courses › Thinking

Weigh each outcome by its chance before you decide.

In your head, jot if needed · no calculator why?

Learn first (about 3 minutes)

Opens at level 21.

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Builds on: Chance basics (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Is the bet worth it? par 20 s not tried yet

  worked example

  It costs $18 to play. You win $200 with a 1-in-20 chance, otherwise nothing. What is your expected profit per play? (Use a minus sign for a loss.)

  Answer: -$8.00

  1. Expected winnings: $200 × 1/20 = $10.
  2. Minus the $18 cost: −$8 per play on average.

• Break-even chance par 20 s not tried yet

  worked example

  A $10 bet pays back $20 in total (including your $10) if it wins, and nothing if it loses. What win probability makes it break even? Give a percent.

  Answer: 50%

  1. You break even when chance × payout = stake: p × $20 = $10.
  2. So p = 10 ÷ 20 = 50%.

• Insurance & warranties par 25 s not tried yet

  worked example

  Phone insurance costs $280 a year and covers a $900 screen replacement. There is a 25% chance you'll need one this year. What does expected value say?

  1. Buy — on average it pays out $55 more than it costs
  2. Buy — it saves $620 on average
  3. Skip — you lose the whole $280 on average
  4. Skip — on average it costs $55 more than it pays out

  Answer: Skip — on average it costs $55 more than it pays out

  1. Expected payout: 25% × $900 = $225.
  2. It costs $280, so on average you lose $55. (It can still make sense if the loss would really hurt.)

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

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