On average the offer leaves you $25 ahead, and most people still say no. In 1979 the psychologists Daniel Kahneman and Amos Tversky put the reason in one line, in an economics journal: "losses loom larger than gains". Losing a sum hurts more than winning the same sum feels good, so most people turn down a fair coin toss, and turn it down harder the bigger the stake.

Kahneman later asked how big the win must be to balance an equal chance of losing $100. For many people, he wrote, about $200: twice the loss. A review of 607 measurements put the ratio at about 2; a review of risky choices found about 1.3. Experience shrinks it, but almost nobody is free of it. Kahneman won the Nobel prize in economics in 2002; Tversky had died six years before.

The better guess weighs a choice by what can happen and how likely, not by how the loss will feel. The coin toss here is a thought experiment about value, and the seesaw and the crowd are sketches.

So, what would heads have to pay you?

Sources: Daniel Kahneman and Amos Tversky, "Prospect Theory: An Analysis of Decision under Risk", Econometrica 47(2), 1979; Daniel Kahneman, Thinking, Fast and Slow, 2011, chapters 25 and 26; Brown, Imai, Vieider and Camerer, Journal of Economic Literature, 2024; Walasek, Mullett and Stewart, 2024.
Sounds: Apple iMovie sound effects.