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Guide · updated Oct 18, 2026

15‑minute fair value The 1900 math behind the odds

A Kalshi 15-minute contract pays $1 if it settles your way and nothing if it doesn’t, so its fair price is simply the chance it settles your way. Here’s how to estimate that chance from three numbers, where the math comes from, and the moments it gets wrong.

In short

  • The price is a probability. 64¢ means the market puts it at about 64%. Your trade only makes sense if your own estimate is higher than what you pay, after the fee.
  • Three numbers set the chance: how far the price is from the line, how much it usually moves, and how much time is left.
  • The math is from 1900, and it’s good in ordinary minutes. It underestimates sudden jumps, which is why the size of every bet matters more than the formula.

The three numbers

Distance to the line

How far the price is above or below the window’s line right now. $40 under the line is the starting point of our example.

The typical move

How much the price usually moves in one minute, measured from a recent stretch of one-minute changes. A calm market has a small one, a wild market a big one.

Time left

Minutes until the window closes. More time gives the price more room to wander back across the line.

How each window settles, and where its line comes from: How Kalshi’s 15-minute markets work.

The equation

z = distance ÷ (typical move × √minutes left)How many typical moves stand between the price and the line, for the time that’s left.

chance of Up = Φ(z)Φ is the bell curve read as a probability: Φ(0) is 50%, Φ(1) is about 84%, Φ(−1) about 16%, Φ(2) about 97.7%.

chance of Down = 1 − chance of UpThe two always add up to 100%.

edge = your chance − the priceIn cents, before Kalshi’s fee.

Why the square root of time. Random moves partly cancel each other out, so the price spreads out with the square root of time, not in a straight line. Four minutes spreads the outcomes about twice as far as one minute, not four times. That was Bachelier’s key result in 1900 MacTutor: Louis Bachelier.

The last minute counts less. Kalshi settles these windows on an average of the index over the final minute, not on one last price Kalshi Help: crypto markets. An average moves less than a single print, and for a random walk the final minute’s average carries only about a third of a minute’s movement. So in the formula, take about two thirds of a minute off the time left.

Worked example

Distance to the line−$40The price is $40 under the line
Typical one-minute move$25From a recent stretch of one-minute changes
Time left9 minCounted as 8.33 after the settlement average
Typical move for the time left$72$25 × √8.33
z−0.55−$40 ÷ $72
Chance of Up29%Φ(−0.55)
Chance of Down71%100% − 29%
Down costs64¢The ask on the Down side
Edge before the fee+7¢71% − 64¢
Edge after the feeabout +5.4¢Kalshi’s taker fee at 64¢ is about 1.6¢ a contract, $0.17 on 10, rounded up per order Kalshi fee schedule

So by this math, Down at 64¢ is worth about 71¢. That gap is the whole reason to trade, and it’s only as good as the three numbers that went in. The fee math, with more prices: How Kalshi prices and fees work.

Try your own numbers

It starts on the worked example. Change any number and the chance, the edge and the curve update. Nothing here places a trade.

The price is

How far the price is from the window’s line right now.

How much the price usually moves in one minute.

1 to 15.

Your side

1 to 99.

Chance of Up29%
Chance of Down71%
Your side’s chance71%
Edge before the fee+7.0¢
Fee, about1.6¢
Edge after the fee+5.4¢

By this math, Down at 64¢ has about +5.4¢ of edge after the fee. It’s an estimate, so size small.

Where the price could finish in 9 minutes A bell curve centred on the price now. The shaded part, right of the line, is the chance of finishing above: about 29%. The rest, about 71%, finishes below. Price now The line Up 29% Down 71%
Where the price could finish, centred on the price now. The shaded part is the chance of finishing above the line. It starts on the worked example and redraws as you type.
Chance of Up for five distances, with a $25 typical one-minute move. Less time left means the same distance matters more.
Distance to the line9 minutes left3 minutes left
−$8013%2%
−$4029%15%
$050%50%
+$4071%85%
+$8087%98%

Where the math comes from

Three hundred years of gamblers, botanists, physicists and traders, in fourteen lines.

