Expected Value
- Showdown EV
- Fold EV
Understanding both showdown EV and fold EV is crucial for any serious poker player. These concepts allow you to evaluate the profitability of your decisions in various scenarios, ensuring that you maximize your winnings and minimize your losses over time. By mastering these elements of expected value, you can make more informed and strategic choices during gameplay, significantly enhancing your overall performance.
Showdown Expected Value (Showdown EV):
Showdown EV refers to the expected value of a hand when it goes to showdown, meaning when all remaining players reveal their cards at the end of the betting rounds to determine the winner. It calculates the potential winnings or losses based on the probability of having the best hand at showdown. Understanding showdown EV helps players make better decisions about whether to continue betting, calling, or checking, especially when they anticipate that their hand will likely go to showdown.
Fold Expected Value (Fold EV):
Fold EV considers the expected value of folding a hand. When a player folds, they forfeit their current investment in the pot but avoid losing any additional chips. Additionally, when your opponent folds, you deny them the opportunity to realize their equity in the hand, which can be a strategic advantage. Fold EV helps players evaluate the cost of continuing with a weak hand versus the benefit of folding and potentially saving chips for future, more favorable situations. By comparing the fold EV to other possible actions, players can make more strategic decisions about when to cut their losses and when to stay in the game.
Applied Example:
Consider you hold a strong hand, like a set of aces, on the turn. The board shows A♠ 7♣ 4♦ 9♥. Your opponent calls your bet on the turn. On the river, the board now reads A♠ 7♣ 4♦ 9♥ 3♣. You decide to make a sizable bet, and your opponent folds a straight draw.
Here’s why this matters:
- Fold EV: By betting and causing your opponent to fold their straight draw, you deny them the chance to hit their straight on the river, which would have beaten your set of aces. You gain EV by preventing them from realizing their equity.
- Denying Equity: If your opponent’s hand had any chance of improving to beat your set, their fold means they can no longer outdraw you. This denial of equity increases your expected value for that hand.
- Showdown EV: Conversely, if your opponent had a weaker hand, like a pair of 9s or 7s, you would prefer they call your bet, as you would gain additional value from those hands at showdown. However, if those weaker hands have the potential to improve (e.g., hitting two pairs or a straight), it might sometimes be better to see them fold to avoid losing a significant portion of your stack.
- Balancing Act: Ideally, you want worse hands to call you to maximize your showdown EV. However, when those worse hands have high implied odds or potential to outdraw you, denying their equity through Fold EV can sometimes be the preferable play.
This example highlights the strategic importance of understanding when to leverage Fold EV to deny your opponent’s equity and protect your hand, versus when to maximize your showdown EV by enticing calls from weaker hands.
Calculating EV:
Expected value can be calculated using the following equation:
EV = (Probability 1 × Outcome 1) + (Probability 2 × Outcome 2) + (Probability 3 × Outcome 3) + …
Example 1: Two Outcomes
Let’s say you are in a poker game where you go all-in on the river. There are two possible outcomes: you either win the pot or lose your bet. Suppose the pot is $100, and your bet is $20. You estimate that you have a 60% chance of winning (Probability Win = 0.6) and a 40% chance of losing (Probability Loss = 0.4).
Using the two-outcome EV equation:
EV = (0.6 × 100) + (0.4 × (-20))
EV = (0.6 × 100) – (0.4 × 20)
EV = 60 – 8
EV = 52
In this example, the expected value of your decision to go all-in is $52, indicating a profitable move over the long run.
Example 2: More than two outcomes
Imagine you are in a poker game and decide to bet $20 on the turn. There are several possible outcomes with different probabilities and corresponding values. Let’s consider three possible outcomes:
- Outcome 1: You win a pot of $80 (Probability = 50% or 0.5).
- Outcome 2: You lose your bet of $20 (Probability = 30% or 0.3).
- Outcome 3: Your opponent folds, and you win a smaller pot of $40 (Probability = 20% or 0.2).
Let’s plug in the values using the EV equation:
EV = (0.5 × 80) + (0.3 × −20) + (0.2 × 40)
EV = 40 – 6 + 8
EV = 42
In this example, the expected value of your $20 bet on the turn is $42, indicating that, on average, you can expect to make $42 from this decision over the long run, considering all possible outcomes and their probabilities.