RizonBitcoin Up or Down fair price: what a 5-minute window is worth right now
The fair price of Polymarket's Bitcoin Up or Down markets, live, by how far the average is from the price to beat and how long is left. With the formula.
Short answer: A Bitcoin Up or Down window is worth the chance that Bitcoin's 60-second average at the close finishes at or above its 60-second average at the open. That chance depends on two things: how far the average is from the price to beat, and how long is left. At 2 minutes left, $25 above is worth about 64¢. At 30 seconds left, the same $25 is worth about 98¢, because most of the closing average is already known. If the market's price is above fair, buying it loses money on average, before the fee.
The tool reads Bitcoin from Coinbase through Rizon's public API. Polymarket's windows settle on Chainlink's BTC/USD 60-second average instead, which can differ by a few dollars, so treat the last few cents as noise.
Fair price by distance and time left
Each cell is the fair price of Up in cents, for Bitcoin moving $8 per root second (about 56% a year at $80,000). Down is 100 minus it.
| Average above the price to beat ($) | 4:00 left (¢) | 2:00 left (¢) | 1:00 left (¢) | 0:30 left (¢) | 0:10 left (¢) |
|---|---|---|---|---|---|
| 0 | 50.0 | 50.0 | 50.0 | 50.0 | 50.0 |
| 5 | 51.8 | 52.8 | 55.6 | 65.4 | 98.0 |
| 10 | 53.5 | 55.6 | 61.0 | 78.5 | 100 |
| 25 | 58.7 | 63.7 | 75.8 | 97.6 | 100 |
| 50 | 67.1 | 75.8 | 91.9 | 100 | 100 |
| 100 | 81.2 | 91.9 | 99.7 | 100 | 100 |
Two things stand out. Nothing much happens until the last minute: with 4 minutes left, even $50 above the line is only worth 67¢. Then it goes fast: the closing number is an average of the last 60 seconds, so by the final 10 seconds there's almost nothing left to decide. In the last row of a real window, a $5 lead is close to settled.
The formula
Call the moves in Bitcoin's price a random walk with volatility σ, in dollars per root second. The number that settles the window is the average over its last 60 seconds, so the sum has two parts: where the price goes before that minute starts, and how the average drifts inside it.
| Time left, t | The closing average's expected value | Its standard deviation |
|---|---|---|
| More than 60 s | The price now | σ × √(t − 40) |
| Under 60 s | (seconds of the last minute gone × their average + t × the price now) ÷ 60 | σ × √(t³ ÷ 3) ÷ 60 |
Fair Up = Φ((expected closing average − price to beat) ÷ standard deviation), where Φ is the normal distribution's CDF.
The −40 comes from the average: a price over a minute's average has a third of a minute's variance, so a window with t seconds left behaves like one with t − 40. Windows that settle on one price have σ × √t instead, which is why tables built for the old rule overstate how much can still happen at the end.
What it's for
| If you're | Use it to |
|---|---|
| Taking a price | See how much you're paying over fair. At 50¢ Polymarket's taker fee is 1.75¢ a share, so you need that much edge just to break even: fee calculator |
| Making a market | Sanity-check your quotes before they go stale: how market makers make money |
| Building a bot | Start from a fair value instead of a hunch: build one with Claude Code |
Why fair isn't the same as profitable
The tool assumes Bitcoin has no drift and that volatility holds. Neither is exactly true, and volatility is the one that bites: it jumps around CPI, FOMC and liquidations, and a table at $8 is wrong by a lot at $20. Real windows also show effects this ignores, like how often Bitcoin reverses in the last 30 seconds.
And a fair value is only useful if you can trade at it. Late in a window the book thins, the spread widens and fast bots get there first. To see how that feels with nothing at risk, Rizon's Bitcoin books run on the same price with paper money, and a bot on them picks off any quote that goes stale.
FAQ
How does Polymarket decide Bitcoin Up or Down?
By Chainlink's BTC/USD 60-second average: the average at the window's start sets the price to beat, the one at its end is the final price, and Up wins if the final price is at or above it. Polymarket's market rules name the Chainlink stream.
Why is the fair price 50¢ when the price is at the line?
Because with no drift, the closing average is as likely to finish above the line as below it, however long is left. Distance from the line is what moves it, and time left decides how much that distance is worth.
What's a good price to buy Up at?
Any price below fair by more than your costs. At 50¢ that's more than the 1.75¢ taker fee plus the half-spread you cross, and more than the error in your volatility.
Does this work for the 15-minute market?
Yes: the same formula, with more time left. The tool shows both. Kalshi's 15-minute market settles on a different index, so its numbers will differ a little.