Expected Value (EV) In Poker
Expected Value Is The Average Result Of A Decision If You Could Repeat It Forever: Calling 50 To Win 150 With 30% Equity Is Worth 10 Chips A Time On Average, Even Though It Loses Most Of The Times You Make It.
Math Lesson From Smarter.Poker, Updated
The Formula
EV Multiplies Each Possible Outcome By Its Probability And Adds Them Up. For A Call, That Is Your Chance Of Winning Times What You Win, Minus Your Chance Of Losing Times What You Lose. Chips Already In The Pot Are Not A Cost Of The Call; They Are Part Of What You Are Playing For.
Take A Pot Of 100 And A Bet Of 50, So 150 Is In The Middle And You Must Call 50. With 30% Equity You Win 150 Three Times In Ten And Lose 50 Seven Times In Ten. The EV Is 0.3 Times 150 Minus 0.7 Times 50, Which Is 10 Chips Per Call. With 20% Equity The Same Call Is Worth -10 Chips, A Losing Play. The Break Even Point Is 25%, The Pot Odds Price.
| Equity | EV Per Call |
|---|---|
| 15% | -20 |
| 20% | -10 |
| 25% | 0 |
| 30% | 10 |
| 40% | 30 |
Decisions Not Results
EV Is The Reason A Good Decision Can Lose And A Bad One Can Win. The 30% Call Above Loses Seven Times Out Of Ten, And It Is Still The Right Call, Because The Three Wins Pay More Than The Seven Losses Cost. Judging The Call By Whether It Won That Time Would Teach You To Fold A Profitable Spot.
This Is The Core Of Results Oriented Thinking And Why Avoiding It Matters. Over A Small Sample, Luck Dominates. Over Thousands Of Hands, The Sum Of Your EV Decisions Dominates, And That Is The Only Part Of The Game You Control.
EV Beyond A Single Call
Every Option Has An EV, And The Best Play Is The One With The Highest, Not Merely One That Is Positive. A Call Can Be Profitable And Still Be Worse Than A Raise That Wins The Pot More Often, Or Worse Than A Fold That Saves Chips For A Better Spot.
For Bets And Raises, EV Includes The Times Your Opponent Folds. A Semi Bluff With A Draw Has Two Ways To Win: An Immediate Fold, And Hitting When Called. That Is Why A Draw Can Be A Profitable Bet Even When It Is Not Strong Enough To Call A Bet Of The Same Size.
Real EV Estimates Are Only As Good As The Inputs. Your Opponent's Range, Their Tendencies And How The Rest Of The Hand Is Likely To Play All Feed The Numbers. The Formula Is Exact; Your Assumptions Are Not, Which Is Why Reviewing Hands Against Honest Ranges Improves Your EV More Than Memorising Results.
Keep Learning
- Pot Odds: How To Know If A Call Pays
- Results Oriented Thinking In Poker
- Implied Odds: When A Draw Can Call
- Poker Variance And How To Survive It
Poker Terms In This Lesson
Practise It On Smarter.Poker
The Answer Above Is Complete. When You Want To Drill It, These Are The Matching Training Tools.
- Play EV Calculations The Training Game For This Lesson.
- Open The Equity Calculator
- Open Jarvis Training Insights Jarvis Explains Your Training Decisions In Words.
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