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In my last campaign, one of my players' PC died and he wants to use his old character going forward.

What equipment should he start with?

There will be a difference in treasure, as the older character had more levels actually played (1–8). The other players haven't played that many level with their current characters (5–8).

We are starting the new adventure at level 9.

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    \$\begingroup\$ In theory, there shouldn't have been a major difference in treasure between a character played from 1 to level 8 and a character created as level 5 and played to 8. \$\endgroup\$ – JohnP Jan 15 '15 at 18:41
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Theoretically, the character starting at first level should have gotten some gold and some items and some more gold and items should have been awarded to him during adventuring up to level 5, while the characters who started at 5 should have started with three magic items and some gold. From that moment onwards the two characters should have gained the same while adventuring since they're both level 8 but since they played two different adventures, YMMV.

The difference shouldn't be much, since the starting equipment for characters higher than level 1 is supposed to give them more or less what they should have found by adventuring.

However, this is not even relevant to your case. The new character should start with an equipment comparable to those of the other characters. D&D 4e isn't a game where you gain privileges by playing longer. It is a game where everyone is given the same resources to be able to contribute equally to the here and now.

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The standard method is for the player to pick items as if he were a brand new level 9 character: a level 10 item, a level 9 item, a level 8 item, and gold equal to the value of a level 8 item, as JohnP linked on Zachiel's answer.

The wealth difference of this method versus his character who started at level 1 versus the characters who started at level 5 depends on how generous you are as a DM, I suppose, but if you are playing by the books should be fairly negligible. The new items method should net him fewer items, but of higher value, so might actually be beneficial to him over persisting his old items.

Total expected net wealth of a level 9 character is 20,495 gp (level 8 is 14,195 gp). It may be worth doing the math on both his and one or two of the other level 8 characters to see where they sit relative to each other, and deciding how to handle it based on that, rather than based on suggestions-in-a-vacuum based on assumptions that may prove inaccurate.

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