The Lab

Where the idea comes from

• How long you hold changes the odds. That a steady average shows through the noise only over time is the square-root rule behind every average: the noise of an average shrinks with the square root of how many months it covers. It goes back to Abraham de Moivre (1733) and Pierre-Simon Laplace (1812).
• Picking the strategy by the market's state is the question of our earlier pages "Two conditions together: does a grid do better?" and "Stay out in bad markets?", and of our page on the bots' market words, "Does the market's mood warn of a bot's losses?". Those asked it for grids alone, or for the paper bots hour by hour. This page asks it between strategy types.
• The four types are exactly as their own pages have them: "Two opposing Bitcoin grids: do they beat holding, or the carry?" and "The same long, held two ways: plain coins, or coins plus a hedge that earns funding".

How we tested

• Bitcoin, month by month, April 2020 to September 2026: 78 months.
• Four types, each with its real fees and funding:
  • Hold: Bitcoin bought and held, no leverage.
  • Carry: Bitcoin held and the same dollars shorted, collecting the funding: the carry page's book.
  • Two grids: a long and a short grid on the same rungs, 30% range, 20 rungs, 2x each, set fresh each month: the two-grid page's book.
  • One grid: the long grid of that pair alone, all the money at 1x.
• How long: from every start month, each type run for 1, 3, 6, 12, 24 and 36 months. How often did it end ahead, and ahead of each other type?
  • Start months next to each other share most of their months, so 43 three-year runs are really only about two separate three-year spans. The band beside each share shows this. It reshuffles the history in runs of about 6 months, 1,000 times, and gives the middle 90% of what came out.
• When, with the bar fixed before the run:
  • each start month labelled by the month before it: Bitcoin up or down; calm or wild (how much it moved hour to hour); funding low or high;
  • the first 39 months learn which type did best after each label, alone and all three together (8 labels). A label seen fewer than 5 times is "unknown", and runs the default;
  • the default is the first half's best type overall;
  • the last 39 months judge. Following the labels (paying 0.2% to switch type) must beat always running the default, by more than 95% of shuffled and shifted labels manage.

The maths, step by step

1. Each type's month, in two numbers. Its average month and how much months swing around it:

In log terms, which compound simply.

2. Over n months, the average adds up n times, but the swing only √n times. Holding for 12 months: 12 × 3.3% = 39.5% against √12 × 17.3% = 59.9%.

3. The chance of ending ahead is how often a bell curve lands above 0. Here that is 39.5 ÷ 59.9 = 0.66 swings above 0: about 75%. For the carry: 12 × 0.9% = 10.8% against √12 × 1.6% = 5.6%, 1.9 swings above 0: about 97%.

4. So a small, steady return wins the odds sooner, and a large, wild one wins the size. The carry needs months to be nearly sure. Holding needs years, and is still not sure.

What we found: how long

1. How often each type was ahead, by how long it ran.

Share of start months that ended ahead. In brackets, the band.

• The carry was ahead in 92% of 3-month runs and every run of 2 years or more. It lost money in 12 single months of the 78.
• Holding was ahead in only 58–69% of runs until 3 years. Every 3-year run was ahead, but the band runs from 26% to 100%: those runs all started between 2020 and 2023, at the start of a long rise. The bell curve in step 3 gives about 87%.
• The single grid was ahead about three times in four, and in 95% of 2-year runs.
• The two grids were ahead least often over a year or more (69–77%).

2. What each run typically ended at (the middle run):

3. Who beat whom.

• Holding usually ended with more than the carry, and more often the longer it ran. But not reliably: the bands are wide.
• Two grids almost never beat the carry over a year or more: 25% of 1-year runs, 2% of 2-year runs, none of the 3-year runs.

What we found: when

4. No label said which type to run. The first half's best type overall was holding. So holding was the default, and in almost every label holding was also the first half's best:

• Three maps never switched, so they could not beat holding. The funding map switched 13 times and ended with less.
• Eight labels split 39 months into groups of 2 to 8. Four were too thin to name at all. That is why "when" can't be proven on this history: there are too few months in each kind of market.
• The market changed under the labels. Of the last 39 months only one was "wild" by the first half's measure. A cut from one era says little about the next, as our page "Stay out in bad markets?" also found.
• Hindsight is no guide: picking the best type each month after the fact would have made ×16.75 over the second half. No label came close.

5. Looking back, holding did best on average whatever the month before was. The average month over all 78 months, by the month before:

Every type did better after an up month and after a wild one. Their order hardly changed.

What it means

• The answer to "when" on this history is "how long", not "which month". The month you start in, read by trend, swing or funding, did not tell which type would win.
• Small and steady wins the odds early. The carry was nearly always ahead after 3 months, but ended with far less than holding.
• Large and wild needs years. Holding ended with the most, but a 1-year run was ahead only 60% of the time.
• Two grids were the weakest by both measures: least often ahead over long runs, and ended with the least.
• This agrees with our page on the bots' market words. At its look of 16 October 2026 those words had not been shown to warn of losses. Its next look is due 21 October 2026. Both pages say the same: no reading of the market has yet been shown to say what comes next.

Credits

• Abraham de Moivre, The Doctrine of Chances, 2nd edition, 1738 (first in a 1733 note), and Pierre-Simon Laplace, Théorie analytique des probabilités, 1812: the bell curve, and why an average's noise shrinks with the square root of its count.
• Dimitris N. Politis and Joseph P. Romano, "The Stationary Bootstrap", Journal of the American Statistical Association, 1994: the resampling behind the bands.
• R. A. Fisher, The Design of Experiments, Oliver and Boyd, 1935: the shuffled labels.
• Our own: the four types side by side, the horizons and the labels.
• Data: Binance's public 1-minute futures trade prices; Bybit's public funding history and fees.
• PerpGremlin and Claude, How long until a strategy comes out ahead, and can the market say which to run?, TerminalGremlin, 2026: the tests, the code and the words.