Scaling Type:
Linear scaling (additive) for proc chances (+1 dice roll per copy)
Detailed Explanation
Overpowered lamp gives you a +1 chance to proc on hit effects.
In practical terms, this means that any item with a chance-based effect (such as the Ice Cube, which has a 20% chance to trigger on hit - gets an extra independent chance to activate.)
Without Overpowered Lamp, a single Ice Cube effectively rolls one 20% chance each time you hit an enemy.
With 1 Overpowered Lamp, you gain one extra roll. You now roll two independent 20% chances on every hit.
An intuitive way to think about this is dice:
No lamp → one 5-sided die (20% chance)
One lamp → two 5-sided dice rolled simultaneously
If either die succeeds, the effect procs.
If both dice succeed, the effect procs twice.
So each additional overpowered lamp adds another independent proc roll. These rolls are not additive; they are seperate checks, meaning multi-procs are possible.
This ability to trigger multiple times on a single hit is what makes Overpowered Lamp "OP".
You can however get more anyway with a lucky shady guy. The items the shady guys sells are determined as soon as you enter the stage, and they can have an overpowered lamp. If you get 2 OP lamps from chests, the shady guys that spawned in will still be able to sell you an extra copy, although you theoretically are over the limit.
You may also be able to get another one with microwave shenniangens (although if you try to microwave one after getting 2, you will get an error message). But you are able to leave one in the microwave and come back later after getting more than 2 to pick it up.
In practical terms, this means that any item with a chance-based effect (such as the Ice Cube, which has a 20% chance to trigger on hit - gets an extra independent chance to activate.)
Without Overpowered Lamp, a single Ice Cube effectively rolls one 20% chance each time you hit an enemy.
With 1 Overpowered Lamp, you gain one extra roll. You now roll two independent 20% chances on every hit.
An intuitive way to think about this is dice:
No lamp → one 5-sided die (20% chance)
One lamp → two 5-sided dice rolled simultaneously
If either die succeeds, the effect procs.
If both dice succeed, the effect procs twice.
So each additional overpowered lamp adds another independent proc roll. These rolls are not additive; they are seperate checks, meaning multi-procs are possible.
This ability to trigger multiple times on a single hit is what makes Overpowered Lamp "OP".
Note that under normal conditions you can MAX get 2 copies of overpowered lamp in-game.
You can however get more anyway with a lucky shady guy. The items the shady guys sells are determined as soon as you enter the stage, and they can have an overpowered lamp. If you get 2 OP lamps from chests, the shady guys that spawned in will still be able to sell you an extra copy, although you theoretically are over the limit.
You may also be able to get another one with microwave shenniangens (although if you try to microwave one after getting 2, you will get an error message). But you are able to leave one in the microwave and come back later after getting more than 2 to pick it up.
How it Stacks
Op lamp scales linearly.
If 1 lamp gives you +1 dice roll, 2 lamps give you +2 dice rolls and so on.
If 1 lamp gives you +1 dice roll, 2 lamps give you +2 dice rolls and so on.