Risk Of Ruin Calculator

Instantly calculate your Risk of Ruin (RoR) with our free Risk of Ruin Calculator. Understand the probability of blowing your trading or investment account based on your system’s parameters. Make informed decisions about bankroll management.

Calculate Your Risk of Ruin

Win Rate	R – 0.2	R Current	R + 0.2

Table: Sensitivity of Risk of Ruin (%) to Win Rate and Payoff Ratio (R)

What is the Risk of Ruin?

The Risk of Ruin (RoR) is a statistical concept used primarily in trading, investing, and gambling to determine the probability that a person will lose a significant portion of their capital, rendering them unable to continue their activity. It quantifies the likelihood of hitting a “ruin point” – a predefined level of capital loss (often 100%, but can be less) – given a certain strategy or system with known parameters like win rate and average win/loss size.

Anyone engaging in activities with probabilistic outcomes and financial risk should understand and ideally use a risk of ruin calculator. This includes stock traders, forex traders, options traders, sports bettors, and poker players. It helps in assessing the sustainability of a strategy and in determining appropriate position sizing or bet sizing to manage risk effectively.

Common misconceptions about the Risk of Ruin include thinking that a positive edge (expectancy) guarantees no ruin (it doesn’t, it just lowers the probability if bankroll is sufficient), or that it’s a fixed number (it changes based on bankroll, bet size, and system parameters). A risk of ruin calculator helps dispel these by showing the dynamic nature of RoR.

Risk of Ruin Formula and Mathematical Explanation

There are several formulas to estimate the Risk of Ruin, depending on the assumptions. A common and relatively simple approximation for eventual ruin, when the system has a positive edge and fixed bet/trade outcomes, is:

RoR ≈ exp(-2 * E * T / V)

Where:

• E is the Edge (or Expectancy) per trade/bet.
• T is the Total Bankroll.
• V is the Variance of outcomes per trade/bet.

The steps to calculate these are:

1. Calculate the Loss Rate (L): L = 1 - W (where W is Win Rate)
2. Calculate the Edge (E): E = (W * A) - (L * B) (where A is Avg Win, B is Avg Loss)
3. Calculate the Variance (V): V = W * A2 + L * B2 - E2
4. If E > 0 and V > 0, calculate RoR using the exponential formula above.
5. If E ≤ 0, the eventual Risk of Ruin is theoretically 100%.

This formula gives the probability of *eventually* losing the entire bankroll T if the trading/betting parameters (W, A, B) remain constant and the edge E is positive. The risk of ruin calculator uses this approximation.

Variables Table

Variable	Meaning	Unit	Typical Range
W	Win Rate (Probability of Win)	Decimal	0 to 1
A	Average Win Amount	Currency/Points	> 0
B	Average Loss Amount	Currency/Points	> 0
T	Total Bankroll/Capital	Currency/Points	> 0
L	Loss Rate (1-W)	Decimal	0 to 1
E	Edge per trade/bet	Currency/Points	Any value
V	Variance of outcomes per trade/bet	(Currency/Points)^2	> 0 (if A, B > 0)
RoR	Risk of Ruin	Percentage/Decimal	0% to 100% (0 to 1)

Practical Examples (Real-World Use Cases)

Example 1: Day Trader

A day trader has a system with:

• Win Rate (W): 0.60 (60%)
• Average Win (A): $300
• Average Loss (B): $200
• Total Bankroll (T): $20,000

Using the risk of ruin calculator:

• L = 1 – 0.60 = 0.40
• E = (0.60 * 300) – (0.40 * 200) = 180 – 80 = $100
• V = 0.60 * 300² + 0.40 * 200² – 100² = 54000 + 16000 – 10000 = 60000
• RoR ≈ exp(-2 * 100 * 20000 / 60000) = exp(-4000000 / 60000) = exp(-66.67) ≈ 0% (very low)

The trader has a very low risk of eventual ruin with this bankroll and system parameters.

