Bet Sizing Optimizer

How the optimizer finds the right stake

Mathematical Audit Benchmark

How Does This Compare to 0% House Edge Protocols?

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If you hold a genuine mathematical edge — say, in sports betting or value play at a casino — raw speed of growth matters less than survival. Doubling your stake does not double your compound growth. Returns multiply geometrically, so extra size adds volatility first and returns later. Push far enough and the geometric growth rate turns negative even with positive expected value.

The tool applies Kelly Criterion logic with one addition: a **Ruin Tolerance Cap**. It plots expected growth ($g(f)$) across every fraction of your bankroll ($f$), then reports the largest stake that still keeps your probability of going broke below the threshold you chose.

The formulas behind the sweep: g(f) and ruin probability

Two functions compete during the search:

1. The Geometric Growth Rate (g(f))

Expected logarithmic growth per round, expressed against the staked fraction ($f$):

g(f) = p * ln(1 + b * f) + q * ln(1 - f)

Where:

• $f$: Fraction of your bankroll placed on each round.
• $p$: Probability that the bet wins.
• $q$: Probability it loses ($1 – p$).
• $b$: Decimal payout odds (e.g., $b = 1$ for even money).

2. The Geometric Ruin Approximation

To keep you from chasing peak growth straight into bankruptcy, the tool estimates the long-run odds of hitting ruin:

P(Ruin) ≈ exp(-2 * |μ| * B / σ²)

Here $mu$ stands for your average edge in units, $B$ for bankroll size in units, and $sigma^2$ for outcome variance.

Worked example: $5,000 bankroll, 55% win rate

Picture a $5,000 bankroll and an even-money sports bet where your win probability sits at 55% ($p = 0.55$, $b = 1$, a 10% edge). You refuse any ruin probability above 5%:

1. Type in your total bankroll ($5,000) plus the game metrics ($p = 0.55$, $b = 1$).
2. Set the maximum acceptable Ruin Probability to 5%.
3. Click “Verify.” The optimizer sweeps fractions from $f = 0.01$ up to $f = 0.30$.
4. Read the growth curve. Full Kelly calls for 10% of the bankroll ($500) per game — maximum growth, but ruin risk well above your line.
5. The tool lands on the “constrained optimal” stake (e.g., 5%, or $250): roughly 75% of the maximum growth rate with ruin probability forced under 5%.

Frequently asked questions