# Complete Poker Math Formulas, Equations & Solver Proofs Reference Hub

> Source: [Poker Math Formulas & Equations Reference Hub on Smarter.Poker](https://smarter.poker/learn/poker-math)

## Core Poker Math Equations Reference
- **Required Calling Equity**: `Equity_Req = Call / (Pot_Before_Call + Call)`
- **Expected Value (EV)**: `EV = (Win% * Pot_Won) - (Lose% * Cost_Risked)`
- **Minimum Defense Frequency (MDF)**: `MDF = Pot / (Pot + Bet)`
- **Bluff Break-Even Frequency (Alpha)**: `Alpha = Bet / (Pot + Bet) = 1 - MDF`
- **Optimal Polarized River Bluff-To-Value Ratio**: `Bluff_Ratio = Bet / (Pot + 2 * Bet)`
- **Stack-To-Pot Ratio (SPR)**: `SPR = Effective_Stack / Pot`
- **Geometric N-Street Bet Sizing**: `g = 0.5 * ((1 + 2 * SPR)^(1 / N) - 1)`
- **Brownian Motion Risk Of Ruin**: `RoR = exp(-2 * Winrate * Bankroll / Variance)`
- **Dan Harrington M-Ratio**: `M = Stack / (SB + BB + Total_Orbit_Antes)`

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