Mixed Strategies And Frequencies

Why Mix

At Equilibrium, Some Hands Are Exactly Indifferent Between Two Actions. Raising Them And Folding Them Win The Same Amount On Average. For Those Hands The Precise Split Does Not Change Their Own Value, But It Changes The Value Of Every Other Hand In The Range, Because It Decides How Many Hands Your Opponent Has To Worry About In Each Line.

If You Always Take The Same Action With Every Hand Of A Type, An Observant Opponent Can Read Your Range From Your Action. Mixing Keeps Each Line Supplied With A Believable Number Of Strong Hands And Bluffs, So No Line Can Be Attacked Cheaply.

The Indifference Principle

The Key Idea Is That A Balanced Bettor Makes The Caller Indifferent, And A Balanced Caller Makes The Bettor Indifferent. On The River, A Polarised Pot Sized Bet Should Contain Bluffs 33.3% Of The Time, So A Bluff Catcher Gains Nothing By Calling Or Folding. A Half Pot Bet Should Contain Bluffs 25% Of The Time. Against Those Frequencies No Single Response Is Better Than Any Other, Which Is Exactly The Goal.

The Same Logic Sets The Caller's Frequency. Facing A Pot Sized Bet, A Defender Who Continues 50% Of The Time Leaves A Pure Bluff With No Profit, And The Bettor Is Then Indifferent Between Bluffing And Giving Up.

Mixing In Practice

You Cannot Randomise Perfectly At A Table, And You Do Not Need To. A Common Approach Is To Use Something That Varies But That You Cannot Control, Such As The Second Hand Of A Clock Or The Suits Of Your Cards, To Decide The Rare Mixed Spots. For Most Hands, The Mix Matters Far Less Than Getting The Overall Range Right.

Frequencies Are Also Where Exploitative Adjustments Live. If An Opponent Over Folds, Shift Your Mixed Hands Toward Aggression. If They Over Call, Shift Your Mixed Bluffs Toward Checking. Knowing Which Of Your Hands Are Close Enough To Mix Tells You Which Ones Can Be Moved Without Costing Much When The Read Is Wrong.

The Preflop Charts In This Series Show This Directly: Every Cell Below 100% Is A Mixed Hand. Those Are The Hands Where Your Read Of The Table Should Make The Decision, And The Listed Frequency Is Where To Start When You Have No Read.

Practise It On Smarter.Poker

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

• Play Mixed Strategy Lab The Training Game For This Lesson.
• Open Jarvis Training Insights Jarvis Explains Your Training Decisions In Words.