Path of Achra – Explanation of Speed

Guide to Speed

Everything in the game with a speed (the player, allies, enemies, and game turn) has an internal counter. The game runs a check against all of these counters at once, and does 1 of 2 things. If the counter is < 100, it adds the unit’s speed to its counter and it does not get a turn. If the counter is >= 100, it subtracts 100 from the counter and the unit gets a turn.

A speed of 100 is important, because it means you pass 1/2 of these checks, in other words you get a turn one check and have to “refresh” the next (i.e. add your speed). At a speed of 200, you pass 2/3 of these checks or have to “refresh” every 3rd check, and so on.

We can generalize this as having a turn-to-check rate of x/(x+1) (or, needing to refresh every (x+1)th turn), where x is your speed divided by 100.

This results in the diminishing returns of speed at high numbers, a speed of 100 is 1/2 (0.5), 1000 is 10/11 (~0.91), 10,000 is 100/101 (~0.99) – even if you have billions of speed, you’re gonna get basically the same rate of turns as something with 10,000 speed.

Not gonna go much deeper into it here, but there’s some more things that are relevant in practice if you’re racing the game turn:

• Game turn’s internal counter is set to 1 on entering a floor. It’s speed is 5, so it’s turn rate is (5/100)/(1+(5/100)), which is 1/21. That means on the 21st check from entering the floor (and thereafter for each game turn) the game turn will always fire, even if you have infinite speed.
• Even if your last action in a stage is entering the stairs, if you do it when the game turn passes a check, it will still count as a game turn passing – so you want to leave by the 20th check after entering/the last game turn passing.
• The player’s internal counter gets set to 100 on entering a floor (this is why the player always gets a turn immediately on entering). This also means that in practice, you always fail your 2nd check, which is when you first add your speed to your internal counter – this means the speed used to increment your counter is from the end of your 1st turn, so if you can increase your speed during turn 1 it has the same impact as your entrance speed.
• On the current version, a game turn always passes when you enter level 1 floor 1.

Here are some graphs of player speed X needed to get Y turns per game turn using the above details. The 2nd graph takes into account the delayed player speed check on floor entrance to show the min turns you’ll get for a given speed after your 1st turn before the 1st game turn will be counted.

You can beat these graphs and eke out more turns by getting a multiple of your speed before your next speed check. In particular for racing game turn, if you know that you’ll hit the 1st game turn on a floor, it’s worth it to get speed greater than 2000 in order to avoid losing any turns to a check before next game turn.