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There's a chest downgrading mechanic in place to prevent you from seeing to many red or black chests in a run. There's basically two numbers that will diminish your ability to get "rare chests" (that being an A or S tier chest).

1. Rare chests created during floor generation. If one of the chests generated is rare, the counter goes up by 1. If the second chest generated is also rare (which is already unlikely since the downgrading effect is already in place after the first one), the counter goes up by 1 again.
When you open or destroy these chests (and ONLY these chests, not any other rare chests you may have gotten on the floor!), they will decrease said counter by 1 again. I'm currently unsure if any rare Floor Generation chests you leave behind when changing the floor also decrease the counter, or if you carry your penalty to the next floor when you ignore them.

2. Picking up any item or gun of A or S quality gives you +1 to your magnificence stat. It will only happen the first time you pick up that particular instance of the item, so you can drop it and pick it up again without increasing your magnificence further. On the other hand, the increase is permanent and you can't get rid of it by dropping, selling or destroying the item. This magnificence counter will carry over to the next floor.

Now, whenever the game wants to generate a floor reward item (be it a Floor Generation chest, a Room Clear Reward chest, a Boss Reward item or even a Shop item) and the result turns out to be an A or S tier reward, the game tries to downgrade the quality. For this, the two numbers above get added together, your magnificence counter and the number of unopened/undestroyed Floor Generation chests still around. If the resulting number is 0, everything's fine and it's very unlikely that anything happens. But when the number is above 0, the chance that the reward quality is downgraded rises logarithmically. Even just a number of 1 will increase the chance that your chest will be downgraded to just under 80%. The exact formula for the downgrade chance is this:

( 1 - ( 0.006260342 + 0.9935921 * e^( -1.626339 * [number] ))) * 100

You can copy the above formula into WolframAlpha with varying values for the number to quickly see how they effect downgrade chance.
So what exactly happens when you downgrade? The game just rerolls the quality of the item with the same chance distribution as before, but just takes the A or S tier chances out. So your resulting rerolled item or chest can only be of D, C or B quality.
As an example, if you rolled two Red Chests during floor 1 generation, the second red chest will be rerolled into a lower one with a ~80% chance. It will probably be a brown or blue chest instead. And the more high-tier items you collect, the less high tier items you will encounter during the rest of the run.

I just wanted to have this on here for posterity, even if it's not exclusive to chests. No idea how to implement this into the wiki.

Notable implications here are: - If there's still an unopened rare chest on the level, your Boss reward and your Shop selection (generated on entry) suffer from the increased downgrade penalty. So do all random chests spawned after a room clear. Most of the time it doesn't matter, since opening a rare chest and picking up the item gives you the chance decrease again. It might be relevant for high-tier active items which you don't plan on taking anyways.

I just encountered a Glitch Chest and tried dropping and picking up a gun in the pre-boss room as suggested, to ensure a mix of guns and items as rewards. It didn't work though - I dropped and picked up a random Blunderbuss and got eight guns as the rewards. Anyone know the weighting of guns vs items for rewards? Is it plausible I just got an unlikely event if guns are more common, or is it 50/50? The latter would mean that mechanic was likely changed as getting eight guns would be a 0.4% chance.

I encountered a Glitch Chest, and after defeating the two Beholsters I went to pick up one of the (many) guns when all but 3 turned out to be mimic pedestals, unfortunately I was too surprised to get a screengrab. So apparently mimic pedestals are a thing now.

Yes, this is on the Mimic page and not here since it's not really chest-related. --Exschwasion (talk) 22:24, 24 July 2018 (UTC)

On Reddit, one of the devs notes that the chance of a Rainbow Chest taking the appearance of a Brown Chest is a separate chance from finding a Rainbow Chest. Has anyone found what the probability of this separate roll is (which effectively increases the chance to find a Rainbow Chest of any kind?)

Is it possible to destroy a rat chest?