How Games Maintain Consistent Speed Across Different Devices

moonwalker — Sun, 09 Feb 2025 18:05:10 +0000

Our game wants to rotate something at 3 radians/second on every device. Let's see how this works at different framerates.

For a device running at 60 FPS:

Delta time (time for 1 frame) = 0.0167 seconds
Rotation covered in 1 frame = 0.0167 * 3 (radians/second) = 0.05 radians
Total rotation in 60 frames = 0.05 * 60 = 3 radians

For a device running at 30 FPS:

Delta time (time for 1 frame) = 0.033 seconds
Rotation covered in 1 frame = 0.033 * 3 (radians/second) = 0.1 radians
Total rotation in 30 frames = 0.1 * 30 = 3 radians

The key insight here is that based on FPS, the amount of rotation that happens in a single frame changes. For higher FPS it's lower (smaller steps), and for lower FPS it's higher (bigger steps).

But the total rotation over one second remains the same: 3 radians.

This is why we use delta time - it ensures consistent motion regardless of the device's frame rate. Instead of applying rotation (3 radians/second) directly per frame, we calculate the appropriate rotation for each frame by multiplying our desired rate by delta time (seconds/frame).

So time dependency becomes frame dependency that resolves itself on each device.

Counting in Probability: A Dev's 2x2 Cheat Sheet

moonwalker — Fri, 07 Feb 2025 05:20:42 +0000

I enjoy probability and statistics, but counting problems often confuse me - especially with questions of replacement and order in experiments.

Here's a 2X2 matrix that handles these 4 possibilities:

Selection Type \ Order	Order Matters	Order Doesn't Matter
With Replacement	n^r	C(n+r-1,r)
Without Replacement	P(n,r) = n!/(n-r)!	C(n,r) = n!/(r!(n-r)!)

Where:

n = total items to choose from
r = items being chosen
P(n,r) denotes Permutation
C(n,r) denotes Combination

To classify any counting problem, ask two questions:

Can I use the same item again?
Does sequence matter?

Examples:

Candy jar

Allows replacement - can pick a candy, return it, and pick it again
Deck of cards

No replacement - once drawn, a card stays out of the deck
Password

Allows replacement - can reuse letters, and order matters
Committee

No replacement - each person picked once, order doesn't matter

DEV Community: moonwalker

How Games Maintain Consistent Speed Across Different Devices

For a device running at 60 FPS:

For a device running at 30 FPS:

Counting in Probability: A Dev's 2x2 Cheat Sheet