EV Thinking for Everyday Decisions

🎯 EV: The Universal Decision Formula

Expected Value (EV) is the average outcome of a decision repeated many times. It is the single most important concept in rational decision-making:

$$EV = \sum_{i} P(\text{outcome}_i) \times \text{Value}(\text{outcome}_i)$$

Or in the simple two-outcome case:

$$EV = P(\text{win}) \times \text{Gain} - P(\text{lose}) \times \text{Cost}$$

Every decision has an expected value — whether you calculate it or not. The goal of EV thinking is to make decisions where the calculated EV is positive, and to avoid decisions with negative EV.

Why Results ≠ Decision Quality

This is the most important lesson from poker that applies everywhere: a good decision can have a bad outcome, and a bad decision can have a good outcome.

Example: You cross the street without looking and survive. The outcome was good — but the decision had terrible EV. A drunk driver who makes it home safely made a bad decision, not a good one.

🌍 EV in Real-World Decisions

Example 1: Job Offer Decision

You have a stable job paying $80k/year. A startup offers equity worth $500k if it succeeds (30% chance) or zero if it fails (70% chance), plus a $60k salary during the period.

Stable job EV (over 4 years): \(4 \times \$80{,}000 = \$320{,}000\)

Startup EV:

$$EV_{\text{startup}} = 0.30 \times (\$60{,}000 \times 4 + \$500{,}000) + 0.70 \times \$60{,}000 \times 4$$ $$= 0.30 \times \$740{,}000 + 0.70 \times \$240{,}000 = \$222{,}000 + \$168{,}000 = \$390{,}000$$

The startup has higher EV (+$70k over 4 years). But risk matters too — if you cannot afford the downside (lower salary), the pure EV calculation may not capture your full situation.

Example 2: Insurance

Car insurance costs $1,200/year. Without insurance, there is a 2% annual probability of a $30,000 accident.

$$EV_{\text{no insurance}} = -0.02 \times \$30{,}000 = -\$600/\text{year}$$ $$EV_{\text{insurance}} = -\$1{,}200/\text{year}$$

By pure EV, skipping insurance saves $600/year. But insurance makes sense because:

• $30,000 would be financially devastating (utility is non-linear)
• Risk tolerance matters — the variance reduction has real value
• This is why rational people buy insurance despite negative EV

Example 3: Study vs Leisure

Spending 1 hour studying poker strategy might improve your win rate by 0.1 bb/100. At 200 hands/hour and $1/bb stakes, that is:

$$EV_{\text{study hour}} = 0.1 \times 200 / 100 \times \$1 = +\$0.20/\text{hour played}$$

Over 1,000 future hours: +$200. The study "investment" of 1 hour has a clear positive return.

📋 The 5-Step EV Decision Framework

🧠 Cognitive Biases That Destroy EV Thinking

1. Loss Aversion

Humans feel losses roughly twice as strongly as equivalent gains (Kahneman & Tversky). This causes systematic undervaluation of positive-EV gambles:

$$\text{Perceived EV} \approx P(\text{gain}) \times \text{Gain} - 2 \times P(\text{loss}) \times \text{Loss}$$

Result: people fold too often (in poker and in life) when the EV is clearly positive.

2. Outcome Bias

Judging decisions by their results rather than their process. The poker equivalent: criticizing a correct all-in call just because you lost the flip. This bias prevents learning and degrades future decision quality.

3. Availability Heuristic

Overweighting outcomes that are vivid or recent. If you recently saw a bad car accident, you overestimate the probability of accidents and over-insure. If you recently won a hand with a bad call, you overestimate future call EV.

4. Sunk Cost Fallacy

Including past costs in future EV calculations. The chips you already put in the pot are irrelevant to whether calling is +EV. In life: continuing a bad project because you "already invested so much" is irrational.

$$EV_{\text{future}} = P(\text{win}) \times \text{Future gain} - P(\text{lose}) \times \text{Future cost}$$

Past costs are irrelevant. Only future probabilities and payoffs matter.

⚠️ EV vs Risk: When to Adjust

Pure EV maximization ignores risk. But rational agents should account for:

Diminishing Marginal Utility

The utility of money is not linear. $1,000 means more to someone with $500 in savings than to a millionaire. This means:

• Accept negative-EV insurance against catastrophic losses
• Avoid positive-EV bets that risk financial ruin
• The Kelly Criterion formalizes this: maximize log-wealth, not wealth

$$\text{Kelly fraction} = \frac{p \cdot b - (1-p)}{b}$$

Where \(p\) = win probability, \(b\) = net odds. This fraction of your bankroll maximizes long-run growth while avoiding ruin.

The EV-Risk Trade-off Table