How Often A Bluff Must Work

The Formula

A Bluff Risks The Bet To Win The Pot. It Breaks Even When The Chance Of A Fold Equals The Risk Divided By The Risk Plus The Reward, Which Is The Bet Divided By The Pot Plus The Bet. This Number Is Often Called Alpha. With 100 In The Pot, A Bluff Of 50 Needs A Fold 33.3% Of The Time, And A Bluff Of 100 Needs A Fold 50% Of The Time.

Alpha And Minimum Defense Frequency Are Two Sides Of One Equation. Alpha Is How Often The Bluff Must Work, MDF Is How Often The Defender Must Continue To Stop It Working, And The Two Always Add Up To 100%.

How Many Bluffs A Balanced Range Holds

The Last Column Answers A Different Question. On The River, A Bettor With A Polarised Range Of Strong Hands And Bluffs Wants A Caller Holding A Bluff Catcher To Be Indifferent Between Calling And Folding. That Happens When Bluffs Make Up The Bet Divided By The Pot Plus Twice The Bet Of The Betting Range. For A Pot Sized Bet That Is 33.3%, About One Bluff For Every Two Value Hands. For A Half Pot Bet It Is 25%, One Bluff For Every Three Value Hands.

It Is The Same Fraction As The Caller's Pot Odds, Which Is Not A Coincidence. A Caller Who Needs 33.3% Equity Against A Pot Sized Bet Is Exactly Indifferent When That Share Of The Hands That Bet Are Bluffs.

Using It Against Real Opponents

Against A Player Who Folds Too Often, Bluffs Work More Than Alpha Requires And You Should Bluff More, Often With Smaller Sizes That Risk Less. Against A Player Who Never Folds, Even A Well Chosen Bluff Loses, So Bluff Less And Value Bet Thinner Instead.

Choose Bluffs That Have Something Going For Them Besides Fold Equity. Hands That Block Your Opponent's Strongest Calls, And Hands That Can Still Improve If Called Before The River, Make Better Bluffs Than Hands That Are Dead When Called. On The River, Where No Card Is Left To Come, The Blocker Question Matters Most.

Keep Track Of What The Table Sees. A Player Who Shows Down Bluffs Often Will Get Called More, And A Player Who Has Not Been Caught For An Hour May Get More Folds Than The Math Expects. Neither Changes The Formula; Both Change Your Estimate Of How Often This Opponent Will Fold.

Practise It On Smarter.Poker

The Answer Above Is Complete. When You Want To Drill It, These Are The Matching Training Tools.

• Play Bluff Catcher The Training Game For This Lesson.
• Open Jarvis Training Insights Jarvis Explains Your Training Decisions In Words.