I wrote this guide to help players (better) understand widely unknown, misunderstood, or hidden mechanics used by the game. A lot of these are quite useful to know and can improve your runs significantly.
Please note that this guide aims to explain and clarify mechanics that aren't immediately obvious or have parts to them that most players don't know about. There won't be anything obvious, so don't expect a list of Lucky Charms and what they do, or how to do an Interest build. Although the guide does outline strategies on how to use the mechanics to your advantage, it's not intended as a general strategy guide.
I got most information from reading the decompiled code, with some in-game tests to ensure correctness. It is still possible that some of the information is inaccurate or contains mistakes, however. If you find anything is wrong, please let me know in the comments.
Spoilers are minimal and information about secret content is put in spoiler tags.

The probabilities listed on the left are the chances of each symbol type appearing for each individual spot, being picked for rerolls, and being picked for Luck triggers (see below). The starting weights are as follows:
Lemon : 1.3 (19.4%)
Cherry : 1.3 (19.4%)
Clover : 1.0 (14.9%)
Bell : 1.0 (14.9%)
Diamond : 0.8 (11.9%)
Treasure : 0.8 (11.9%)
Seven : 0.5 (7.5%)

Every (+1) in the game increases the weight by 0.8
If you, for example, pick Sevens to manifest more often (+1) on the phone, the probabilities become:
Lemon : 1.3 (17.3%)
Cherry : 1.3 (17.3%)
Clover : 1.0 (13.3%)
Bell : 1.0 (13.3%)
Diamond : 0.8 (10.7%)
Treasure : 0.8 (10.7%)
Seven : 1.3 (17.3%)

Due to being based on weights, increasing them has diminishing returns. Increasing Sevens by 1 the first time increases the chance of them appearing by 9.8% while increasing it again after only increaces the chance by 8.0%. By the 10th increase, you'll be down to +2.4%.

Halving the chances works as expected, just halving the weight. Division only applies to the current value. Symbols will still increase by 0.8 regardless of being halved.

Luck is straightforward: each point of Luck forces one of the slot symbols to change into a specific symbol.

• With 7 Luck, at least 7 symbols will match.
  
• With 10 Luck, at least 10 symbols will match and you are guaranteed to win something unless overridden by sixes.
  
• At 15+ Luck, a jackpot is guaranteed unless overridden by sixes.

The chosen symbol is determined by the regular probabilities (on the left of the slot machine).

In addition to base Luck provided by Charms, the slot machine itself can grant random Luck boosts called Spontaneous Luck. These occur under various conditions, explained below.

During the first debt, random luck events are a bit more likely and impactful than after. These are called Initial Luck Spins (ILS). They happen in set sequences. Below are the five possible sequences of random ILS:

• 3 9 17 20 35 39 43 89 94 99 104 109 114
  
• 2 8 16 19 34 38 42 83 88 93 98 103 108
  
• 5 7 15 18 29 33 37 77 82 87 92 97 102
  
• 4 6 11 14 28 32 36 71 76 81 86 91 96
  
• 3 10 13 23 27 31 65 70 75 80 85 90

These sequences are complete. No ILS will happen after the last one. They only apply for the first debt though. You usually won't see past 21, but I wrote them out for completeness for e.g. increased rounds or infinites.
For math/programming nerds, the actual algorithm is:
When triggered, sparks appear and Luck increases by a random amount between 4 and 8 (with 6 being twice as likely as the other values).

Random Luck after the first debt follows a (different) schedule called Occasional Luck Spins (OLS).

• The first OLS happens randomly within the first 5 spins after the first deadline.
  
• After that:
  
  Next OLS = (Current Spin #) + 4 + (# of Completed Deadlines) + 50% chance to add 1

In simpler terms, OLS will happen every 5-6 spins on the second debt (after the first one), 6-7 on the third, 7-8 on the fourth, etc.
When triggered, sparks appear and Luck will be increased through these steps:

• If the spin number is a multiple of 7 → +7 to +9 Luck.
  
• If the spin number is a multiple of 3 → +5 to +7 Luck.
  
• If the spin number is not a multiple of 3 → +3 to +5 Luck.

