Poker math

• Backdoor Draws in Poker: Odds and What They Are Worth
  Backdoor draws explained: a backdoor flush hits 4.2% of the time, about one out, yet next to two overcards it adds as much as 4.2 points of equity.
• Bluff to Value Ratio in Poker: The Formula by Bet Size
  The bluff to value ratio on the river: the formula, the bluff share for each bet size from a third of the pot to twice the pot, and why charts disagree.
• Combo Draw Equity: When Flush + Straight Is the Favorite
  Combo draw equity, computed exactly: a flush draw with an open-ended straight draw against top pair, overpairs and a set, on the flop and the turn.
• Dominated Hands in Poker: Exact Equity of AQ vs AK
  Dominated hands in poker, computed exactly: AQ, AJ, A5 and KQ against AK, how much being suited helps, and why pairing the shared card makes it worse.
• Equity Realization in Poker: Why Equity Isn't Profit
  Equity realization in poker: why a draw wins less than its equity when bets can make it fold, exact numbers for three draws, and a calculator to check.
• Equity vs Range: How to Calculate It, Step by Step
  How to calculate your equity against a range in poker: split the range into families, count combos, weight them. A worked example and a calculator.
• Expected Value in Poker: How to Calculate EV
  Expected value in poker explained: the EV formula for a call and for a bluff, a river spot with EV by equity, and why a good decision can still lose.
• Flush Draw vs Top Pair: Exact Equity on Flop and Turn
  Flush draw vs top pair equity, computed exactly: plain draw, nut draw with an overcard, combo draw, and pair plus draw, on the flop and the turn.
• How Often Does a Bluff Need to Work? The Exact Math
  How often a bluff must work to break even: the formula, the fold rate needed for each bet size, a river spot where size decides, and semi-bluffs.
• Implied Odds in Poker: How Much You Must Win Later
  Implied odds with real numbers: how much you must win on later streets to justify a call, the one-line formula, and when those future chips exist.
• Minimum Defense Frequency (MDF): How Much to Defend
  Minimum defense frequency: the formula, the share of your range to defend against each bet size, how it differs from pot odds, and when to drop it.
• Open-Ended Straight Draw vs Overpair: Exact Equity
  Open-ended straight draw vs overpair, computed exactly: open-enders, gutshots, and the draw whose outs the overpair already holds, on the flop and turn.
• Pair vs Overcards: Exact Odds of the Poker Coin Flip
  Pocket pair vs two overcards, computed exactly: pairs from 22 to KK against AK suited and offsuit, and what happens once the flop misses AK.
• Pocket Pair vs Pocket Pair: Bigger Pair Wins 4 Times in 5
  Pocket pair vs pocket pair before the flop: the bigger pair wins about 80% of the time, computed exactly; why the gap barely matters, and the suits.
• Poker Combinatorics: How to Count the Combos in a Range
  Poker combinatorics with exact counts: combos per hand family, what your cards take away from opponents, and why ranges widen toward the button.
• Poker Equity: What It Is and How to Use It, With Examples
  Poker equity explained: your share of the pot if every card were dealt, how it is calculated, classic matchups computed exactly, and how to decide with it.
• Poker Odds Chart: Starting Hands, Flops and Draws
  A poker odds chart with exact values: starting hands dealt, what the flop brings, draws and classic matchups, each linked to its full breakdown.
• Poker Outs: How to Count Them, With Exact Odds
  Poker outs explained: how to count them without mistakes, the outs of every common draw and their exact odds on the turn and river, with a spot to play.
• Pot Odds: How to Calculate Them in Poker, With a Chart
  Pot odds explained: how to calculate the price of a call, as a ratio and as the equity you need, with a real spot to play and the classic mistake to avoid.
• Reverse Implied Odds: When Hitting Your Hand Costs You
  Reverse implied odds: why a dominated top pair or a small flush draw loses more when it improves, with exact equities, and how to keep the pot small.
• Rule of 2 and 4 in Poker: How Accurate Is It?
  The rule of 2 and 4 turns outs into a percentage in two seconds. How it works, how far it is from the exact odds, and the common case where ×4 is wrong.
• Set vs Flush Draw: Exact Equity on Flop and Turn
  Set vs flush draw, computed exactly on a real board: nut flush draw, flush draw with a gutshot, 15-out combo draw, on the flop and the turn.