Tool
Position size and risk of ruin
Start with $10,000 and make 100 trades at fixed odds. You choose one thing: how much of the account each trade risks. The page counts how often that choice ends ahead, and how often the account falls to $5,000 first.
How it works. You start with $10,000. You make 100 trades in a row. Each trade wins or loses at fixed odds: in the opening example each trade has a 60% chance to win, so about 60 trades in 100 win, and a win pays what the trade risked. Step 2 lets you change both.
You choose one number: the share of the account each trade risks. That is your size. The trade's dollar amount changes as the account grows or shrinks; the share stays the same. Everything else is luck.
One set of 100 trades is a run. The page works out every possible run and how likely each one is. Then it counts two things: the runs that end above $10,000, and the runs that fall to $5,000, half the start, at some point. A run that falls to $5,000 stops there. That is what this page calls ruin.
The edge is what a trade earns on average for each $1 it risks. Here a trade wins 60 cents and loses 40 cents for each $1 it risks, on average. The difference, +20.0%, is the edge.
Step 1 · Choose how much each trade risks
The example: a 60% win chance, even money, 10% of the account on each trade
Risking 10% on each trade, 88% of runs end above $10,000 and 9% fall to $5,000 on the way.
These 30 drawn runs: 25 ended above $10,000 · 5 fell to $5,000 and stopped · 0 ended between $5,000 and $10,000.
The sentence above the chart is exact, worked over every possible run. The 30 drawn runs are one fixed sample, the same at every size, so their count can differ from it.
At 10%, the first trade risks $1,000 of the $10,000. A win adds $1,000, to $11,000. A loss takes $1,000, to $9,000. Each later trade risks 10% of what the account holds then.
As of your numbersSource computed on this page. Sample odds, not anyone's record.
Step 2 · Change the odds
The chart, the answers, the bars and the lesson all follow these two numbers.
Every size, the same odds
Each row is one size. Green is the share of runs that end above $10,000. Red is the share that fall to $5,000 and stop. The grey rest end in between.
As of your numbersSource computed on this page, the exact odds over every possible run, no simulation
What it shows
The odds are the same in every row. Only the size changes, and the size decides how the runs end.
Why: a loss hurts more than a win of the same size helps. Take even money: win 10% and then lose 10%, and $10,000 becomes $9,900. At 50%, a win and then a loss leave $7,500. The bigger the size, the bigger that leak.
So one size grows the account fastest over many trades: the edge divided by the payoff. At a 60% win chance and a 100% payoff, it is 20%. A smaller size grows more slowly but falls to $5,000 less often: at 10%, 9% of runs do. A bigger size takes more risk and grows more slowly too: at 40%, 84% of runs fall to $5,000. Even at 20% itself, 42% of runs fall to $5,000 at some point on the way.
Traders call this question position sizing.
How it is computed
Method. Every run starts at $10,000 and is 100 trades long. Each trade risks the same share of the account as it stands then. A win adds that amount times the payoff; a loss takes it. Trades are independent and the odds never change. A run stops if the account falls to $5,000 or lower. Otherwise it ends after 100 trades, and it is ahead if it ends above $10,000. The shares are the exact odds over every possible run, not a simulation. The size that grows the account fastest over many trades is the win chance, less the loss chance divided by the payoff.
Limits. Real trades do not have fixed odds or fixed payoffs, and one trade's result can affect the next. The figures cover 100 trades and say nothing past them. Half the start is one line among many a trader could draw. Commissions, taxes and slippage are left out. The examples are samples, not anyone's record. This page does not use your accounts or positions. This is a hypothetical illustration of position sizing math.