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It has been clearly shown that the fewer chips you have the more they are worth to you.
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I agree with that, at least in theory, but this effect is very small at the start of the tournament. At the start of a tournament, chip value is close to linear.
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Therefore, the immediate rebuy is a rip off since you are buying chips worth less at the same cost as your initial buy-in.
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No, that doesn't follow.
In a PokerStars $10+$1 rebuy tournament, I might expect to get back about $30 for my initial $11. From the immediate $10 rebuy, I expect to get less than $30, but much more than $10. It still looks like a good deal.
Rebuying immediately makes sense for a good player because there are so many wild players, and you want to have the maniacs covered. See
this example.