Lesson 20 [Beginner] Expected Value Basics

Expected Value (EV) indicates how much an action will, on average, win or lose in the long run. In poker, all decisions are evaluated based on EV.

Basic Strategy

Expected Value (EV) is the sum of the probabilities of each outcome multiplied by their respective monetary values.

Basic Premise: All poker decisions should aim to maximize Expected Value

Basic Formula:

EV = (Win Probability × Amount Won) + (Loss Probability × Amount Lost)

Example: Pot $100, Bet $50, Win Probability 30%

• If you win: Win $150 ($100 pot + $50 bet)
• If you lose: Lose -$50
• EV = (0.3 × $150) + (0.7 × -$50) = $45 – $35 = +$10
• Conclusion: Call is +EV (+$10)

Three States of Expected Value:

• Positive EV (+EV): An action that makes money in the long run
• Zero EV (0 EV): An action that breaks even in the long run
• Negative EV (-EV): An action that loses money in the long run

Why this approach?

• While a single outcome is influenced by luck, in the long run, the player who consistently makes high-EV decisions will win
• Pot odds and implied odds are ultimately tools for calculating EV
• Mastering EV thinking allows you to make correct decisions without being swayed by emotions or short-term results

Situational Responses

1. When Choosing Among Multiple Actions

Calculate the EV of each action and choose the one with the highest value. Since the EV of a fold is always $0, if another action has a positive EV, choose that action.

2. When Considering a Bluff

Calculate the EV of the bluff. If your opponent's fold probability is sufficiently high, the bluff becomes +EV. Example: If the pot is $100 and you bet $50, the bluff is profitable if your opponent folds 33% or more of the time.

3. When Deciding Value Bet Sizing

Compare the EV of a large bet versus a small bet. A large bet wins more when called but has a higher fold rate, while a small bet has a higher call rate but wins less. Calculate the EV for both and choose the higher one.

4. In Tournaments

Chip EV and dollar EV can differ. In bubble situations, survival might be more important than gaining chips, so avoiding a negative chip EV action could be a positive dollar EV play.

How to Think

Try to think in this sequence when making important decisions:

1. What are the possible actions? Fold, call, raise, etc.
2. What are the possible outcomes for each action? Opponent folds, calls, or raises.
3. What is the probability of each outcome? Estimate, even roughly.
4. What is the monetary value of each outcome? How much do you win if you succeed, and how much do you lose if you fail?
5. What is the EV of each action? Choose the highest EV action.

Example Hand Analysis

Example 1: Calling a Draw (EV Calculation)

Game: Cash Game 1/2, Stack 200BB

Position: BTN

Turn: Board K♠ 9♠ 4♣ 2♠, Hero A♠ 7♠ (Nut Flush Draw)

Pot: $100, Opponent bets $50

Thought Process:

1. “Who is structurally favored on this board?”

→ Opponent is currently ahead, but I have a nut flush draw (9 outs, approx. 20% win probability).

2. “What role does my hand play within my range?”

→ A strong draw. If a spade comes on the river, I'm almost certainly winning.

3. “Does my opponent have enough hands to fold / do they call a lot?”

→ EV Calculation:

• If you win (20%): Win $150 (Current pot $100 + bet $50)
• If you lose (80%): Lose -$50
• EV = (0.2 × $150) + (0.8 × -$50) = $30 – $40 = -$10
• → Although it's -EV, it could become +EV when considering implied odds.

Conclusion: Call $50 (Potentially +EV when considering implied odds)

Comment: While it's -EV based on simple pot odds, it's actually +EV because there's a high chance of winning additional money if the flush completes on the river.

Example 2: Bluff EV Calculation

Game: Cash Game 1/2, Stack 200BB

Position: BTN

River: Board A♠ K♣ Q♦ 7♥ 2♠, Hero 6♠ 5♠ (Complete Air)

Pot: $100, Opponent checks

Thought Process:

1. “Who is structurally favored on this board?”

→ I have nothing. Cannot win at showdown.

2. “What role does my hand play within my range?”

→ Only bluffing is possible. If I don't get my opponent to fold, I lose the pot.

