Cold-Blooded Mathematics Work in progress

Free to read // The Math of Enough

You just scrolled past a $5,000 screenshot.

Suddenly your $100 day feels like nothing.

It shouldn’t. Small, steady gains add up, as long as the losses stay small too. Here’s the math.

$25,200

$100 a day × 252 trading days. A made-up average across every day, good and bad, before costs and taxes.

These are hypothetical calculations, not forecasts.

01 // Small adds up

What does “a little” add up to?

$20 a day$5,040 $100 a day$25,200 $500 a day$126,000

That’s an average across all 252 days, losing days included, before costs and taxes. It’s arithmetic, not a paycheck. The point is simple: small, steady numbers add up to more than they look like. If $25,200 a year is what you want, that’s a great goal.

The math: about 252 trading days a year × the daily amount. No compounding, no withdrawals, no costs or taxes.

02 // Small percentages compound

And small percentages build, too

Some traders want to grow the account instead of taking money out. Then small percentages do the building.

$5,000 → $1,000,000

in 268 trading days, at an average of 2% a day, reinvested.

“Average” is the key word. There will be losing days. The math only works if those losing days stay small.

Look where it starts: 2% of $5,000 is $100. That’s the point of starting small. You build your skill and your reflexes while each mistake is cheap, and the size grows only as the account (and you) do.

By day 200 the account is about $262,000, and the next day’s 2% is about $5,250. Same percentage, much bigger number, and a much bigger loss if a day goes wrong. That’s why keeping losses small matters more the bigger you get.

Show me the math

Account × 1.02 each day, before costs. Day 268 is the first day over $1M. After day 200: $5,000 × 1.02²⁰⁰ ≈ $262,424; day 201’s 2% ≈ $5,248.

03 // Steady vs swinging

Same average. Very different year.

Two made-up traders. Both make the same $30 per trade on average. That average holds only while a trader is still trading: a wiped-out account stops.

Steady wins a little, loses a little.
Swinger swings for the fences: one huge win now and then, lots of small losses.

Same average. Very different years. Swinger is the screenshot, until the year it wipes out.

One honest catch: Steady only wins because we gave both traders an edge of $30 a trade. Take the edge away and Steady loses too, just slowly. Steady protects an edge; it doesn’t create one.

Show me the math

The model, its sizes and odds, stated plainly. Illustrative, not real trades. Both start each simulated year with $9,000 and take one trade a day. Steady wins $120 or loses $60, half the time each. Swinger wins $3,000 one time in ten, otherwise loses $300. Both average +$30 a trade. A year stops if the account hits $0.

10,000 simulated years for each trader. The first simulation uses fixed random seeds (one per trader), the run we checked; each new simulation draws new ones. No costs, no new money. A year’s drop is its biggest fall from a high, as a share of that high; the median drop is the middle year’s, and the worst drop is the biggest in all 10,000. The +$30 is an edge assumed for the example, not one found in any market; the $0 setting keeps the same payoffs and lowers the win chances (1 in 3 for Steady, 1 in 11 for Swinger).

04 // Losses

Why losses hurt more than wins feel good

A reference example: lose 50%, and you need +100% just to get back to where you started.

That part is arithmetic: a loss leaves a smaller account, so the comeback has to be bigger. Separately, researchers who studied how people weigh gains and losses found that “losses loom larger than gains” (Prospect Theory, Econometrica, 1979).

05 // Risk and reward

“Cut it now?” vs “It’ll come back”

You’ve heard it, maybe from yourself:
Up 10%: “Should I take it now?”
Down 30%: “I’m sure it’ll come back.”

That habit has a price. Take your winners at +10% and ride your losers to −30%, and you need to win 3 out of every 4 trades just to break even (same size each time, before costs). Flip it, and small losses with bigger wins let you be wrong more often and still come out ahead. That’s risk/reward.

And yes, sometimes it does come back. That’s the trap. In a coin-flip market (no edge either way, no costs, no expiry), a trade down 30% gets back to even before falling to −60% about half the time, so hope gets rewarded just often enough. The other half keeps falling, and one of those can erase six small wins. In that fair model neither rule wins on average. Holding just makes the bad years worse.

With options, time can work against you too: a bought option’s time value tends to shrink as expiry gets closer, other things equal (OIC on theta).

Researchers have a name for this: the disposition effect. A study of 10,000 brokerage accounts found investors had a “strong preference for realizing winners rather than losers.” Read the study (Journal of Finance, 1998).

06 // Losing streaks

Six losses in a row doesn’t, on its own, mean you’re broken

Win 55% of your trades, and over 252 trades (about a year at one a day) there’s about a 7 in 10 chance you’ll hit six losses in a row at some point.

Each trade is treated as independent: the chance of the next loss is still 45%, even after a streak.

A streak alone doesn’t tell you whether a method works. But bigger bets after a streak make whatever comes next bigger too.

07 // The screenshot

What the screenshot doesn’t show

A screenshot is a picture someone chose to share.

It doesn’t show the trades before it. It doesn’t show how big the account was. And the people whose accounts ran out aren’t the ones posting screenshots.

Made up: the screenshot

+$1,000

one winning trade

Made up: the whole trade block

  1. Trade 1+$1,000
  2. Trade 2−$100
  3. Trade 3−$100
  4. Trade 4−$100
  5. Trade 5−$100
  6. Trade 6−$100
  7. Trade 7−$100
  8. Trade 8−$100
  9. Trade 9−$100
  10. Trade 10−$100
  11. Trade 11−$100
  12. Trade 12−$100
  13. Trade 13−$100
  14. Trade 14−$100
  15. Trade 15−$100
  16. Trade 16−$100
  17. Trade 17−$100
  18. Trade 18−$100
  19. Trade 19−$100
  20. Trade 20−$100

20 trades: one +$1,000, nineteen −$100. Total −$900.

The same trade block, 20 made-up trades: the screenshot shows the one win; the ledger shows all of them.

In a study of day traders in Brazil’s futures market (2013–2015), 97% of those who kept at it for more than 300 days lost money after fees (Day Trading for a Living?, 2020). In Taiwan, fewer than 1% of day traders kept beating the market after fees from one year to the next (Journal of Financial Markets, 2014).

In the US, a study of retail trades in S&P 500 options that expire the same day (0DTE) found retail traders lost about $241,000 on an average trading day from February 2021 to September 2023, more than $125 million in all, and most of it went to the cost of trading (Retail Traders Love 0DTE Options… But Should They?, 2023). Across US stock and ETF options, a Journal of Finance study estimated retail traders lost $2.1 billion from November 2019 to June 2021 (Journal of Finance, 2023). Not every study agrees on how big the losses are: one that followed 2.2 million trades from US retail brokerage accounts found smaller losses per options trade, with the smallest traders losing about 3.4% a trade (An Anatomy of Retail Option Trading, 2024).

Small average gains, small losses, and time. That’s the whole idea. Whether your goal is $100 a day or building the account at 2%, the math is the same, and it’s yours to use.

A good-looking total is only the beginning of the question.

This page is arithmetic and a labeled model. It’s education, not advice, and it doesn’t tell anyone what to trade. 18+.

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