02 Dec 2024 Intermediate This material is for medium-skilled players bluff EV semi-bluff In this article we explore two examples that show how semi-bluffs can be more profitable than pure bluffs. C-bet bluff on the flop Check-raise bluff on the turn Let's dive in! C-Bet Bluff on the Flop We open to 3bb from late position in a $25NL cash game. Everyone folds except the player on the BB, who calls. Flop: Pot: $1.60 Our opponent checks, and now it’s our turn to act. Let’s assume we know that if we c-bet $1.20, our opponent will fold 40% of the time. When he calls (the other 60%), he will have hands like pairs, medium pocket pairs, straight draws, flush draws, or better. For simplicity, assume the opponent never check-raises on the flop. Also, if our c-bet gets called, we both check down the turn and river to showdown (unlikely, but let’s focus on EV). Now, let’s calculate the EV of bluffing with three types of hands: – A pure bluff. – A weak semi-bluff (one overcard). – A strong semi-bluff (open-ended straight draw + backdoor flush draw). Pure Bluff Our equity with against the opponent’s calling range is just 5%. EV Calculation: EV = EV Fold + EV Call EV Fold: The opponent folds 40% of the time, and we win the pot ($1.60): $1.60 × 0.4 = $0.64 EV Call 1 (Opponent calls, and we improve): We improve and win the pot ($2.80) 5% of the time: $2.80 × 0.05 = $0.14 EV Call 2 (Opponent calls, and we don’t improve): We lose our bet ($1.20) 95% of the time: -$1.20 × 0.95 = -$1.14 Total EV: EV = $0.64 + (0.6 × [$0.14 - $1.14]) EV = $0.64 - $0.60 EV = +$0.04 Weak Semi-Bluff Our equity with against the opponent’s range is 18%. EV Calculation: EV Fold: $1.60 × 0.4 = $0.64 EV Call 1 (Opponent calls, and we improve): $2.80 × 0.18 = $0.50 EV Call 2 (Opponent calls, and we don’t improve): -$1.20 × 0.82 = -$0.98 Total EV: EV = $0.64 + (0.6 × [$0.50 - $0.98]) EV = $0.64 - $0.29 EV = +$0.35 Strong Semi-Bluff Our equity with against the opponent’s range is 45%. EV Calculation: EV = EV Fold + EV Call EV Fold: $1.60 × 0.4 = $0.64 EV Call 1 (Opponent calls, and we improve): $2.80 × 0.45 = $1.12 Pot Equity 2 (Opponent calls, and we don’t improve): -$1.20 × 0.55 = -$0.66 Total EV: EV = $0.64 + (0.6 × [$1.12 - $0.66]) EV = $0.64 + $0.28 EV = +$0.92 Having equity can easily turn a breakeven situation into a +EV one. The difference in EV between these c-bets is significant and highlights the power of semi-bluffing with equity. Check-Raise Bluff on the Turn Opponent opens to 4bb from the BTN in $100NL cash game. We call from the BB; everyone else folds. Flop: Pot: $8.50 We check, the opponent bets $5.50, and we call. Turn: Pot: $19.50 We check again, and the opponent bets $13. We decide to check-raise all-in for $50. Pot after our shove: $82.50 Opponent needs to call $37 to win $82.50. We estimate his fold frequency to be 35%. If he calls (65%), his range includes top pairs, strong draws, and better hands. EV Calculations The calculations are the same, so we’re just showing the results: Pure Bluff () Equity: 7% EV = -$15.66 Medium Semi-Bluff () Equity: 26% EV = -$0.92 Strong Semi-Bluff () Equity: 43% EV = +$12.28 Key Takeaways Semi-bluffing with equity can turn losing situations into winning ones. The less fold equity you have, the more raw equity you need to make semi-bluffs profitable. Without fold equity, it’s often better to check and take a free card with your draws. Consider implied odds, but don’t ignore reverse implied odds when bluffing with weaker draws.