Note that the "multiple of 7" bonus stacks with the other two.

If multiple spins give no rewards, the game increases Luck:

• After 4 consecutive misses → +5 Luck.
  
• Each additional miss → +1 more than the last boost.
  
• Sparks appear when this happens (so it may look like an ILS/OLS, but it isn't).

This happens after the previous steps.

If your base Luck (before slot effects, i.e. Luck from Charms) is between 1 and 7, you may get small extra boosts:

• 1-4 Luck → 1/2 chance to gain +1 or +2 Luck.
  
• 5-6 Luck → 1/4 chance to gain +1 Luck.
  
• 7 Luck → 1/6 chance to gain +1 Luck.

These stack with the previously mentioned other boosts. No sparks appear when this is triggered.

This happens after the previous steps.

The Depression charm disables ALL Spontaneous Luck boosts. With Depression enabled:

• ILS will still follow the usual schedule. Ones with Depression enabled are just skipped.
  
• Any OLS scheduled to happen while enabled will happen on the first spin after Depression is no longer enabled and the next one will be scheduled based on this spin.
  
• Spins without wins are still counted but Pity Spins isn't triggered (until disabled)

You wouldn't most of the time, but there are a few very niche uses for it. For example, it can enable Charms benefiting from bad luck like the train-type ones, and you can use it to make bigger patterns less common if your small ones are more valuable.

Due to how ILS and OLS work, it's quite easy to predict when the next one will happen.

ILS is the easiest of the two. Just note the first spin that had sparks and find which sequence starts with this. For '3', you'll also need to check the second one.
CAREFUL! Pity Spins also show sparks. Do not let this throw you off. It's possible for an ILS and Pity Spins to happen at the same time, so you might need more data points when this happens to accurately determine the sequence.

OLS is a bit more difficult because it has some randomness. Still, you can always narrow it down to a 50/50 after the first one. When the first one happens, just put in the numbers in the formula and take the two numbers that come out with the random value being 0 or 1.
For convenience, you can ignore the "Current Spin #" and re-interpret it as "spins until the next OLS".
Example.
When the first OLS happens (assuming you're still on the second debt, which should be the case 99.9% of the time):
Next OLS After = 4 + 1 + [0/1] = 5/6 spins.
So the next OLS will either be 5 or 6 spins after that one.
Carrying over between deadlines, you should follow the original number, then use the new "completed deadlines" value when the OLS is triggered in this new deadline for calculating the next one.
The most effective way of learning when an OLS is guaranteed to happen is just performing the first predicted spin, and if it's not an OLS, you are 100% guaranteed to see one next spin. If it is an OLS, just try again for the next one.
As with ILS predicting, be careful with the sparks from Pity Spins!

If it's not clear to you how you can use this to your advantage, below are some examples.

• You can intentionally pick less spins so that Rotated Hamsa overlaps with an ILS/OLS for a very lucky last spin.
  
• You can stack Red Shiny Rock, Ancient Coin, Golden Horseshoe with ILS/OLS for extra lucky spins.
  
• During the early debts, you can determine when two (or more) ILS/OLS are due for the next 7 spins and focus using your triggerable/specific Charms on this.

The probabilities for rolling sixes work as follows:

• Triple Six () → Chance as listed, capped at 30%.
  
• Double Six () → 6%
  
• Single Six () → 7.5%

The chances of and are set and will never change.
The checks run in order:

• Roll for .
  
• If failed, roll for .
  
• If failed, roll for .

Example (1.5% chance):

• → 1.5%
  
• → 6% (5.91% when accounting for previous condition)
  
• → 7.5% (6.94% when accounting for previous conditions)
  
• Total chance of any sixes = 14.4%

Sixes are rolled after everything. You can't prevent them from showing up, no matter how high your Luck is. They are completely unaffected by Luck.

