Why every market on Rizon is 50/50 (and why that's where your edge is worth most)

Short answer: A better forecast earns the most where the market is most uncertain. Your edge in probability is roughly your forecast edge times the density at the strike, and the density peaks near the median, where a contract costs 50¢: know the median 0.2 standard deviations better than the market and a 50¢ contract is worth 7.9¢ more to you, a 3¢ one 1.6¢, at half the Sharpe ratio. Yet of 173 prices we recorded on the Polymarket and Kalshi markets that Rizon's markets replace (Oct 29, 2026), 98 were under 10¢ or over 90¢ and 5 were between 40¢ and 60¢. Rizon's books move the strike instead of the price, so every contract trades at 50/50.

This post works through the arithmetic behind the first claim of the manifesto, the survey of today's prices, and the caveats a careful trader should raise.

The argument in one line#

A contract that pays $1 if a number X finishes above a strike k is worth P(X > k), so its price is the market's probability. If your forecast of X is the market's, shifted up by a small amount δ, your probability is about P(X > k) + f(k) × δ, where f(k) is the density of X at the strike. Your edge, in cents per $1 contract, is your forecast edge times the density at the strike.

For any single-peaked distribution the density is highest in the middle and thin in the tails. So the same forecast is worth the most on contracts priced near 50¢ and the least on contracts priced near 0¢ or 100¢, whose strikes sit far from where the number is likely to land.

What a 0.2σ edge is worth, contract by contract#

Take a number that's normally distributed, the market's median at m and yours at m + 0.2σ. Each row is the contract that pays $1 if X finishes above the strike the market prices at that level; with your forecast, you'd buy it.

Edge is your probability minus the price. The Sharpe per contract is the edge divided by the standard deviation of the $1 payout under your probability. Kelly growth is the expected log growth of a bankroll that puts the Kelly fraction, (your probability − price) ÷ (1 − price), into each trade.

Three things stand out:

• The edge in cents peaks in the middle: 7.93¢ at 50¢, against 1.64¢ at 3¢ and 1.13¢ at 97¢.
• So does the edge per unit of risk: the Sharpe at 50¢ (0.161) is about twice the Sharpe at 3¢ (0.078).
• So does what compounds: Kelly growth at 50¢ (1.26% a trade) is about three times the growth at 3¢ (0.40%).

For a finite edge the exact peaks sit a few cents off 50¢ (the edge in cents peaks at 46¢, the Sharpe at 53¢, Kelly growth near 44¢), and 50¢ is within 1% of each. As the edge shrinks, all three converge on the median. A contract that pays 2× is the 50¢ row: you risk $1 to make $1.

Where today's markets are priced#

On Oct 29, 2026, between 08:05 and 08:40 UTC, we recorded the mid price (the average of the best bid and best ask) of every bucket, date or strike in 18 markets on Polymarket and Kalshi that Rizon's markets replace. Three are sampled: 9 of the US–Iran ceasefire market's 22 dates (the others include the dates from Sep 20 to Oct 24, already resolved), and the middle 9 or 10 of the roughly 30 ranges in each of Elon Musk's two weekly post-count markets. The prices left out are further into the tails, so the full count would be more lopsided, not less.

None of the 13 bucket markets, which sell ranges or outcomes, had a single price between 40¢ and 60¢. Four of the five cumulative ladders ("by" dates, "above" and "how high" levels) did, because a ladder lists some date or level near the median. That's the horizon idea with a short list of strikes the venue picked, each its own market with its own book: Polymarket's ceasefire dates near the median traded $147K–$654K each, while its Anthropic "IPO by" dates near the median traded $4K–$65K.

The caveats#

Cheap tails pay more per dollar, and lose more often. At 3¢ the expected return per dollar paid is 54.7%, against 15.9% at 50¢. But you lose 95.4% of the time, the Sharpe is half, and the Kelly growth is about a third. Per unit of risk, and for a bankroll that compounds, the middle wins.

The density peaks at the mode, not the median. For a symmetric number they're the same point. For a skewed one, like a market cap or a count with a long right tail, the density peaks a little off the median, so the 50/50 strike is near, not exactly at, the strike where a forecast edge is worth the most.

Some numbers have no middle. On Oct 29 the Fed's December 9 decision had two likely outcomes: a 25 bp hike at 76.5¢ and no change at 21.5¢ (Polymarket mids). Any strike between them is a hike-or-not contract worth about 79¢, so a book at 2× would be one-sided. Rizon lists the rate at the end of 2027 instead, where more than a year of meetings spreads the outcome out: see Bucket markets vs one book: the Fed's December decision.

The edge has to be real, at the strike you trade. At 2× you need to be right more than half the time. As a taker you trade at the far side of the book (Higher at the best ask strike, which sits above the midpoint), so your forecast has to beat that strike, not the midpoint.

What 50/50 at 2× means for sizing#

At 2× your risk equals your reward: a $100 contract makes $100 or loses $100. Over a run of trades at one size, your PnL is that size times the number of wins minus the number of losses, and break-even is a 50% hit rate. For an even-money contract you expect to win with probability q, the Kelly fraction is 2q − 1 of your bankroll: 15.9% at q = 57.9%, the 0.2σ example above. Forecast edges are uncertain, so many traders size at a fraction of that.

On Rizon you'd express the same view on any listed market the same way, one contract at the market's median: Higher on House seats if you think Republicans will win more than the book's median (the buckets implied 196.6 on Oct 29), Lower on the Fed's 2027 rate if you think it will end below the book's.

FAQ#

Why does every contract on Rizon pay 2×?#

Because the price is fixed and the strike moves. Paying your size to get 2× back is the same as buying a $1 contract at 50¢, so the book competes on the strike, and it settles around the strike the market sees as 50/50.

Is a 3¢ contract a better deal if I'm right?#

It pays more when it wins, and per dollar its expected return can be higher, but it loses most of the time. With a 0.2σ forecast edge, a 3¢ contract has about half the Sharpe ratio of a 50¢ one and about a third of the Kelly growth.

Where does the 50/50 strike come from?#

From the order book: Higher orders bid strikes, Lower orders ask them, and they meet around the strike the market sees as equally likely to be beaten or not, its median. The midpoint of the best bid and ask is the forecast.

Does every number have a 50/50 strike?#

Only if its outcome spreads over enough values. A number with two lumpy outcomes, like the Fed's December decision on Oct 29, 2026 (a hike at about 77¢), has no strike near 50/50, so Rizon lists a version that does: the rate at the end of 2027.

Is Rizon real money?#

No. Rizon is paper trading: practice money, no deposits. The prices in this post are Polymarket's and Kalshi's, recorded on Oct 29, 2026.