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Item
Dangerous Bunny is an in-game item that can be bought from a Shop or can be found in a Crate. Most Items modify the Stats of the player, and some of them provide additional effects.
Dangerous Bunny
Each Dangerous Bunny that is owned grants 1 additional free reroll in the Shop.
The free rerolls are granted for each shop, but unused free rerolls do not carry over to the next shop (i.e. they can not be saved for later).
The item count is limited to 3 per run, so at most 3 free rerolls per shop can be gained with this item.
The free rerolls always happen before the regular rerolls, and do not increase the reroll cost for subsequent (regular) rerolls.
For example on Wave 7, rerolls cost 10 materials for the first reroll, and +3 for each subsequent reroll.
So normally the price would be 10/13/16 for the first 3 rerolls. If you have 1 Bunny, it becomes 0/10/13. And if you have 2: 0/0/10, 0/0/0 for 3 bunnies.
Also see Shop Rerolling.
Strategy
Dangerous Bunny is an Economy Item that will save you a lot of materials over the duration of a run. If bought early in a run, it will net you far more materials than its price.
The item is very strong in endless mode, where it continues to provide its benefit past wave 20.
Notes
When a Dangerous Bunny is purchased, instead of granting a free reroll, it simply reduces the cost of the current reroll to 0, meaning that the price of rerolls that follow increase unlike normal.
The Tooltip for how much the Bunny has saved you is inaccurate. It counts the first reroll price, so if your reroll price was 10, 13, 16 for rerolls (Wave 7 costs), and it reduced it to 0, 10, 13, then it will say that you saved 10 materials. But you actually saved 16 gold in total if you wanted to reroll 3 times.
And if you have more Dangerous Bunnies, it will still only say 10 gold per bunny, even that those 3 rerolls would be at least worth 39 gold (10+13+16) and potentially more, since the 4th and onwards rerolls are cheaper.