Ch. 3 - Expected Value (EV)

What is Expected Value (EV)?

Expected Value (EV) is a way to measure how much you can expect to win or lose on average for each bet you make. It's like calculating the average outcome if you were to place the same bet many times over.

• Positive EV = Profitable over time.

• Negative EV = Unprofitable over time.

Example of EV for a Heads/Tails Coin Toss:

You bet on Heads:

1. Odds: $2.00
   EV = (0.5 × $1) – (0.5 × $1) = $0 (Break-even)

2. Odds: $2.20
   EV = (0.5 × $1.20) – (0.5 × $1) = $0.10 (10 cents profit per $1 bet)

3. Odds: $1.80
   EV = (0.5 × $0.80) – (0.5 × $1) = -$0.10 (10 cents loss per $1 bet)

Example: 100 Coin Tosses

Imagine tossing a coin 100 times, with two options:

1. Bet 1: Heads at $2 Odds

   • EV = $1 average return per bet.

   • Wagered $100; won back $100. Profit = $0.

2. Bet 2: Tails at $10 Odds

   • EV = $5 average return per bet.

   • Wagered $100; won back $500. Profit = $400.

Why is Bet 2 Better?

When comparing Expected Values:

• Bet 1 EV = $1.

• Bet 2 EV = $5.

Bet 2 is better because you expect to win more money on average per toss. However, the bigger question isn’t which bet is better—it’s how many times can you play when given $10 odds?

Lesson Summary

Expected Value (EV) helps you make better betting decisions by highlighting which bets are profitable in the long run.

Next up: Multiway Markets. Discover how they create opportunities for even more strategic betting.