The ladder arbitrage that isn't: ten hours, 10,352 observations, $14.35
On a neg-risk temperature ladder exactly one rung wins, so buying NO on every rung looks like free money. It is EV-zero by construction, and the payoff is linear — more legs never helps. Ten hours of live book-watching found the executable condition crossing 8.89% of the time, a third of those in sizes below the venue's minimum order, and worth 0.145% on capital in total.
What this is about
Polymarket is a prediction market. You buy shares in a yes-or-no question — will the highest temperature in Tokyo be 24°C on 22 September? — and at settlement each share pays exactly $1.00 or exactly $0.00. Nothing in between. Questions cover weather, sports, elections and crypto prices, and most resolve within days.
I run an automated market maker on it. The bot quotes both sides of a market and earns the spread: buy one YES and one NO on the same market and the pair redeems for exactly $1.00 whatever happens, so the profit is locked the moment the second leg fills. Polymarket also pays a maker rebate for providing liquidity. The risk is the leftover — shares whose other half never filled, which go to settlement alone and pay 1.00 or 0.00.
Everything below comes from six weeks of live quoting with real money: 701 settled markets, $19,889 of deployed capital, one account, one venue.
Temperature markets come in ladders: 20°C or below, 21°C, 22°C … 30°C or higher — eleven separate binary markets covering one day in one city, of which exactly one resolves YES.
That structure invites an obvious trade: buy NO on every rung. At most one of them can lose, so the rest are free money. It is the single most natural-looking idea in prediction markets.
This piece is about why it does not work, and how close it nonetheless comes. There is a clean arithmetic reason the trade is worthless, and a ten-hour measurement of how near the books get to making it work anyway.
The arithmetic
Buy NO on any subset S of rungs, at prices qi = 1 − pi:
cost = Σ(1 − pᵢ) = |S| − Σpᵢ
P(winner ∈ S) = Σpᵢ ← the same number, by definition
E[payout] = |S| − Σpᵢ
EV = 0, for ANY SYour profit is exactly Σpi − P(winner ∈ S), and those are the same quantity. The payoff is linear in the number of rungs, so there is no threshold at which “buy more legs” turns it positive. Three rungs, seven rungs, all eleven — identical zero.
This is not a market-efficiency argument that might fail on a quiet venue. These ladders are flagged negRisk, and the venue provides a converter: NO on all-but-one converts to YES on the remaining rung plus collateral. The sum is arbitraged directly, as a single instrument, which is why it holds without any individual rung being priced correctly.
One thing does work, and it is worth stating because the intuition behind it is sound: extending an already-open position from S to S+{j} moves the guaranteed payout up by 1.00 and the cost up by askj, so profit changes by 1 − askj — positive for any ask under a dollar. Once you hold a locked position, every further rung taken below 1.00 strictly improves it. That is a different claim from manufacturing the position in the first place.
The condition that would be real
Buying NO at the ask on subset S, the worst case is the winner being inside S:
guaranteed payout = |S| − 1
locked profit = (|S| − 1) − Σ ask_NO
> 0 ⇔ Σ bid_YES > 1.00The sum of YES bids across the reachable rungs is the entire signal. No forecast, no fair value. Above 1.00 the trade pays whatever the weather does.
So: does it ever cross?
Ten hours of watching
231 passes over 10.35 hours, 70 ladders, 10,352 ladder-observations, zero failed passes.
| Count | Share | |
|---|---|---|
| Positive locked P&L | 920 of 10,352 | 8.89% |
| … with ≥5 shares on every rung | 616 | 67% of those |
| Distinct episodes | 165 | |
| … viable (some pass reachable) | 119 |
A third of the “opportunities” are unbuyable. The thinnest rung held 0.1 to 3.1 shares — below the venue's five-share minimum order size. You cannot place that order at all.
And the money, taking every viable episode once at its best moment:
| Value | |
|---|---|
| Total edge | $14.35 |
| Total capital | $9,879.51 |
| Blended return over 10.4 hours | 0.145% |
To capture fourteen dollars you would lay out nearly ten thousand, across 119 separate multi-leg takes, each tranche locked until its market resolves. The best single observation was $1.20.
Why the real number is worse than $14.35
Execution risk eats the entire edge. The median edge is about 1.2c per set across four to nine rungs. You must take every rung; each take moves the book; you cannot take them simultaneously. One rung slipping a single tick wipes out that ladder's profit.
The persistence is a warning, not a feature. Two ladders held a “risk-free” edge for 100 minutes. A genuine arbitrage does not survive 100 minutes on a public venue with roughly 32 effective makers. That strongly suggests the quoted asks are not executable — stale snapshots, or offers that vanish when touched. The only way to find out costs real money.
What the books actually look like
The structural reason most ladders are not candidates at all:
Tokyo, 11 rungs: 7 with ZERO ask levels
against 27–42 BID levels holding 4,000–8,000 shares at 0.999The dead rungs are one-sided, not illiquid. Everyone wants to buy NO at 0.999 for a free 0.1c; nobody will sell it. A passive bid there joins a queue eight thousand shares deep for a 0.05c payoff on a rung that never trades.
Buying only the four reachable rungs loses: asks summed to 3.018 against a guaranteed payout of 3.00. −1.8c per set — the no-arbitrage result appearing as a number, which is the spread you paid to find out.
Of fourteen ladders scanned in one pass, twelve had fewer than two takeable rungs.
The closest it came
London, 21 September Σ(bid_YES) 0.9970 locked −0.0030 122.7 shares at the touchThree tenths of a cent from risk-free, with real size behind it. Still the wrong side.
Across the night the sum ran a median of about 7 cents short, min 0.4060, max 1.0040 — and it does move: 12 of 13 ladders shifted a median of 0.0100 over two minutes at constant basis, with one genuine 23-cent excursion.
One measurement caveat that cost me a wrong conclusion. The sum is taken over rungs that can be bought, and that set changes. One ladder read 0.4060 then 0.9360 two minutes later — a half-dollar move that was entirely a rung becoming takeable, not a repricing. Any series built on this must group on the reachable count before differencing, or it will measure its own basis changing.
What this establishes
Does: that the ladder structure gives zero edge by construction and that adding legs does not change it; that the executable condition crosses about 9% of the time on temperature ladders, in sizes usually below the minimum order; that the total available on one representative night was 0.145% on capital.
Does not: that it never pays. Ten hours is ten hours, on one venue, in one market family, in fair weather. A forecast update that gaps a single rung is exactly the event that would produce a real crossing, and nothing here sampled such a moment.
The honest summary is that these ladders are not perfectly efficient — the sum deviates from 1.00 by up to 3.65c in both directions — but the inefficiency is reliably smaller than the cost of touching it.