Bankroll Management Calculator — Staking Plan Comparison

The bankroll management calculator helps you determine exactly how much to bet on each wager based on your chosen staking strategy. Enter your starting bankroll, your estimated win probability (drag the slider), the decimal odds you expect to be betting at, and choose a staking method. Click "Calculate Bankroll Projections" to see your recommended stake, edge per bet, and a deterministic projection of how your bankroll grows (or shrinks) over 10, 50, 100, and 200 bets.

The projections use expected value (EV), not random simulation. This shows the mathematical trajectory of each staking plan given your inputs — the actual path will vary due to variance, but the EV projection is the long-run expected outcome.

The Kelly Criterion option auto-calculates the mathematically optimal stake. If your estimated edge is zero or negative, the Kelly recommendation is £0 — in that scenario, the correct action is not to bet.

The calculator uses three staking methods, each with a distinct growth formula:

1. Fixed Stake

You bet the same dollar amount every time regardless of bankroll size. The bankroll after n bets is:

• bankroll_n = bankroll + n × stake × edge
  where edge = p × (odds − 1) − (1 − p) = (p × odds) − 1

This is linear growth (or loss). With positive edge it grows steadily. The downside: as your bankroll grows, your fixed stake becomes a smaller and smaller percentage, so you never accelerate your growth through compounding.

2. Fixed Percentage

You bet a fixed percentage of your current bankroll on every bet. This compounds:

• bankroll_n = bankroll × (1 + stakePercent/100 × edge)^n

With positive edge this grows exponentially. The risk is symmetrical: a losing run shrinks your bankroll faster than fixed staking. Common choices are 1–5% of bankroll per bet, with most professional bettors using 1–3%.

3. Kelly Criterion

The Kelly fraction is the mathematically optimal percentage of bankroll to bet, given your edge and the odds:

• f* = (b × p − q) / b
• where b = decimal odds − 1 (net odds), p = win probability, q = 1 − p (loss probability)

The Kelly fraction maximises the long-run geometric growth rate of your bankroll. It is also the staking plan that is least likely to lead to ruin, given accurate probability estimates. Like fixed percentage staking, it compounds. The Kelly projection uses the Kelly fraction as the stake percentage in the same formula above.

Edge Per Bet

The edge (expected value per unit staked) determines whether any staking plan can be profitable:

• edge = p × (odds − 1) − (1 − p)
• Positive edge → long-run profitable; negative edge → long-run losing bet
• At even-money odds (2.0) you need greater than 50% win rate to have a positive edge

Example 1 — Fixed Stake, Positive Edge

Bankroll: $1,000. Fixed stake: $50. Win probability: 55%. Decimal odds: 2.0.

• Edge = 0.55 × 1.0 − 0.45 = 0.10 (10% per bet)
• After 10 bets: $1,000 + 10 × $50 × 0.10 = $1,050
• After 100 bets: $1,000 + 100 × $50 × 0.10 = $1,500
• After 200 bets: $1,000 + 200 × $50 × 0.10 = $2,000

Linear growth: steady but slow. Your $50 stake remains the same even as your bankroll doubles.

Example 2 — Fixed 5%, Same Edge

Bankroll: $1,000. 5% fixed percentage. 55% win probability, 2.0 odds.

• Growth per bet = 1 + 0.05 × 0.10 = 1.005
• After 100 bets: $1,000 × (1.005)^100 ≈ $1,648
• After 200 bets: $1,000 × (1.005)^200 ≈ $2,712

Compounding accelerates growth. After 200 bets with percentage staking you have $2,712 versus $2,000 with fixed staking — 35% more.

Example 3 — Kelly Criterion

Bankroll: $1,000. 55% win probability, 2.0 decimal odds.

• b = 2.0 − 1 = 1.0; p = 0.55; q = 0.45
• Kelly fraction: f* = (1.0 × 0.55 − 0.45) / 1.0 = 0.10 (10%)
• Kelly stake: 10% × $1,000 = $100
• Growth per bet = 1 + 0.10 × 0.10 = 1.01
• After 100 bets: $1,000 × (1.01)^100 ≈ $2,705

Full Kelly bets aggressively and grows fast, but produces high variance. Most professionals use half Kelly ($50 in this case) to reduce volatility while capturing most of the long-run growth benefit.

Pros and Cons of Each Method