The actual math behind "a winning strategy can still blow up": the classic gambler's-ruin formula worked with real numbers, why that formula quietly assumes a 1:1 payoff nobody actually trades, and why our own calculator abandons the closed form for 3,000 simulated accounts instead.
Know your real survival odds first.Bybit での取引 — 豊富な流動性、低手数料、最大 30,000 ドルのウェルカムボーナス。Bybitアカウントを開設 →Not "will this trade win" and not "is my edge real" — those are separate questions. Risk of ruin asks: given a real, positive edge, what's the probability a losing streak wipes the account before the edge has time to play out? The uncomfortable answer is that a genuinely profitable strategy can still have a high chance of blowing up, purely because of how much is staked per trade. Edge and survival are two different numbers, and traders who only track the first one are the ones who disappear.
The classic version of this problem comes from 18th-century gambler's-ruin math: a gambler with edge E (where E = 2p − 1 for win probability p, on a fair 1:1 payoff) and a bankroll worth N fixed-size bets, risks everything on repeated 1:1 wagers until either doubling up endlessly or hitting zero. The probability of hitting zero has an exact closed form:
R = ((1 − E) ÷ (1 + E))N
Take a 55% win rate at a 1:1 payoff — edge E = 0.10. N, the number of risk units in your bankroll, is just 1 ÷ (fraction risked per trade). Risk 20% per trade and N = 5; risk 2% per trade and N = 50. Plugging straight into the formula above:
| 取引ごとのリスク | Risk units (N) | Ruin probability |
|---|---|---|
| 20% per trade | 5 | 67.02% |
| 10% per trade | 10 | 13.44% |
| 5% per trade | 20 | 1.81% |
| 2% per trade | 50 | 0.0044% |
Nothing about the edge changed across these four rows. Win rate: still 55%. Payoff: still 1:1. The only variable is how big a bite is taken out of the bankroll per trade, and it moves ruin odds from two-out-of-three down to essentially zero. This is the single clearest argument for small, fixed-fractional position sizing that exists in trading math — see it on your own numbers with the 破滅のリスク計算機.
Hold risk per trade fixed at 10% per trade (N = 10) and vary only the win rate:
| Win rate (1:1 payoff) | Edge (E) | Ruin probability at N=10 |
|---|---|---|
| 52% | 0.04 | 44.91% |
| 55% | 0.10 | 13.44% |
| 60% | 0.20 | 1.73% |
Doubling your edge from 4% to 10% cuts ruin odds roughly 3.3×. But look back at the previous table: cutting risk per trade from 20% to 2% (a 10× reduction in bet size) cut ruin odds over 15,000×. Position size is the more powerful lever, by a wide margin — which is exactly why overconfidence in an edge (the estimation-error trap covered in the Kelly Criterion explainer) is so dangerous: it tempts traders to size up on the lever that barely helps, while ignoring the one that actually determines survival.
Here's the part most explanations skip. The clean closed form above only exists because wins and losses are the same size. The instant you introduce a real reward:risk ratio — say the 1.5:1 edge from our Kelly example (55% win rate, win $1.50 per $1 risked) — the random walk is no longer symmetric, and there is no equivalent algebraic solution for hitting a ruin boundary. This isn't a simplification we're choosing to skip; it's a genuine gap in closed-form probability theory once step sizes differ.
That's exactly why the 破滅のリスク計算機 on this site doesn't use the formula above at all. It runs 3,000 simulated accounts, each playing out 200 random trades at your actual win rate and reward:risk, sized as a fixed percentage of the current (not starting) balance, and counts what fraction hit your chosen drawdown threshold — default −50% — before the 200 trades are up. That's Monte Carlo simulation, and it's the only honest way to answer the question once real, asymmetric payoffs are involved.
The 18th-century formula defines ruin as hitting exactly ゼロ, over an unlimited number of trades. That's a clean math problem but a useless trading one — nobody keeps a 2% position size running forever with no stop on strategy review, and almost no account that's actually in trouble dies by hitting literal zero. It dies by drawing down 40-60% and the trader either quitting, getting margin-called, or losing the discipline to keep following the system.
Our calculator's definition — probability of hitting a chosen drawdown threshold within a finite trade horizon (200 trades) — matches how accounts actually fail. It's a harder number to compute (hence Monte Carlo, not algebra), but it's the number that matters before you risk real capital. Pair it with the 最大ドローダウン計算機 to see what a given ruin threshold actually costs an equity curve in dollar terms, and the 貿易期待計算機 to confirm the edge feeding into either tool is real.
For a 1:1 payoff (win and lose the same unit), risk of ruin is R = ((1-E)/(1+E))^N, where E = 2p - 1 is your edge (p = win probability) and N is your bankroll measured in risk units (N = 1 / fraction risked per trade). A 55% win rate (E=0.10) risking 10% per trade (N=10) gives roughly 13.4% ruin odds; the same edge risking 2% per trade (N=50) drops that to 0.004%.
Not with a clean closed form. The classic gambler's-ruin equation only has an exact solution for a symmetric 1:1 payoff. The moment wins and losses are different sizes — which is every real trading setup — there is no simple formula, which is why practical risk-of-ruin tools (including ours) switch to Monte Carlo simulation: thousands of random trade sequences at your actual win rate and reward:risk, counting how many sequences hit a ruin threshold.
True gambler's ruin asks the probability of hitting exactly zero over an infinite number of trades, which is a different and less useful question than the one traders actually care about. Our calculator asks a more honest question: given your real win rate, payoff, and position size, what is the probability your account drops by a chosen threshold (default 50%) within the next 200 trades? That matches how accounts actually die — a deep enough drawdown, not a mathematical trip to literal zero.
Most professional risk frameworks target low single digits for probability of a severe drawdown over a meaningful trade sample. Our worked table shows that moving from 20% risk per trade down to 5% can take the same 55% win rate / 1:1 edge from 36.7% ruin odds to 1.8% — the position size lever matters more than almost any other variable traders obsess over.
⚠️ 教育のみを目的としており、経済的なアドバイスではありません。レバレッジ取引では入金額全額を失う可能性があります。