Last week#

A round is a container.

Commands go in, an order comes out, everything resolves, repeat.

Pokémon sorts. Dragon Quest rolls.

This week#

Final Fantasy X has no rounds.

Two ways to be fast#

ATB — a bar fills continuously. Full bar, you act.

Speed is throughput. A fast character fills faster.

Two ways to be fast#

CTB — a counter ticks down. Zero, you act, counter resets.

All counters tick at the same rate.

Speed is the size of the reset.

The formula#

counter = tickSpeed × rank × hasteMultiplier

Three inputs. Everything in the fight comes out of them.

Input 1: tick speed#

Agility goes into a lookup table, tick speed comes out.

A table is a step function — gains arrive in jumps, and the designer chooses where the steps are.

Find where yours flattens before you spend on it.

Input 2: rank#

What rank buys#

A rank 1 action costs a third of a rank 3.

Three cheap turns in the time somebody else takes one.

This is why Defend is a real move in FFX.

Rounding#

Every step rounds down.

At high Agility with Haste, two rank 1 actions can cost fewer ticks than one rank 2.

That’s the arithmetic, not a bug.

Input 3: Haste#

Halves the reset. Slow doubles it.

Casting it also halves the current counter, once.

Dispelling it doesn’t give the counter back.

So Haste is worth most early#

Its value is measured in resets avoided, not speed gained.

The prediction#

Tick speeds plus ranks gives you the next five turns.

FFX prints the same list on the HUD.

Rare thing: you can check your model against the game’s.

Where the list breaks#

It assumes everyone takes a rank 3 action.

Defend, an item, a Haste, a Slow — invalid from there on.

Ties don’t break it: fixed order, party first, Cid last.

This week’s activity#

One row per combatant, one column per tick.

Implement the formula. Feed it a real fight. Compare.

Then cast Haste at tick 0 and at tick 40.

The failure worth meeting#

Implement Haste as a change to the rate.

Your model drifts slowly and stays plausible for about a dozen ticks.

Better to meet that in a spreadsheet than in a fight.