DEV Community

BinaryOptions.app
BinaryOptions.app

Posted on

Coding the Break-Even Win Rate for Fixed-Payout Trades (JavaScript)

#javascriptmathbeginnersfinance

Fixed-payout trading products (often marketed as "binary options") look simple: pick up or down, and if you are right you get a fixed percentage of your stake back as profit. The maths behind them is a nice little exercise in expected value, and it is worth coding up because the numbers surprise most people.

The model

  • You stake S.
  • If you win, you receive profit S * p where p is the payout (e.g. 0.85 for 85%).
  • If you lose, you lose S.

Expected value per trade with win probability w:

EV = w * (S * p) - (1 - w) * S
Enter fullscreen mode Exit fullscreen mode

Set EV = 0 and solve for w:

w_breakeven = 1 / (1 + p)
Enter fullscreen mode Exit fullscreen mode

In code 

const breakEven = (payout) => 1 / (1 + payout);

const expectedValue = (stake, payout, winRate) =>
  winRate * stake * payout - (1 - winRate) * stake;

for (const p of [0.7, 0.8, 0.85, 0.9, 0.92]) {
  console.log(
    `${Math.round(p * 100)}% payout -> break-even ${(breakEven(p) * 100).toFixed(1)}%,`,
    `EV at 50% wins: ${expectedValue(100, p, 0.5).toFixed(2)} per $100`
  );
}
Enter fullscreen mode Exit fullscreen mode

Output:

70% payout -> break-even 58.8%, EV at 50% wins: -15.00 per $100
80% payout -> break-even 55.6%, EV at 50% wins: -10.00 per $100
85% payout -> break-even 54.1%, EV at 50% wins: -7.50 per $100
90% payout -> break-even 52.6%, EV at 50% wins: -5.00 per $100
92% payout -> break-even 52.1%, EV at 50% wins: -4.00 per $100
Enter fullscreen mode Exit fullscreen mode

A quick Monte Carlo

Expected value hides how volatile the path is. A small simulation makes the drawdowns visible:

function simulate({ balance = 1000, stake = 20, payout = 0.85, winRate = 0.5, trades = 500 }) {
  let low = balance;
  for (let i = 0; i < trades && balance >= stake; i++) {
    balance += Math.random() < winRate ? stake * payout : -stake;
    low = Math.min(low, balance);
  }
  return { final: Math.round(balance), low: Math.round(low) };
}

const runs = Array.from({ length: 10000 }, () => simulate({}));
const busted = runs.filter(r => r.final < 20).length / runs.length;
console.log(`Accounts wiped out after 500 trades: ${(busted * 100).toFixed(1)}%`);
Enter fullscreen mode Exit fullscreen mode

With a coin-flip win rate and an 85% payout, a large share of simulated accounts are wiped out well before 500 trades. Changing winRate to 0.55 shows how thin the margin is even for a trader with a real edge.

Takeaways

  1. The payout percentage is not a return; the break-even win rate is the number that matters.
  2. On very short expiries, price moves are mostly noise, so sustaining a win rate above break-even is hard.
  3. Regulators agree: the UK FCA banned retail sales of binary options in 2019 and ESMA restricted them across the EU, while the US CFTC warns about unregistered platforms.

If you want to play with the numbers without writing code, there is a plain-English explainer and calculator-style breakdown on binaryoptions.app.

Risk warning: binary options are high-risk products and most retail traders lose money. This post is educational and is not financial advice.

Top comments (0)