The total value of a winning pattern is calculated as follows:
All of these are displayed to either side of the slot machine. Symbol Multiplier and Pattern Multiplier are essentially the same, multiplying the total value. The only difference is which Charms, Traits, etc. affect them. In fact, all of these are practically the same. Doubling one of them will always double the total.
When considering which to increase, it's most efficient to look at the ratios of the increase. For example, increasing Sevens from 35 to 42 (+20%) is less effective than increasing Symbol Multiplier from 2 to 3 (+50%).
It's not always optimal to just pick the one with the highest ratio though, as some of the values are harder to increase than others. Patterns Multipliers are generally less common and smaller than Symbols Multipliers, so you may want to consider picking a Patterns Multiplier over a Symbols Multiplier even if the ratio is slightly smaller to take another Symbols Multiplier later on.

Lucky Charms have a rarity assigned. This is indicated by the pepper displayed by them. The game only shows 4 of them, but there actually are 7; the last three groups are split up in two subgroups with different sub-rarities. As you can guess, the higher the rarity, the less likely it is to show up.

• COMMON Charms (Charms with ) are the most likely
  
• UNCOMMON Charms (Of : Crowbar, Hamsa, Calendar, Super Capacitor, Property Certificate, Demon's Horn, Necronomicon, Gabihbb'h, Clover Picture, Bell Picture, Sheep, Wheat) are 10% less likely than COMMON
  
• MILDLY RARE Charms (Charms with , except above) are 20% less likely than COMMON
  
• RARE Charms (Charms with , except below) are 35% less likely than COMMON
  
• VERY RARE Charms (Of : Pareidolia, Number One, Chastity Belt, AA Batteries, Vorago, Barathrum) are 50% less likely than COMMON
  
• LEGENDARY Charms (Charms with , except below) are 65% less likely than COMMON
  
• ULTRA LEGENDARY Charms (Of : Electricity Meter, Music Tape, Dark Lotus, Swole Cat, Megaphone) are 80% less likely than COMMON

Keep in mind that these probabilities apply to individual Charms, not rarity groups. Charms show up more than ones simply because more Charms are of rarity.
In practice, a random item is picked and randomly rerolled with the above probabilities (COMMON never rerolls, UNCOMMON has a 10% chance to reroll, etc). In most cases, this detail can be ignored. However, there is a limit of 100 rerolls to this. If this limit is reached, the original item is kept. The store initializes with four basic Charms before stocking for the first time to make sure it always has a Charm to fall back to. Reaching this limit is very unlikely though.

Rarities for Memory Cards work the same as Charms, but they have different rarities, changed probabilities, and no subgroups.

• COMMON Cards () are the most likely
  
• UNCOMMON Cards () are 15% less likely than COMMON
  
• RARE Cards () are 35% less likely than COMMON
  
• EPIC Cards () are 50% less likely than COMMON

The game choosing them also works the same as Charms by rerolling higher rarities more often. If 100 rolls fail, it will default to Cold Affection.

Sometimes the phone will have red options. This is an "Evil Call". Evil Calls aren't actually random. They activate if:

• 666 was unlocked at the start of the deadline.
  
• Super 666 was unlocked at the start of the deadline.
  
• The PREVIOUS round (ignoring skipped ones) scored a 666 on the slot machine.

It's important to note that the game only determines the type of call you'll get when you pick up the phone for the first time. This is only relevant to the third condition, but you must remember this when aiming to intentionally get Evil Calls (or not). As soon as you roll the slot machine, you'll lose any scheduled Evil Calls by the third condition. This works the other way around too though: you can get an Evil Call by scoring a 666 in the previous round of the same deadline, but only if you haven't picked up the phone yet this deadline.
The previous distinction means that you must always pick up the phone to cross out the sixes on the floppy disk. Even if an Evil Call is guaranteed during a deadline by one of the first two conditions, the game will not register as such if you never pick up the phone, and the floppy won't get a six crossed out.

Phone call options also have rarities. These work the same as Charms and Memory Packs.

• COMMON appears the most.
  
• UNCOMMON appears 15% less often than COMMON.
  
• RARE appears 35% less often than COMMON.
  
• ULTRA RARE appears 60% less often than COMMON.
  
• LEGENDARY appears 75% less often than COMMON.

Rerolling works slightly differently. The limit for this is 1000, but for the last 10 rolls, abilities will never reroll because of rarity (but they will still reroll if ineligible or duplicate). This limit applies to all 4 generated options (the fourth one is always pregenerated) and if the limit is reached, all remaining ones will be set to the first possible option (see table below).