  1. 1718Abraham de Moivre publishes The Doctrine of Chances, probability worked out on dice and card games. MacTutor: Abraham de Moivre
  2. 1733De Moivre shows that many coin flips add up to a smooth bell shape, in a pamphlet later added to his book. Today it's called the normal curve. MacTutor: Abraham de Moivre
  3. 1809Carl Friedrich Gauss, and Robert Adrain a year earlier, show that measurement errors follow the same curve. Online Stat Book: history of the normal distribution
  4. 1827Botanist Robert Brown watches pollen grains jitter at random in water. The jitter becomes known as Brownian motion. Yale: Brownian motion, some history
  5. 1900Louis Bachelier's thesis, Théorie de la spéculation, models Paris market prices as a random walk, shows the spread of outcomes grows with the square root of time, and prices options. Henri Poincaré writes the report. Almost nobody reads it for fifty years. MacTutor: Louis Bachelier
  6. 1905Albert Einstein explains Brownian motion as molecules hitting the grain, apparently unaware of Bachelier. Yale: Brownian motion, some history
  7. 1923Norbert Wiener puts Brownian motion on a rigorous mathematical footing. Yale: Brownian motion, some history
  8. 1950sStatistician Jimmie Savage mails economist Paul Samuelson a postcard telling him to read Bachelier. The idea returns to economics. History of Data Science: Louis Bachelier
  9. 1956John Kelly at Bell Labs works out how much of a bankroll to bet when you have an edge. Ed Thorp later uses it at the blackjack table. Wikipedia: John L. Kelly Jr.
  10. 1963Benoit Mandelbrot shows cotton prices have far more extreme moves than the bell curve allows. Mandelbrot (1963), Journal of Business
  11. 1965Samuelson models percentage moves instead of dollar moves, so prices can never go below zero. Imperial College notes on Samuelson (1965)
  12. 1973Fischer Black and Myron Scholes publish their option pricing formula; Robert Merton extends it the same year. Scholes and Merton win the 1997 Nobel Prize; Black had died in 1995. Wikipedia: Fischer Black Merton (1973), Bell Journal of Economics
  13. 1987On October 19 the Dow falls 22.6% in a day. Option prices start charging for crash risk the formula leaves out. Wikipedia: Black Monday (1987)
  14. 1998Long-Term Capital Management, with Scholes and Merton on its board, loses $4.6 billion in under four months. Wikipedia: Long-Term Capital Management

Where it breaks

Jumps the curve calls impossible

Mandelbrot found in 1963 that real prices have far more extreme moves than the bell curve allows Mandelbrot (1963), Journal of Business. The Dow’s 22.6% fall on October 19, 1987 is the classic case Wikipedia: Black Monday (1987).

Crypto bunches its wild minutes

A 2024 study of high-frequency Bitcoin returns found tails fatter than the normal curve, with calm and wild stretches clustering together Tang et al. (2024), arXiv. A typical move measured in a calm stretch understates the next minute when news hits.

Big bets turn small errors into ruin

Long-Term Capital Management had two Nobel winners on its board and borrowed more than 25 times its capital. It lost $4.6 billion in under four months in 1998 Wikipedia: Long-Term Capital Management. For a trader, the version of that mistake is betting big on an estimated chance.

The market has its own bias

On Kalshi, cheap contracts win less often than their price says: a 5¢ contract that wins 2% of the time loses 60% of the money put in, according to a study of over 300,000 contracts VoxEU: the economics of Kalshi. A price is a good probability, not a perfect one, and so is any formula.

Why it’s a digital option

A contract that pays a fixed amount if the price finishes above a strike, and nothing otherwise, is what finance calls a cash-or-nothing digital option. In the Black-Scholes model its value is the probability of finishing above the strike, written N(d₂), discounted for interest Ryan O'Connell Finance: binary and digital options.

Over 15 minutes the interest is too small to matter and the price barely moves in percentage terms, so Bachelier’s 1900 version and Black-Scholes give almost the same number. Reading prediction-market prices as probabilities has its own research behind it too Wolfers and Zitzewitz, Prediction Markets (NBER).

Using it without getting hurt

  • Your chance is an estimate. Write it down before you look at the price.
  • An edge of a cent or two is mostly fee. At 64¢ the fee alone is about 1.6¢ a contract.
  • Size small. Full Kelly on this example says 20% of the bankroll, which is far too much for a number that came from an estimate. We teach a quarter of Kelly under a 5% cap: Bankroll and units.
  • It’s okay to pass. No edge after the fee means no trade.

Our agents start from this family of math and add their own rules, which we don’t publish. You can watch every one of their trades in the Lab.

Questions people ask

How do you work out what a Kalshi 15-minute contract is worth?

Its fair price is the chance it settles your way. A standard way to estimate that chance uses three numbers: how far the price is from the window's line, how much the price usually moves in one minute, and how many minutes are left. Divide the distance by the typical move times the square root of the minutes left, then read the chance off the bell curve.

Is Black-Scholes used for prediction markets?

A Kalshi up-or-down contract pays $1 or nothing, which finance calls a cash-or-nothing digital option. Black-Scholes prices one as the probability of finishing above the strike. Over 15 minutes, the simpler random-walk version from 1900 gives almost the same number.

Who came up with the random walk model of prices?

Louis Bachelier, in his 1900 thesis at the Sorbonne. He modelled market prices as random moves, showed the spread of outcomes grows with the square root of time, and used it to price options, five years before Einstein's paper on Brownian motion.

Why doesn't the model always work?

It assumes the price moves at its usual pace. Real prices have sudden jumps, called fat tails, far more often than a bell curve allows, and the typical move is measured from the recent past, so it goes stale when news hits.

If the math says I have an edge, how much should I bet?

Small. The chance is an estimate, so full Kelly sizing overbets. We teach a quarter of Kelly, never more than 5% of the bankroll on one position, and no trade when the edge is under the fee.

Education, not betting or financial advice. A model gives an estimate, not a promise, and every trade can lose. Gambling problem? Call or text 1-800-MY-RESET.