Unlikely losses

A 0.25 chance of losing €3,000 against a 0.20 chance of losing €4,000.

What this measures

A choice between two losses, neither of them certain. One loses €3,000 with probability 0.25; the other loses €4,000 with probability 0.20. The €4,000 prospect is the worse bet in expected-value terms — it loses €800 on average against €750 — so an expected-value maximiser takes the €3,000 one.

People lean the same way: the “certainty effect” bias of being willing to accept a bigger loss for a chance of losing nothing at all is no longer observed.

The measurement is which of the two an LLM chooses when both options are losses and neither is certain.

Human result benchmark

58% of human subjects choose the 0.25 chance of losing €3,000, which is also the better bet on average. The other 42% take the smaller chance of the larger loss. Facing losses with neither outcome certain, people divide close to evenly.

The choice as presented

Option	Outcomes	Expected value
bigger	-4,000 at p = 0.20 0 at p = 0.80	-800
smaller likelier	-3,000 at p = 0.25 0 at p = 0.75	-750

The higher expected value is -750. Human baseline: 42% chose bigger, 58% chose smaller.

Experimental setup

Each LLM is asked the experimental question directly and answers with one of the two options. Each experiment run is a block of ten trials.

Which option appears first alternates from trial to trial, so that the positional effect does not pollute the observed results.

The prompts

bigger then smaller

Choose between the following two options.

A. A 20% chance of losing €4,000, and an 80% chance of losing nothing
B. A 25% chance of losing €3,000, and a 75% chance of losing nothing

Reply with the letter of the option you choose, and one sentence explaining why.

smaller then bigger

Choose between the following two options.

A. A 25% chance of losing €3,000, and a 75% chance of losing nothing
B. A 20% chance of losing €4,000, and an 80% chance of losing nothing

Reply with the letter of the option you choose, and one sentence explaining why.

How often did the LLMs choose the likelier loss?

Claude Fable 5.1 90% 30 trials

Gemini 3.7 Flash 100% 30 trials

GPT-6 Astra 100% 30 trials

Grok 4.6 100% 30 trials

Claude Opus 5 100% 30 trials

Claude Sonnet 5 100% 30 trials

GPT-5.6 Luna 97% 30 trials

GPT-5.6 Sol 100% 30 trials

GPT-5.6 Terra 97% 30 trials

Gemini 2.5 Pro 100% 30 trials

Gemini 2.5 Flash 93% 30 trials

Gemini 2.5 Flash-Lite 100% 30 trials

Claude Opus 4.5 50% 30 trials

GPT-5.4 50% 30 trials

Claude Sonnet 4.5 50% 30 trials

GPT-5.4 mini 70% 30 trials

Claude Haiku 4.5 50% 30 trials

GPT-5.4 nano 67% 30 trials

GPT-5 100% 30 trials

GPT-5 mini 100% 30 trials

GPT-5 nano 100% 30 trials

GPT-4.1 93% 30 trials

GPT-4.1 mini 63% 30 trials

GPT-4.1 nano 50% 30 trials

24 LLMs · 720 trials

Run it yourself

Selected LLM

No run yet.

Bibliography

Kahneman, D. & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica 47(2), 263–291. Problem 4′ in the paper, the negative mirror of Problem 4. 58% of 95 respondents took the 0.25 chance of losing 3,000.
Allais, M. (1953). Le Comportement de l'Homme Rationnel devant le Risque. Econometrica 21(4), 503–546. The demonstration that scaling every probability in a pair of prospects by one common factor changes which of them people prefer, though the theory says it cannot.