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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.

But I cant understand how "sure gain of $240" option is transformed to "25% chance to win $240" and why these suggestions are equivalent? Am I missing something?

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    $\begingroup$ That's more a probability than a psychology question. In AD there are two scenarios, first you win 240 and then you might either lose 1000, or, not lose anything. In these scenarios you walk away either with -760 or with the 240 you won. $\endgroup$
    – Quora Feans
    Oct 10, 2019 at 21:40
  • $\begingroup$ Ohh, great thanks! $\endgroup$
    – Narek
    Oct 11, 2019 at 0:46
  • $\begingroup$ Closing as answered in comments. $\endgroup$
    – Arnon Weinberg ♦
    Oct 13, 2019 at 18:54

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