Table of Normal Call options:

* Options are grouped for convenience. They are still considered as individual items in terms of probability.

Table of Evil Call options:

* Options are grouped for convenience. They are still considered as individual items in terms of probability.

Modifiers have different probabilities to be applied to Charms.
In most cases, the following probabilties are used:

Forced Modifiers usually use the probabilities listed in the table above. However, phone calls instead have an equal probability for each Modifier for choices that apply a random Modifier. These phone call choices also ignore the conditions described in the next section.

Charms aren't always eligible to get Modifiers. There are a few conditions that need to be met:

• Instant Charms will never have Modifiers. This includes most phone call choices. The "I need to heal myself." Holy phone call choice is an exception to this due to an oversight.
  
• One of the following conditions needs to be met for Charms to be able to have Modifiers at all:
  
  • At least 3 runs have been done (regardless of outcome).
    
  • At least 1 drawer is unlocked.
    
  • It is the second debt or later.
• The Devious Modifier will never be applied randomly if no drawers are unlocked.

The first nine deadlines have fixed amounts of debt that don't follow a formula. See the table below for these values.
From the 10th deadline onwards, following formula is used:
This number (or the fixed value for the first 9 deadlines) is then multiplied by the penalty from skeleton Charms and the "Delusions of Grandeur" Memory Card:
In short, the skeleton Charms apply additively and the Grandeur card doubling applies after the skeleton Charm penalty.

I'm sure most of you are more interested in the raw numbers, so here's a big table to stare at with the debts for the first 100 deadlines (with no penalties):

Not enough for you? Fine, here's some more for the larger deadlines:

I hope that's enough for even the most die-hard big number nerds. Don't forget to apply the penalties!

The base cost of restocking the Charm shop is the current debt divided by 20, except for the first 9 deadlines, for which fixed values are used:

With each restock done that is not free, the cost increases by the current cost divided by 5 (rounded down, but at least 1). Keep in mind that is the current cost, not the base cost, so it will scale exponentially. This additional cost resets at the start of each deadline, so you don't have to worry about buying many restocks making future ones more expensive. Each deadline starts at its base cost.

Phone rerolls are very simple, having the current deadline minus 1 as base cost and increasing by 1 with each reroll. Likewise, this extra cost resets at the start of every deadline.

(Steam's spoiler tags suck. Sorry :'3)

999

999 has the same logic as 666, paying out all the currently earned coins in the round again instead of taking them away (regardless of Super 999 being active)

Holy (Good) Calls

Holy phone calls work the same as Evil Calls (just replace 666 with 999), with one Holy Call being forced when 999 is unlocked.

Table of Holy Call options:

Ability Name

Ability Description

Rarity

Max Picks

I'm re-organizing my mind!

Symbols Multiplier +3

COMMON

∞

I see the patterns in my behaviour.

Patterns Multiplier +1

COMMON

∞

I'm feeling more energetic recently.

All equipped Lucky Charms triggered by the Red Button take 1 less Charge to restore, permanently. (Minimum 1 )

RARE

2

I need to heal myself.

Modify all Lucky Charms in the store, then make one free.

UNCOMMON

∞

I'm being constant!

Patterns trigger 1 more time, permanently.

LEGENDARY

1

Help!

Spawn a Sacred Lucky Charm on the Table. Then halven your coins

LEGENDARY

∞

I want to address some stuff.

I'll take back control of my life.

Double the value of all patterns with 3 or less/4+ symbols.

UNCOMMON

∞

* Options are grouped for convenience. They are still considered as individual items in terms of probability.

There have been reports that the game cheats, for example by making the 666 more likely than displayed. Besides the previously mentioned random Luck boosts, I could not find anything that would affect you negatively in the current code. Of course, I may have overlooked something, but I feel like it's more likely that players just have been reporting large outliers. You're expected to see two 666s in 7 spins once every few runs, and even three 666s in 7 isn't that crazy.

I've written the most important mechanics in this guide. If you're interested about something else that's not in it yet, please let me know in the comments. I'll try updating it with highly requested mechanics.