Our Initiative system is a Speed based activation system, akin to what can be found in Shadowrun, Pokemon Legends: Arceus and Honkai: Star Rail.
This means that how often and when you go is primarily based on your speed statistic, in our case it is mostly based on the difference in speed between creatures; instead of your pure stat, allowing for nicely flowing combat where (way) higher-level creatures (like bosses) automatically gain the advantage.
The very short tl;dr version:
All creatures have an Action Value which decides the order of activations in any given encounter, whenever combat starts and “initiative is rolled”, everyone’s Action Value (the Initiative in Foundry; henceforth referred to as AV) is set to their Base Action Value (henceforth referred to as Base AV) which is calculated based on their SPD Stat, as well as the average level of all combatants in the current encounter.
A large number of Effects and Conditions many come with a Stack value, which indicates the number of the afflicted creatures' activations that must pass before the condition ends.
For example, "Poison 3" means that at the end of your first Activation it goes down to Poison 2 -> second activation Poison 1 -> and at the end of the third activation the Poison would wear off.
"Stacks", as the name implies, stack with each other, provided that they're the same effect or condition. A creature affected by Poison 2 that gets Poison 3, will instead of gaining 2 instances of Poison, now have Poison 5.
Some Effects may cause you to trigger multiple stacks of a condition per turn like Blight allowing for an extra potent effect.
"Stage changing effects", like those applied by Leer, Swords Dance, or Curse, work a tad differently. Each of these effects, while having variable effects, still apply unique, independent effects with their own Stacks, ticking down after each Activation. So two instances of Leer on a creature do not "stack", adding to the duration of the original effect, but instead are applied in parallel to a creature.
For example, if a creature is affected by Leer, takes an Activation of its own, is effect by two more Leer, then starts another Activation, that creature will have unique instances of a Leer 4, a Leer 5, and a Leer 5 effect applied to it on that second Activation.
Action Advancing and Action Delay are two mechanics that can alter a single activation of a creature by moving their turn up or down in the initiative tracker. The formula to calculate is quite simple:
So for example; you have an Action Value of 50 and a Base AV of 100, and you get delayed by 25%, your new Action Value would be 50 - 100 * (0 - 0.25) = 75. Similarly, advancing forward by 25% would result in a new AV of 25.
One thing to keep in mind is that the Action Advancement & Delay stack cumulatively, this means in the example above if you Delay for 25% to a new AV of 75, and then Advance for 25%, you calculate it as 75 - 100 * 0.25 = 50 -> effectively no change.
If a turn has passed and your AV has been lowered by 30, leaving you with 45 AV, the advance forward of 25% would still drop you by 25 -> 45 - 100 * 0.25 = 20
Expanding off the above: there is a difference between "Advancing forward by 100%" and "Immediately take action". Any Effect that Advances Forward by 100% does so using the calculation above; meanwhile an Effect that makes you "Immediately take action" sets your AV to 0 with no further math included.
Due to concerns of outright “locking down” creatures, the absolute highest AV2 that can be reached through net increase in AV (meaning, Action Delay exceeding Action Forward) is 150 AV, or 300% Delay, whichever happens first.
Advancement, however, has no such cap going down besides the absolute limit of 0 AV.
A change in speed of △SPD1→2 will lead to a change in Base AV, calculated like so:
Every time another SPD (de-)buff is applied it will change the current base AV multiplicatively; this holds true for Speed Combat Stages too. Meaning the speed increase/decrease stacks additively:
This alteration of the base stat also alters the current speed stat, the calculation for that would be as followed:
Base AV is limited between 70 and 125 at +0 Speed Combat Stages.
Every Speed Combat Stage adds +- 5 to the cap of your Base AV; so if you are at +2 Speed Stages, you minimum Base AV becomes 60 instead of 70. Meanwhile at -2, your max can drop all the way to 135.
This caps out at +-5 stages; meaning a minimum of 45 Base AV and maximum of 150 respectively.
You can find the full math over here
See Math for Nerds if you wish to see the in-depth math.