Isaac

Repentance 1.7.9 on PS5.

What you start with

The mechanics that actually govern this character.

3 red heart containers, 1 bomb, and dead-average stats: 3.5 damage at a 1.00 multiplier, 1.0 speed, 6.5 range, 0 luck. Every other character is measured against this line.
Starts with The D6 (unlocked by beating Isaac as ???): a 6-room-charge active that rerolls every pedestal in the current room, drawing from the CURRENT room's item pool rather than the pool the item originally came from.
In Repentance the D6 is no longer flagged as a special item, so starting with it costs Isaac nothing in terms of item-pool weighting the way it did pre-Repentance.
Birthright makes every newly generated pedestal cycle between two items. Pedestals you have already seen are unaffected, so pick it up before opening treasure rooms, not after.

Treat the D6 as a look-generator, not a jackpot button. Rerolling drains the pool; once a pool is exhausted it falls back to the Treasure Room pool, and when that empties every reroll becomes Breakfast.
Bank charges for multi-pedestal rooms: shops with two or more items, Devil rooms, Angel rooms, the Boss Rush payout, and any There's Options / More Options double.
The D6 needs 6 rooms per charge, so clearing side rooms on Basement and Caves is directly worth more items. Do not beeline floors 1-2 unless you are chasing the 20-minute Boss Rush cut.
Reroll pool awareness wins runs: the item dropped by The Fallen rerolls out of the Devil pool, a Boss Room pedestal rerolls out of the Boss pool, and a normal room rerolls out of the Treasure Room pool.
In an Angel Room, D6 the Key Pieces. Key Piece 1 and Key Piece 2 sit in the Angel pool, so rerolling one hands you a real Angel item for free.
Isaac has no innate damage help, so aim to have either two damage multipliers or an outright tear replacement (Brimstone, Mom's Knife, Polyphemus) by Depths, or Chapter 4 will outscale you.

Strong on this character specifically, not just strong.

Birthright: every new pedestal shows two options, so combined with the D6 you are effectively getting two looks per charge instead of one.
More Options or There's Options: two pedestals per treasure room means one D6 charge rerolls two items at once.
9 Volt: gives a partial charge on room entry, dropping the D6 from a 6-room charge to effectively 5, which is a large percentage gain on a slow active.
The Battery plus 9 Volt: lets you bank a second charge and double-reroll a Devil room or shop in a single visit.
Sacred Orb: quality 0-1 items never spawn at all and quality 2 is rerolled 33% of the time, which raises the floor on every single D6 reroll rather than just changing the outcome.
Schoolbag: lets Isaac carry Pandora's Box or Glowing Hourglass without giving up the D6, which is otherwise his whole identity.
Glitched Crown: one D6 charge rerolls all five cycling items at once, which is the highest item throughput available to him.

Picks that are neutral or good elsewhere and bad here.

Do not keep rerolling a thin pool. When the Treasure Room pool is exhausted every reroll returns Breakfast, and there is no way to refill a pool on console.
Never use the D6 in Mom's boss room unless you intend to skip Chapter 5 entirely: it rerolls The Polaroid and The Negative together, and taking either survivor despawns the other.
Chaos: with Chaos held, any fully depleted pool contains only Breakfast, so it makes late D6 use strictly worse even though it looks like more variety.
Selling all 3 containers to Devil deals in Chapter 1: Isaac has no health economy, and the first deal permanently closes Angel Rooms, which is where the D6-able Key Pieces live.

Verified against 1.7.9 on console — anything patched, PC-only or Repentance+ only is called out rather than listed.

Deal-door maths is the same for everyone, but Isaac has no built-in help so use it deliberately: taking no red heart damage for a whole floor is +99% door chance, blowing up a beggar on that floor is +35%, and blowing up the Shopkeeper is +10%.
Third sacrifice in a Sacrifice Room has a 67% chance of 'You feel blessed!', and in Repentance that guarantees the deal room on that floor becomes an Angel Room if you have not yet seen a deal room.
Sacrifice Room spikes, Blood Donation Machines and Devil Beggars all count as self-damage in Repentance, so they do not reduce Devil room chance and do not destroy the Perfection trinket.
Mama Mega! opens both the Boss Rush door and the Blue Womb passage even after their 20-minute and 30-minute limits have expired, and does not require the boss to be dead first.
The Boss Rush reward drops multiple pedestals in one room, so a single D6 charge rerolls the entire set.

Nothing about Isaac's marks is unusually hard; the constraint is the four-way exclusivity. Isaac plus ???, Satan plus The Lamb, Mother, and The Beast can never be combined, so 12 marks take at least four separate clears plus a Greed-mode run.
The efficient main-path run: Boss Rush before 20 minutes (star), Mom's Heart before 30 minutes (heart), Hush, then descend to Cathedral for Isaac (cross), The Chest for ??? (polaroid), and Mega Satan through the golden door with both Key Pieces (brimstone). Six marks in one clear.
Delirium needs its own run on 1.7.9. Only killing Hush guarantees a Void portal; ??? and The Lamb are 20% each and Mega Satan is 50%.
On 1.7.9 Mega Satan also has a 50% chance of ending the run outright on defeat instead of dropping the Void portal, so do Mega Satan last in any run where you also want something after it.

Open the tracker for the ordered run queue, or how to unlock characters if this one is still locked.