teachersbettextbook 0.2.0

The open betting-math textbook: de-vig, +EV, arbitrage, Kelly sizing, and Kalshi fee math as a pure Python/NumPy library.

teachersbettextbook

The open betting-math textbook — the standard, teachable math behind sports-betting analytics, as a small, dependency-light Python/NumPy library.

It is the open half of Teacher's Bet: the same math the site shows its work with, extracted so you can import it, read it, and check it yourself. Every free lesson at teachersbet.com/learn is built on these functions.

Not betting advice. Every function is a calculation on the inputs you supply — not a prediction, pick, or direction to wager, and no guarantee of any outcome. For informational and educational use. You must be of legal age to gamble in your jurisdiction. Gamble responsibly — 1-800-GAMBLER.

Install

pip install teachersbettextbook

What's inside

Module	What it does
devig	moneyline ↔ implied probability / net odds, the vig, and fair-probability recovery — proportional, power, and Shin methods
kelly	single-bet, fractional, and joint simultaneous Kelly sizing
arb	two-outcome arbitrage detection and the stake split, with execution-risk caveats
simulate	Monte Carlo of repeated fractional-Kelly bets
kalshi	Kalshi event-contract fee math — taker/maker fee with the exchange's ceil-to-cent rounding, fee-adjusted break-even, fee as a share of outlay, round trip vs. hold-to-settlement

See FORMULAS.md for every equation, and the free guides at teachersbet.com/learn for the plain-language lessons.

Quick start

import teachersbettextbook as tb

# De-vig a two-sided moneyline into fair probabilities
tb.devig(-150, 130, method="shin")      # -> (p_a, p_b), summing to 1

# The book's margin (vig) baked into that line
tb.overround(-150, 130)                 # -> ~0.03

# Fractional Kelly stake for a 55% edge at even money (half-Kelly is the default)
tb.fractional_kelly(p=0.55, b=1.0)       # -> 0.05  (half of the full 0.10)

# Is there an arb across these books? How do you split the stake?
tb.find_arbitrage([
    {"book": "A", "ml_a": 110, "ml_b": -105},
    {"book": "B", "ml_a": -102, "ml_b": 115},
], total_stake=1000)                     # -> best prices, is_arb, stakes, return

# Kalshi: what a 100-contract taker fill at 50c really costs
tb.kalshi_fee(100, 0.50)                 # -> 1.75  (dollars; ceil-to-cent on the total)
tb.kalshi_breakeven(0.50)                # -> 0.5175  (price + fee, the true break-even)
tb.kalshi_fee_breakdown(100, 0.50)       # -> the whole worked cost, incl. round trip vs. hold

Worked examples

Runnable, step-by-step walkthroughs live in examples/ — one per topic, each printing the full calculation with labelled intermediate values:

python examples/devig_example.py       # strip the vig from a moneyline three ways
python examples/kelly_example.py       # f*, the growth curve, half-Kelly, joint sizing
python examples/arb_example.py         # detect a two-book arb and split the stake
python examples/simulate_example.py    # Monte Carlo a season of fractional-Kelly bets
python examples/utils_example.py       # moneyline ↔ probability / odds, vig, Kelly ratio

Tests

Every module has a comprehensive suite (known values, edge cases, and mathematical invariants) under tests/:

pip install teachersbettextbook[test]
pytest        # 160+ tests

Scope

This package is math only. It contains no web app, no odds-data feeds, no account or billing code, and none of the hosted service's proprietary sharp-consensus anchor detection. It reads and runs on its own, offline.

License

MIT. Copyright (c) 2026 Alex Thornton.