3. “Does my opponent have enough hands to fold / do they call a lot?”

→ Opponent checked, so they likely have a weak hand. Consider bluffing with a $50 bet.

→ EV Calculation:

• If opponent folds (40% estimated): Win $100
• If opponent calls (60% estimated): Lose -$50
• EV = (0.4 × $100) + (0.6 × -$50) = $40 – $30 = +$10
• → +EV bluff

Conclusion: Bet $50

Comment: The bluff is profitable if the opponent folds 40% or more of the time. Bluffs are evaluated by the opponent's fold probability, not your win probability.

Example 3: Bet Sizing Comparison

Game: Cash Game 1/2, Stack 200BB

Position: BTN

River: Board A♠ A♣ K♦ 9♥ 3♠, Hero A♥ Q♥ (Trips)

Pot: $100, Opponent checks

Thought Process:

1. “Who is structurally favored on this board?”

→ I have a very strong hand with trips. Value bet possible.

2. “What role does my hand play within my range?”

→ Value. Opponent might call if they have a king or a weak ace.

3. “Does my opponent have enough hands to fold / do they call a lot?”

→ Option 1: Small bet $30

• Opponent call probability 70%, fold 30%
• EV = (0.7 × $130) + (0.3 × $100) = $91 + $30 = $121

→ Option 2: Large bet $70

• Opponent call probability 40%, fold 60%
• EV = (0.4 × $170) + (0.6 × $100) = $68 + $60 = $128
• → Large bet has higher EV

Conclusion: Bet $70

Comment: A small bet has a high call rate but wins less, while a large bet has a low call rate but wins more. EV calculation helps find the optimal sizing.

Key Patterns Summary

Pattern 1: EV = (Win Rate × Amount Won) + (Loss Rate × Amount Lost)

Pattern 2: The EV of a fold is always $0

Pattern 3: Always choose +EV actions (long-term profit)

Pattern 4: Bluff EV = (Fold Rate × Pot Size) – (Call Rate × Bet Size)

Pattern 5: Choose the highest EV among multiple actions

Pattern 6: Long-term EV is more important than short-term results

Pattern 7: Pot odds and implied odds are ultimately tools for EV calculation

Quiz

Question 1

Pot $100, Bet $50, Win Probability 25%. What is the EV of calling?

• A) +$10
• B) $0
• C) -$10
• D) -$12.50

Question 2

Pot $100, Bluff Bet $50. What percentage of the time must your opponent fold for the bluff to be +EV?

• A) 25%
• B) 33%
• C) 50%
• D) 60%

Question 3

What is the EV of folding?

• A) Negative EV
• B) $0
• C) Positive EV
• D) Depends on the situation

Question 4

Which of the following is NOT an advantage of EV thinking?

• A) Enables correct long-term decisions
• B) Not swayed by short-term results
• C) Guaranteed win every time
• D) Prevents emotional decisions

Question 5

Compare the EV of two actions. Action A is +$5 EV, Action B is +$8 EV. Which one should you choose?

• A) Action A (safer)
• B) Action B (higher EV)
• C) Both are good
• D) Depends on the situation

Answers and Explanations

Question 1

Answer: D) -$12.50

Explanation: EV = (0.25 × $150) + (0.75 × -$50) = $37.50 – $50 = -$12.50. Since it's -EV, it's better to fold.

Question 2

Answer: B) 33%

Explanation: For a bluff to break even, (Fold Rate × $100) = (Call Rate × $50). If the fold rate is x, then 100x = 50(1-x), 100x = 50 – 50x, 150x = 50, x = 33%. If the opponent folds 33% or more, it's +EV.

Question 3

Answer: B) $0

Explanation: Folding doesn't involve putting money into the pot, so its EV is always $0. If another action has a positive EV, you should choose that action over folding.

Question 4

Answer: C) Guaranteed win every time

Explanation: EV is a long-term average, so you can lose in the short term. It doesn't guarantee a win every time, but it helps you make correct decisions in the long run.

Question 5

Answer: B) Action B (higher EV)

Explanation: In poker, you should always choose the action with the highest Expected Value. Action B has a higher EV of +$8, so choose B.