Square Root Staking Plan
Overview
A proportional staking system that scales stake with the square root of bankroll growth — slower than percentage staking, faster than level stakes. Provides a middle ground between flat and proportional approaches.
How It Works
Stake is proportional to √(current bankroll / initial bankroll). When bankroll doubles, stake increases by √2 ≈ 1.41× (not 2× as with percentage staking).
Formula
\[S_i = S_0 \times \sqrt{\frac{B_i}{B_0}}\]Where:
- $S_i$ = current stake
- $S_0$ = initial stake
- $B_i$ = current bankroll
- $B_0$ = initial bankroll
Example: Start with £10 stakes on £1,000 bankroll. When bankroll = £4,000 (4×), stake = £10 × √4 = £20.
Parameters
| Parameter | Type | Default | Description |
|---|---|---|---|
initial_stake |
number | 10 | Starting stake amount |
initial_bankroll |
number | 1000 | Starting bankroll |
Risk Assessment
- Risk Level: Medium
- Max Drawdown: Slower recovery than percentage staking, faster than level
- Recommended Bankroll: 50× initial stake
- Ruin Risk: Low — growth is dampened compared to percentage staking
When to Use
- You want some compounding but find percentage staking too aggressive
- Long bankroll-building phase expected
- Conservative growth with partial compounding
When to Avoid
- You have a strong edge and want maximum compounding (use Kelly)
- Simplicity is paramount (use level stakes)
Comparison
| Staking Plan | Double Bankroll → Stake Multiplier |
|---|---|
| Level Stakes | 1.0× (no change) |
| Square Root | 1.41× |
| Percentage (2%) | 2.0× |
| Full Kelly | Variable (edge-dependent) |
Betfair Exchange Notes
- Works identically for back and lay — use the same formula
- Square root scaling is gentle enough that commission impact is negligible for stake sizing purposes
Related Plans
- Percentage Staking — Linear proportional staking
- Kelly Criterion — Optimal edge-based proportional staking
- Level Stakes — Zero-growth flat staking
Sources
- Plan catalog reference: The Staking Machine — staking plan software with 50+ plans
- Plan mechanics: Mathematical formulas and plan concepts are in the public domain