Bankroll Management 101: Protect Your Edge with Discipline

Fixed Stakes and Recalculated Stakes Are Different

Start with a hypothetical $1,000 balance. A fixed unit of 20% of the initial balance is $200 on every bet. Five consecutive $200 losses exhaust the initial $1,000. There is then no money for a sixth $200 stake.

Instead, staking 20% of the remaining balance recalculates the amount each time: $1,000 → $800 → $640 → $512 → $409.60 → $327.68. After five losses, 0.8^5 = 32.768% remains, a 67.232% drawdown.

These are deterministic loss paths, not estimates of how likely a losing streak is. A 50% drawdown requires a 100% gain from the reduced balance to recover. No stake fraction is universally ideal.

Expected Growth Requires a Model

Hypothetical assumptions: every bet has win probability p = 0.55, price -110, and no pushes, fees, or taxes. Net winnings per dollar on a win are b = 100/110. Expected net profit per dollar = 0.55 × (100/110) - 0.45 = 0.05, or 5%. The 55% probability is assumed, not established.

At a fixed $20 stake, expected profit is $1 per bet. For 200 such bets, the unconstrained arithmetic sum is $200, or 20% of the initial $1,000. This assumes every stake can be funded; a finite bankroll with a stop-at-insufficient-funds rule needs a separate stopped-process calculation.

If each independent bet instead risks 2% of the current balance, assumes unchanged probabilities and prices, and permits arbitrarily small stakes without rounding, expected balance after 200 bets is $1,000 × [1 + 0.02 × 0.05]^200 ≈ $1,221.28. That is 22.13% expected growth, not a promised outcome, median outcome, or risk-of-ruin estimate.

Expected value weights outcomes by their probabilities; see OpenStax’s definition. Sizing changes exposure, but neither example establishes a real-world edge.

Drawdown Is Not Risk of Ruin

A drawdown measures a decline from a reference balance or peak. Risk of ruin is the probability of reaching a defined failure boundary. State the horizon, stake rule, minimum stake, outcome probabilities, and dependence assumptions before quoting a ruin percentage.

With ideal percentage stakes below 100% and no rounding or minimum stake, a finite string of losses never reaches exactly zero. It can still leave an unusably small balance. Real minimum stakes and an explicit failure threshold change that model. The loss-path table above therefore supplies no universal ruin probability.

Kelly Optimizes a Particular Objective

For a repeated binary model with a known constant win probability p and net odds b, the expected logarithmic growth at fraction f is g(f) = p × ln(1 + bf) + (1 - p) × ln(1 - f). Solving g′(f) = 0 gives f* = [bp - (1 - p)] / b. For a nonnegative-stake choice, a nonpositive result means no stake in this model.

At -110 with an assumed p = 0.58: b = 100/110, so f* = [(100/110) × 0.58 - 0.42] / (100/110) = 0.118 = 11.8%. Quarter Kelly is 2.95%. These are mathematical outputs from assumed inputs, not recommended stake sizes.

The objective is expected logarithmic growth under the model, not maximum expected dollar balance or guaranteed profit. Errors in p, changing odds, simultaneous correlated wagers, minimum stakes, and rounding can invalidate the simple setup. Fractional Kelly reduces the modeled exposure but cannot validate the assumed edge.

Continue to the Kelly sizing guide and statistical variance. Use simulation records to compare rules while keeping assumptions separate from results.

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