THE WORLD OF DR. BAYESA WORK IN PROBABILITY · EST. 2026
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THE ARCHIVE/EPISODE 013
EPISODE 013 · THE POSTERIOR

The Expected Value

The arithmetic of a long shot. At The Posterior, Dr. Bayes prices a proposed campaign: a 20% chance of making $500,000 against an 80% chance of losing $300,000.

Expected valueDecision-makingRisk
THE COMICTap any panel to open it at full size
Episode 013 of the Dr. Bayes comic, “The Expected Value”: At The Posterior, Dr. Bayes prices a proposed campaign: a 20% chance of making $500,000 against an 80% chance of losing $300,000. The full dialogue is in the transcript below.
01 / 04Panel 1 of 4 from Episode 013, “The Expected Value”
02 / 04Panel 2 of 4 from Episode 013, “The Expected Value”
03 / 04Panel 3 of 4 from Episode 013, “The Expected Value”
04 / 04Panel 4 of 4 from Episode 013, “The Expected Value”
A NOTE FOR CURIOUS MINDS

Behind the joke.

Expected value weighs each outcome by its probability: 0.2 × $500,000 is $100,000 of expected gain, against 0.8 × $300,000, or $240,000, of expected loss. The net is −$140,000. A long shot can feel bold, but a campaign like this, repeated many times, loses money on average. There may still be reasons to take the risk; the point is to know the price of the hope before paying it.

SPEECH BUBBLES, IN WORDS

The transcript.

For readers who prefer dialogue without zooming in.

Read the dialogue ↘

Young Executive: What if the campaign has a 20% chance to make $500K?

Young Executive: And an 80% chance to lose $300K. Still worth it?

Dr. Bayes: Let's price the bet.

Dr. Bayes (on his napkin): 0.2 × 500K = 100K. 0.8 × 300K = 240K.

Dr. Bayes: Expected value: −$140K. Not bold. Expensive hope.