# AD/BC problem

From Lesswrongwiki

The chapter "Risk Policies", in Kahneman's "Thinking, Fast and Slow", opens with this example, which makes vivid the pitfalls of relying on our intuitions in choosing between bets:

Imagine that you face the following pair of concurrent decisions. First examine both decisions, then make your choices.

- Decision (i): Choose between

- A. sure gain of $240
- B. 25% chance to gain $1,000 and 75% chance to gain nothing
- Decision (ii): Choose between

- C. sure loss of $750
- D. 75% chance to lose $1,000 and 25% chance to lose nothing

Most people, looking at both concurrently, choose A and D. Now consider this second choice:

- AD. 25% chance to win $240 and 75% chance to lose $760
- BC. 25% chance to win $250 and 75% chance to lose $750

Clearly, any sane person will choose BC here; it dominates option AD. However, AD is exactly the combination of options A and D, while BC is the combination of B and C.