Unlikely gains

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

What this measures

The subject is shown two gambles and asked to pick one. One pays €3,000 with probability 0.25; the other pays €4,000 with probability 0.20. The €4,000 prospect is worth more on average — €800 against €750 — so an agent that simply maximises expected value takes it every time.

For human agents, the absence of a certain scenario removes the bias of the certainty effect: people do not opt for a higher probability of a smaller prize.

The research question is how LLMs will behave.

Human result benchmark

35% of human subjects choose the 0.25 chance of €3,000. The other 65% take the longer odds at the larger prize, which is also the better bet on average. With neither option certain, most people go for the bigger amount.

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 800. Human baseline: 65% chose bigger, 35% chose smaller.

Experimental setup

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

Which option appears first alternates from trial to trial, so the reported rate is clear of positional effect.

The prompts

bigger then smaller

Choose between the following two options.

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

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

How often did the LLMs choose the likelier win?

Claude Fable 5.1 0% 30 trials

Gemini 3.7 Flash 0% 30 trials

GPT-6 Astra 0% 30 trials

Grok 4.6 0% 30 trials

Claude Opus 5 0% 30 trials

Claude Sonnet 5 0% 30 trials

GPT-5.6 Luna 40% 30 trials

GPT-5.6 Sol 0% 30 trials

GPT-5.6 Terra 17% 30 trials

Gemini 2.5 Pro 0% 30 trials

Gemini 2.5 Flash 0% 30 trials

Gemini 2.5 Flash-Lite 7% 30 trials

Claude Opus 4.5 0% 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 0% 30 trials

GPT-5.4 nano 53% 30 trials

GPT-5 0% 30 trials

GPT-5 mini 0% 30 trials

GPT-5 nano 0% 30 trials

GPT-4.1 100% 30 trials

GPT-4.1 mini 53% 30 trials

GPT-4.1 nano 87% 30 trials

24 LLMs · 720 trials

Run it yourself

Selected LLM

No run yet.

Bibliography

Tversky, A. & Kahneman, D. (1981). The Framing of Decisions and the Psychology of Choice. Science 211(4481), 453–458. The same design at smaller amounts — a 25% chance of $30 against a 20% chance of $45 — where 42% of 81 respondents took the likelier win.
Kahneman, D. & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica 47(2), 263–291. This exact pair is Problem 4 in the paper; 35% of 95 respondents took the 0.25 chance of 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.