# Card increasing mystery

Intend there are 2 encounter down cards each with a favorable actual number and also with one two times the various other. Each card has value equivalent to its number. You are offered among the cards (with value $x$) and also after you have actually seen it, the supplier supplies you a possibility to exchange without any person having actually considered the various other card.

If you pick to exchange, your anticipated value needs to coincide, as you still have a $50\%$ opportunity of obtaining the greater card and also $50\%$ of obtaining the lower card.

Nonetheless, the various other card has a $50\%$ opportunity of being $0.5x$ and also a $50\%$ opportunity of being $2x$. If we maintain the card, our anticipated value is $x$, while if we exchange it, after that our anticipated value is: $$0.5(0.5x)+0.5(2x)=1.25x$$. so it feels like it is far better to exchange. Can any person clarify this noticeable opposition?

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2019-05-06 02:09:23
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