Some basic tips

The most important thing is to be able to avoid needless damage so you can go fast and still not die. AKA "don't get hit". Learn all the enemy patterns and pay attention. This is harder in rebirth than it was in WOTL because some enemies can pop up under you on jump onto you in an undodgeable way. oh well, do the best you can.

Always reset for a good starting item. The fastest way is to hold R and not release it until your starting room has a curse room or item room next to it. You're generally looking for something that substantially increases your DPS, preferably while also scaling with tears up and damage up.

Here are some example items I will start:
Knife, ipecac, epic fetus, magic mushroom, 20/20, cricket's head, sad onion, cricket's body, brimstone baby, fly-shooting baby, pact, pentagram, blood of the martyr, quad shot, infestation 2, proptosis, monstro's lung, mulligan, goat head, polyphemus, scythes, small rock, growth hormones

Here are some example items I don't start:
Relic, mitre, mascara, wide odd mushroom, stigmata, technology 1 or 2, any zodiac sign, any item that only gives speed or health, shielded tears

There are some items I used to start in WOTL that I don't start in rebirth. The main difference is that devil deals are no longer a consistent source of "carry items". In WOTL the main purpose of your starting item was to quickly get you to your first few devil deals where you could hopefully find either knife, brimstone, or guppy. A regular tears build was generally something you would be forced to fall back on and be unhappy about it.
In rebirth, devil deals don't consistently give you those things, but there are a lot more items that can give you really good regular tears. So your starting item matters a lot more; you want it to be seriously helping you through the whole run.

The things I used to start and don't anymore include:
Regular shooting familiars like brother bobby or sister maggy, forever alone or distant admiration, halo, sacrificial dagger, a single non-tail guppy touch, mapping, dr fetus (it sucks now)

Bomb lots of mushrooms in the caves to try to find the liberty cap, which is a super common drop from them. You can use it for poor-man's mapping, by walking back and forth through a door until eventually it gives you a compass effect. This is only really worth doing on the last few floors. But if you get this trinket, always pay attention to the map to see if you get a lucky compass effect while doing a floor.

You can also try to get real mapping from a shop, but the pool of shop items is so big now that this is very inconsistent. Mapping is huge though so if you see a map or compass early, do whatever it takes to buy it, clearing the whole floor if necessary.

Try hard to get every devil deal you can, which means don't take red heart damage (especially not on the boss) and bomb beggars on floors when you don't have a guaranteed deal. A deal is guaranteed if these are both true: #1 you haven't taken any red heart damage and #2 you are on basement 2 or you got no devil deals on the previous two floors. 

If you get stuck on god rooms and your build is weak, I think it's usually right to kill the angel to get a double reroll of god items.

The amount of time you're willing to spend finding an item room should be directly correlated with how weak you are. Once your build is good enough, stop spending any time at all going to item rooms, unless there's one like RIGHT THERE. The same applies to clearing rooms for your D6 charges. It is generally worth it in the early game to get your D6 one-away-from-charged before you do the boss room, since rerolling a devil deal can have such a big impact.

All of the above applies to Isaac with the D6. Azazel is faster because you just start with one of the best items, but that's boring so nobody really races azazel.

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