## The Problem of Uncertain Edge
The Kelly Criterion and ruin theory assume you know your edge precisely. In practice, you have an estimate of your edge — and that estimate has uncertainty. This uncertainty is often ignored, with significant consequences.
## Why Edge Uncertainty Matters
Suppose your last 300 bets show 3.5% ROI. Your 95% confidence interval:
Standard error ≈ σ_bet / √n
With typical variance, SE ≈ 3%. So your 95% CI is 3.5% ± 6% = [−2.5%, 9.5%].
Your edge could plausibly be negative. If you stake at Kelly for 3.5% edge but your true edge is 0%, you are betting positive Kelly with zero edge — equivalent to betting at random with declining bankroll.
## The Conservative Response: Shrink the Estimate
A common approach: use 50–70% of your estimated edge in all staking calculations.
At 3.5% estimated ROI: use 1.75–2.45% in staking calculations.
This conservative adjustment builds in a margin for estimation error. If your true edge is better than expected, the stake was slightly sub-optimal. If your edge was overestimated, the conservative stake prevents disaster.
## The Bayesian Update Approach
Formally, combine your prior (pre-season belief about edge) with the evidence from your actual results:
Posterior edge = (Prior edge × Prior weight + Observed edge × Data weight) / Total weight
Early in the season, prior dominates. After 500 bets, data dominates. This approach naturally prevents over-staking on unvalidated edge estimates.
## The Sample Size Rule
Until you have 300+ bets: use flat 1% staking, not Kelly. The edge estimate is too uncertain to justify Kelly-based variable staking. After 300 bets with consistent positive CLV: introduce fractional Kelly gradually.
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