Example 2: Sports Bettor

A sports bettor has:

• Win Rate (W): 0.53 (53%)
• Average Win (A): $100 (betting on even odds with vig)
• Average Loss (B): $110
• Total Bankroll (T): $2,000

Using the risk of ruin calculator:

• L = 1 – 0.53 = 0.47
• E = (0.53 * 100) – (0.47 * 110) = 53 – 51.7 = $1.3
• V = 0.53 * 100² + 0.47 * 110² – 1.3² = 5300 + 5687 – 1.69 = 10985.31
• RoR ≈ exp(-2 * 1.3 * 2000 / 10985.31) = exp(-5200 / 10985.31) = exp(-0.473) ≈ 0.623 or 62.3%

The bettor has a high risk of ruin (62.3%) despite a positive edge, due to the small edge relative to the bankroll and bet size implied by avg win/loss.

How to Use This Risk of Ruin Calculator

1. Enter Win Rate: Input the probability of a winning trade or bet as a decimal (e.g., 0.6 for 60%).
2. Enter Average Win: Input the average amount you make on a winning trade/bet.
3. Enter Average Loss: Input the average amount you lose on a losing trade/bet.
4. Enter Total Bankroll: Input your total capital available for trading or betting.
5. Click Calculate: The calculator will display the estimated Risk of Ruin, Edge, Payoff Ratio, and Variance.

Reading the Results: The primary result is the Risk of Ruin percentage. A high percentage (e.g., above 20-30%) suggests your bankroll is too small for your system’s parameters or your system’s edge is too low/variance too high. A very low percentage (near 0%) indicates a more robust setup against ruin.

Decision-Making: If the RoR is high, consider increasing your bankroll, reducing your bet/trade size (which would reduce average win/loss proportionally if risking a fixed percentage), or improving your system’s win rate or payoff ratio. The risk of ruin calculator helps you see how these factors interact.

Key Factors That Affect Risk of Ruin Results

• Win Rate: Higher win rates generally reduce RoR, assuming the payoff ratio doesn’t decrease proportionally more.
• Payoff Ratio (Avg Win / Avg Loss): A higher payoff ratio (winning more than you lose on average) significantly reduces RoR.
• Bankroll Size: A larger bankroll relative to the average win/loss size drastically reduces RoR. It provides a larger cushion against losing streaks.
• Bet/Trade Size: Implicit in the average win/loss, larger bet sizes relative to bankroll increase RoR exponentially. Although not a direct input, if you change bet size, your avg win/loss would scale.
• Edge/Expectancy: A higher positive edge per trade (E > 0) is crucial for reducing RoR below 100%.
• Volatility/Variance of Returns: Higher variance in outcomes (even with the same edge) increases the RoR because it implies larger swings and potentially longer losing streaks.

Understanding these factors is vital for managing your capital and using the risk of ruin calculator effectively.

Frequently Asked Questions (FAQ)

What is an acceptable Risk of Ruin?

This is subjective, but many traders and gamblers aim for an RoR below 1%, or at most 5%. A very high RoR suggests the strategy or bankroll management is too aggressive.

Does a 0% Risk of Ruin mean I will never lose my bankroll?

No, the calculator provides an approximation. A very low RoR (close to 0%) means the probability is extremely small under the given assumptions, but black swan events or changes in system parameters can occur. It’s about probability, not certainty.

What if my edge is negative?

If your edge (E) is zero or negative, the eventual Risk of Ruin is 100%. You are mathematically expected to lose over time.

How can I reduce my Risk of Ruin?

You can increase your bankroll, decrease your average bet/trade size (which proportionally reduces average win/loss), improve your win rate, or increase your average win relative to your average loss.

Does this calculator account for the number of trades/bets?

The formula used here calculates the *eventual* Risk of Ruin over an infinite number of trades if the edge is positive. The risk over a finite number of trades would be lower but is more complex to calculate precisely without simulations.

Is Risk of Ruin the same as drawdown?

No. Drawdown is the peak-to-trough decline in capital. Risk of Ruin is the probability of the drawdown reaching 100% (or a predefined ruin level).

Why does bankroll size matter so much?

A larger bankroll allows you to withstand longer losing streaks (which are statistically inevitable) without being wiped out, giving your positive edge more time to work.

Can I use this for investing in stocks?

It’s more suited for trading or gambling systems with defined win/loss amounts per event. Long-term investing has different risk dynamics, though the principle of avoiding ruinous losses applies.