# 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.