Mastering Long Bluffs in Poker: The Mathematics Behind Multi-Street Bluffs

A bluff in poker is a fundamental skill that combines deception and strategic calculation to change the course of a hand. The minimum defense frequency (MDF) is used to determine if a bluff is profitable. The expected value (EV) of a bluff is calculated as %fold*(pot size) - %call*(bet size).

For a three-barrel bluff to be profitable, the opponent must fold 72.2% of the time on the river. The risk-reward ratio for long bluffs is worse than for short bluffs because more chips are invested. Three assumptions are made for the calculations: checking always results in a loss, the opponent always wins if they reach showdown, and the opponent never raises, only calls or folds.

Four strategies are considered: checking and folding, betting once and folding, betting twice and folding, and betting three times. The expected value (EV) of each strategy is calculated by multiplying the probability (p) and financial outcome (v) of each event and summing them. A three-barrel bluff strategy can be the most profitable if the opponent's folding frequency on the river is high.