your probability estimates are perfectly calibrated. In reality, every probability estimate carries uncertainty. A stated 65% estimate might be anywhere from 55% to 75%. When you feed an uncertain probability into Kelly, the formula often recommends overbetting.
The Asymmetry of Overbetting vs Underbetting
Betting half-Kelly instead of full Kelly reduces your long-run growth rate by approximately 25% (you capture 75% of optimal growth). But it reduces variance by 75% — a massive reduction in drawdown risk. Because the growth-rate cost is sublinear but the variance reduction is dramatic, half-Kelly is widely considered the real-world optimum for bettors whose probability estimates are uncertain.
Quarter-Kelly for High Uncertainty Markets
For markets where your probability estimate has high uncertainty (thin information, contested evidence, early-stage political races), quarter-Kelly is appropriate. You sacrifice more growth potential but protect against catastrophic drawdowns from estimate error on a single position.
Practical Rule of Thumb
- High confidence estimate (narrow range): half-Kelly
- Medium confidence estimate: quarter-Kelly
- Low confidence / speculative: eighth-Kelly or fixed small fraction (1–2% of bankroll)
- Estimate uncertainty exceeds edge: do not bet
Kelly with Multiple Open Positions
The standard Kelly formula assumes one bet at a time. On Polymarket you'll often have 5–15 open positions simultaneously. Applying naive Kelly to each independently will overbet your total bankroll. The correct approach:
Available Bankroll Method
Always calculate Kelly as a fraction of your available bankroll — total bankroll minus all capital already staked in open positions. If you have $1,000 total and $400 currently staked, your available bankroll is $600. Apply Kelly to $600 for the next bet.
Correlation Adjustment
When multiple open positions are correlated (e.g., several markets affected by the same Fed decision), treat them as a single compound position. The combined Kelly bet on all correlated positions should equal what Kelly would recommend on the single most important market in the correlated group. Splitting a single-event exposure across 4 markets doesn't reduce risk — it amplifies it if the event goes against you.
Maximum Concentration Rule
A practical guard rail: never let a single position exceed 20% of total bankroll regardless of what Kelly recommends. Kelly can suggest large fractions for very high-edge markets, but estimation error at high concentration can cause severe drawdowns. Hard caps protect against tail risk from probability miscalibration.
Kelly on NO Positions
NO positions work identically — just substitute the NO price and your NO probability estimate. A NO share costs (1 − YES price) and pays $1 if the market resolves NO.
Example: Market at 70¢ YES (30¢ NO cost). Your estimate: 45% chance of NO resolution (i.e., you think YES is overpriced at 70¢).
f* = (0.45 − 0.30) / (1 − 0.30) = 0.15 / 0.70 = 21.4% of bankroll
The formula is symmetric — NO positions are treated identically to YES positions with the complementary probability and price.
When NOT to Use Kelly
Your Edge Is Below 10 Points
Sub-10-point edges produce Kelly fractions below 5–10% even at full Kelly. The transaction friction, slippage, and estimation uncertainty on thin markets makes these bets unworthy of systematic capital allocation. Screen for edges above 12 points minimum (the Poly-Sim Daily Edge threshold) before running Kelly.
You're Operating Near Your Bankroll Minimum
If drawdowns have reduced your Polymarket bankroll significantly, Kelly fractions calculated on a depleted base can produce position sizes too small to be practically meaningful. At this point, pause and reassess your probability estimation process rather than continuing to grind on small fractions.
Markets Closing in Less Than 48 Hours
Short-horizon markets have binary outcome risk with no time for reversion. Kelly is designed for long-run compounding — it is less applicable to single ultra-short-horizon bets where you have only one resolution event. Use a fixed small fraction (1–2%) for sub-48-hour markets unless you have near-certainty conviction.
You Can't Estimate a Probability Credibly
If you genuinely cannot form an independent probability estimate — you don't have an information or analytical basis for your view — then you don't have an edge and Kelly is inapplicable. "I have a gut feeling" is not a valid input to the Kelly formula. Only bet when you can articulate a reasoned probability estimate with supporting evidence.
Frequently Asked Questions
What is the Kelly Criterion formula for Polymarket?
f* = (P − price) / (1 − price) for YES bets, where P is your true probability estimate and price is the current market YES price. For a market at 40¢ with 60% estimated probability: f* = (0.60 − 0.40) / (1 − 0.40) = 33.3% of available bankroll at full Kelly.
Why use half-Kelly instead of full Kelly on Polymarket?
Full Kelly assumes perfect probability calibration. In practice, your estimates contain uncertainty. Half-Kelly reduces variance by 75% while sacrificing only ~25% of long-run growth rate — a favourable trade-off when your probability estimate could be off by several points.
How do I apply Kelly with multiple open Polymarket positions?
Apply Kelly to available bankroll (total minus staked capital). For correlated positions, treat them as one compound position. Never exceed 20% of total bankroll on a single market regardless of Kelly output.
What is the minimum edge to use Kelly on Polymarket?
At least 10–15 percentage points of EV edge. Below 10 points, estimation uncertainty swamps the edge. The Poly-Sim Daily Edge surfaces markets with 12+ point AI-estimated gaps — a natural minimum Kelly threshold.
Find High-Edge Markets to Apply Kelly To
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