Glossary

American odds use two formulas depending on whether the implied probability is below or above 0.5. Below: positive odds, +(1-p)/p × 100. At/above: negative odds, -p/(1-p) × 100. Same split as american-decimal-conversion.

american-decimal-conversion: Sportsbook-style odds; positive (e.g. +150) means win $150 on $100 stake, negative (e.g. -120) means stake $120 to win $100. Mimir's canonical even-money form is -100.

american-implied-probability: Sportsbook-style odds; a signed integer like +150 or -120. Positive numbers say what you win on $100 staked; negative numbers say what you stake to win $100.

Headline guaranteed-profit margin on a one-dollar combined position. Kairos computes it as (1 − p_side − p_opp) × 100 where p_side and p_opp are fee-adjusted implied probabilities of the two legs.

A market with exactly two outcomes (e.g. Team A wins vs. Team B wins). The two-way arb formula assumes binary; three-way markets need a different formula.

Combined exposure across two or more legs at different strikes of the same spread or total market. The economically correct view is the sum-by-outcome payoff vector, not the sum-of-stakes.

Kairos's market-type partition: 'game' (moneyline — who wins), 'spread' (margin-of-victory line), 'total' (combined-score line). Each carries different fee rules; in particular, Kalshi spread/total buckets are fee-exempt today while game buckets are not.

Two ways to take the same economic position. Buying No at X cents costs the same payoff structure as selling Yes at (100 - X) cents, modulo execution differences (maker/taker side, queue position, fee schedule).

Kalshi's native price unit. A price of 65 cents means a $0.65 payment for a contract that pays out $1 on the right resolution. Equivalent to an implied probability of 0.65.

The first step of the conversion: a Kalshi cent price X maps directly to implied probability X/100. A Yes at 65¢ implies P(Yes) = 0.65; a No at 36¢ implies P(No) = 0.36.

On a single binary market, yes_price_dollars + no_price_dollars sum to $1.00 (per Kalshi's docs for matched fills). The cent prices on the order book do not sum to exactly 100 — the gap is the implicit cost of crossing the spread plus fees.

When you hold positions across multiple Kalshi strike-binaries on the same game, you are holding a blended-spread-position whose payoff curve is computed by summing per-leg P&L over the integer-margin (or total) outcomes. Each Kalshi binary contributes one leg.

A single implied probability per outcome, aggregated across multiple books' devigged lines. The 'market's collective belief' about the outcome.

The price you actually paid per contract on average across all fills, weighted by quantity. Used to know what your position is worth relative to the current market price.

Two-leg arb where both legs are at sportsbooks (no Kalshi leg involved). Same math; different friction profile.

The operation -P that converts a price on one side of a binary market into a target on the OTHER side. Just the negation of an American odds value.

american-decimal-conversion: Total payout (stake + winnings) per $1 stake; e.g. 2.50 means $2.50 returned for every $1 bet.

expected-value-basic: Total payout per $1 stake, including the stake itself. See american-decimal-conversion.

Stripping the vig out of posted prices to recover the book's underlying fair belief about each outcome.

Common shorthand for positive EV expressed as a fraction of stake. A 5% edge means you expect to win 5 cents per dollar staked over the long run.

The per-side, per-bucket totals (qty, stake, win) you actually want to read on screen, after the aggregator has applied fee handling and venue-format conversion. Stake = cash out of your account; win = net profit on resolution.

Two-tier framework: VF target is the minimum threshold (clearing it means at least fair-probability +EV); MBA target is the true goal (clearing it means better than the consensus implicit position).

A bet whose payout equals its stake — win $1 on $1 wagered, with implied probability 50%. Decimal 2.00; American +100 or -100 (Mimir uses -100 as canonical).

The average return per unit stake over many repeated trials, given a probability of winning. Positive = favorable, negative = unfavorable.

american-implied-probability: The probability of the outcome with the book's vig stripped out — the book's underlying belief about the outcome, not its quoted price. See devigging.

book-vig-overround: The book's underlying belief about an outcome, with the vig stripped out. See devigging.

devigging: Probability of an outcome with vig stripped out — the book's implicit belief, not its quoted price.

expected-value-basic: The probability of an outcome with the book's vig stripped out. The right input to EV when you want a meaningful edge number. See devigging.

The American-equivalent that includes Kalshi's per-trade fee in the risk and profit numerators. Kairos exposes this via kalshi_half_maker(cents); the unadjusted (raw) American conversion ignores fees. The two differ by ~0.3-1.5% depending on price and bucket.

Implied probability computed from the price the operator actually pays, including venue fees. For Kalshi, Kairos uses the half-maker fee (0.875% net of rebate) baked into the AM column.

Spread and total markets on Kalshi are fee-exempt today (game/moneyline markets are not). This affects the cents → American conversion (raw vs. fee-adjusted) and the dollar economics of holding a blend.

A single trade execution — one contract or one bet transacted at one price. The atomic unit of position state; if you bought 100 contracts in three batches, you had three fills.

The .5 in a strike like -3.5 — distinguishes from the integer line -3. A half-point eliminates the push at the integer margin; the price difference between -3 and -3.5 is roughly the market's estimate of the push probability.

