Since 17w47a, blue wither heads can fly away through blocks on the first tick(s?). When looking at the first screenshots provided, we can think that the two neighbouring wither skulls are close enough to the edge of the 3x3x1 bedrock surface to shoot blue wither heads away from the surface. But in fact, those blue wither heads are just going through blocks. When looking at the next screenshots, you can notice that the wither can shoot projectiles underneath the 3x3x1 surface. This wasn't the case before 17w47a.
Steps to reproduce:
Build a 3x3x1 bedrock/barrier area
Put a fence 2 blocks underneath the middle block of the 3x3x1 surface
Put an obsidian block 1 block higher from the middle block of the 3x3x1 surface (or a normal block but don't forget the water on the wither main head to prevent it from blowing it up)
Spawn a wither on the fence (horizontally)
Place blocks around the 3x3x1 surface and hit the wither with projectiles (snowballs)
I've provided screenshots and a world download to help people reproduce this bug ❓ .
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I can confirm this.
Since it was only involving common game mechanics, this is a step back for technical players, as there is no current known way to break blocks reliably.

@unknown, that is completely incorrect.
/setblock <xyz> air destroy
is still a command, is it not? It's completely reliable too.

@CreeperMagnet_ , that is completely correct. For an OP player.
Since update 1.4.2 (and related snapshots) until snapshot 18w08a, the properties of the Wither bosses allow players to use them as a way to break blocks, in survival, without any command.
That's the feature @SebTheThing is aiming to get back with this bug report.
Commands are not part of the survival gameplay, so it's not a good alternative.

Confirmed for 18w09a, 18w10a, 18w10b, 18w10c, 18w10d.

Confirmed for 18w11a.

Confirmed for 18w14a and 18w14b.

Confirmed for 18w15a.

Confirmed for 18w16a.
SebTheThing, no need for a comment each time you update the affected version.

I edited the bug report again to edit the version when the bug first appeared. It seems that the glitch appeared even before 18w08a. I have no access to 17w45, 17w46 and 17w47 but I still have access to 17w43. The bug isn't there in 17w43 and it is there in 17w48, so the glitch happened in the snapshots between 17w45 and 17w47, including those. If some people still have access to the snapshots I have listed, please tell me on which snapshot did MC-126595 first appear.

Edited the bug report again. I obtained the access to older snapshots, and it's now official that MC-126595 was here since 17w47a. Unfortunately, I have no idea what caused it.

Hey, each time you make an edit, you send out email notifications to everyone watching, so try to edit in bulk before you hit "save". And there's no need to repeat your edits in the comments since it's already recorded in the "activity" tab, and also sent via email notification as well.

Possibly related to MC-122988 in which hostiles can see and attack through a block in their head .

The same glitch also allows dispensers to shoot through a block directly in front of them, which is totally wrong.

I think it is caused by this feature. The best thing would be to not only make it have to do with whether a player is doing it, but also limit it to transparent blocks. It doesn't make sense that we could throw things through solid blocks.

I don’t think this anyone has mentioned this, but this also means that if your head is in a cobweb, you can’t break it at all.

Or any other block - i.e. if you spawn inside a tree, or if you ender pearl and end up in a wall...
That would be MC-124126, which I agree likely shares an underlying cause with this issue.

MC-131094 is probably the same, but also descibes behaviour with other mobs.

Video by ilmango on the issue:
https://youtu.be/ryb1_0kg6R4

Thanks [`Drakan1 ] for adding that video. I'm never sure what the proper etiquette is when linking the work of someone else.

Could someone clarify what the old behavior was and what is different now. I'm trying to understand the problem better before attempting a fix for it. Try to ELI5 me on this one, because I have a hard time seeing a problem in the current behavior.

Ilmango has a pretty good and succinct explanation on it in the linked video a couple comments up.
Basically blue skulls are able to escape from a bedrock wither cage where previously they were unable to, due to the skulls now ignoring the first block they encounter after they are shot. This means that wither cages are not reliable anymore as they were being used, because they can now destroy surrounding blocks regardless of the cage. This breaks some farms that use the wither block breaking attack to farm blocks.
However this doesn't just affect blue skulls, but seemingly all projectiles ignore the first block they encounter, so that you can throw ender pearls or snowballs while in a two-high grass block, for example, and they don't collide with the grass. This behavior seems counter-intuitive.
In addition, which may be related, you no longer can attack the block your head is in, which, combined with several bugs related to spawning or teleporting inside walls/leaves, could leave you entombed.

The skull projectiles would be "spawned in" inside the block, and explode without escaping into another block. Possibly have something to do with not having a hitbox from the inside? Also, I believe arrows still work fine as a projectile intuitively in 1.12, so this might be something worth looking into in case the other projectile fix (for enderpearl, snowball etc) needs to be tweaked as well.
Check the related issues, particularly MC-131094, for a more general issue that perhaps contains this one.