Comparing Strategies by Expected Value

Lesson 1 of 2: Comparing Options and Insurance

In this lesson:

• Compute the expected value of each competing option
• Compare the options and recommend one
• Build the insurance expected-cost model

What You Will Be Able to Do

By the end of this lesson, you should be able to:

1. Model each competing strategy as a cost or payoff distribution
2. Compute each strategy's expected value and compare the totals
3. Build a policy's expected cost as premium plus expected out-of-pocket

Two Policies — Which One Wins?

Policy A: $1,200 premium, $250 deductible.
Policy B: $800 premium, $1,000 deductible.

Over a year, which one costs you less on average?

From Scoring One Option to Comparing Several

Last lesson: one game, compute its expected payoff, read the sign.

Now: several options — compute each one's expected value and pick the best.

Model Each Strategy on Its Own

• Give each option its own outcome table
• List the outcomes, their probabilities, and their values
• Compute that option's expected value independently

Fix the Direction Before You Compare

For an expected cost, lower wins. For an expected payoff, higher wins.

Warm-Up: Compare Two Prize Wheels

Wheel X: pay $2, win $5 with probability , else .
Wheel Y: pay $3, win $10 with probability , else .

Compute each expected payoff and pick the better wheel.

Insurance Cost = Premium + Expected Out-of-Pocket

The premium is paid for certain; the deductible is paid only if there's an accident.

The Two Policies and the Driver's Odds

This driver: no accident , minor , major .

Policy A: The Low-Deductible Cost

premium, deductible, accident probability :

Policy B: The High-Deductible Cost

premium, deductible, accident probability :

Your Turn: A Third Policy

Policy C: $1,000 premium, $600 deductible, same accident probability .

Compute Policy C's expected annual cost.

Build premium + expected out-of-pocket before advancing.

Compare the Totals — Recommend B

, . Policy B has the lower expected cost.

Two Cautions to Carry Forward

The premium alone is not the answer — compare full expected costs, not headline numbers

We simplified: both accident types trigger the full deductible

What You Built In This Lesson

✓ Compute each option's expected value, then compare in the right direction

✓ Insurance cost = premium + expected out-of-pocket

✓ Under these odds, Policy B wins

Coming Up Next: It Depends on the Odds

We recommended B — but only for one set of accident odds.

Next lesson: recompute as the odds change, and find the break-even probability where the better policy flips.