Sportsbook spreads typically use half-points (-3.5, -7.5) to eliminate pushes. Kalshi binary markets use integer thresholds ('win by 4 or more'). The semantic equivalence is: -3.5 sportsbook cover = 'win by 4 or more' Kalshi binary.

A second bet placed to offset the directional risk of a first bet. In an arb, the two legs are mutual hedges — whichever side wins, the other loses, and the combined position pays a fixed amount.

Same as vig from the book's perspective — the share of money wagered that the book expects to keep over time.

A range of final-margin (or total) outcomes between two strikes of the same market where you collect on one leg and don't lose (or only partially lose) on another. Hooks are the structural 'free' value of holding a blend across strikes.

american-implied-probability: The probability a posted price would represent if the price were fair (no vig). Expressed as a fraction in [0, 1]. Real prices have vig built in, so implied probability usually needs to be devigged before it represents the book's true belief.

book-vig-overround: The probability a posted price implies if you treat it as fair (no vig). See american-implied-probability.

Each Kalshi strike-binary is its OWN market, with its OWN order book, its OWN Yes/No prices, and its OWN fee model. Different strikes do not share probability mass at the order-book level — they are correlated only through the underlying game.

Same as vig — the bookmaker's margin built into the prices.

A final-margin value that occurs disproportionately often in a sport. NFL: 3 and 7 (most common margins of victory). NBA: smaller hooks. MLB run lines are mostly 1 or 2. The half-point either side of a key number is more valuable than the half-point elsewhere.

An open piece of a position that hasn't been closed yet. If you bought 100 then sold 30, the remaining 70 sit as one or more lots, each with its own entry price.

The curated set of sharp books used in MBA computation — typically Pinnacle, BetOnline, Circa, BetCRIS in Kairos.

Major Book Average — the cross-book average of customer-facing American odds on each side of a market. Includes the vig (because customer-facing prices include the vig). Notation: MBA-Magic, MBA-Lakers.

The mirror — a claim that pays $1 if the market resolves No and $0 if it resolves Yes. Price in cents; implied probability of No-resolution.

Direction-of-question gotcha. Converting a Yes price gives American odds for the Yes outcome; converting the matching No price gives American odds for the No outcome. These are NOT the same number on opposite sides of the same game — they price different events with the spread loaded onto opposite sides.

Sum of implied probabilities across all sides of a market, minus 1. A measure of how much vig is built into the market.

Averaging in implied-probability space (then converting back to American), rather than averaging American-odds integers directly. The probability-space average is the canonical one.

Devig method that solves in z-score space: convert each implied probability to its inverse normal CDF, then find a constant shift c such that the shifted Φ-values sum to 1.

An outcome that lands exactly on a whole-number strike, refunding the bet. -3 has a non-zero push probability when the actual margin is 3; -3.5 has none.

Holding a leg at a strike that returns your stake when the game lands on a key margin, while another leg in the same blend pays out. The integer-strike leg pushes (refund) instead of losing, turning what would be a dead-zone outcome into a positive one.

EV computed using the price's own implied probability (vigged) as the win-probability input. Always zero by construction; not actually informative.

A book whose prices are considered to reflect the true market — typically Pinnacle, Circa, Bookmaker. Contrast with 'soft book.'

A book whose prices may lag or be biased relative to sharp books — typically mass-market US retail books. They take recreational action and price for that audience.

A bet on margin of victory rather than who wins outright. -3.5 means 'this team must win by more than 3.5 points'; the line equalizes the matchup.

The line at which a spread or total is priced — e.g. -3, -3.5, +7. Each strike is a different bet, even on the same market.

On Kalshi, a spread or total is expressed as a series of independent binary markets at different integer thresholds — e.g. 'Patriots win by 3 or more', 'Patriots win by 7 or more', 'Patriots win by 10 or more'. Each market is its own Yes/No book.

The price you need to beat on the side you're considering, derived from the OTHER side's MBA or VF via the cross-side flip.

A bet on the combined score of both teams (e.g. 'over 47.5'). Independent of which team wins.

Buying one side of a binary market at one venue and the opposite side at another, where the combined fee-adjusted implied probabilities sum to less than 1.0. Profit is guaranteed regardless of outcome, modulo execution risk.

Vig-Free — a devigged price pair where implied probabilities sum to exactly 1.0. Can be computed from a single book's two-sided line OR from the MBA pair. Strips the vig.

Kairos shorthand for the devigged fair price on a given side — the American odds equivalent of the fair probability after probit devigging.

The bookmaker's built-in margin — what they take per dollar of risk. Also called juice, the take, the cut, or hold. Compensation for warehousing risk on both sides of an event.

EV computed using the devigged fair probability as the win-probability input. The meaningful number for sharp pricing.

How much each book's contribution counts in the average — equal, volume-, recency-, or quality-weighted.

A claim that pays $1 if the market resolves Yes and $0 if it resolves No. Price is quoted in cents (0-100); the cent price is the implied probability of Yes-resolution treated as a fair price.

The per-market choice of which outcome is labelled 'Yes' and which is 'No'. Made by Kalshi when the market is created and varies market-by-market — it is NOT a fixed convention like 'home team is always Yes'.

Within a Side A / Side B panel layout, the side that holds the Kalshi YES contract for this market. Determined dynamically because Kalshi's YES designation can map to either team depending on the market.