Re: the thing with jumping in audiogames, just why
I have no idea. If you can spam a higher horizontal velocity while jumping, we'd all get around like grasshoppers.
Math time: how long one stays airborne from a vertical jump is dependent on one's initial velocity. The formula for distance traveled is dx = v0×t + 1/2×a×t^2, but that's a pain for jumping, since you have a symmetrical curve due to gravity, so I simplify it with these two:
v = v0 + a×t
dx = 1/2×a×t^2, when v0 is 0 (which it is at the peak of a jump).
Then I just decide how much airtime I want, or how high the character should be able to jump, and solve for v.
So if you want 1s of airtime, that means you're at v = 0 at 0.5s. For normal earth Gravity, a = 9.81m/s^2, and I usually round to 9.8 or 10 because even mainstream games exaggerate jumping a little for playabil"ity, so why not?
So 9.8m/s^2 × 0.5s = 4.9m/s. That means 4.9m/s is how fast you're moving both when you leave the ground, and when you land.
Your max height would be 1/2×a×t^2, and since t is 0.5, we get 1/8×9.8 =1.225m. Since we like to horizontal jump and also round things, maybe making v0 5 would be easier, but this seems reasonable-ish.
But then there's horizontal jumping. The thing is, you're jumping with the same velocity, just in a different direction. Games who get this weird tend to keep the same vertical velocity, then either don't change or increase the horizontal velocity gained from movement. Every game design tutorial I've read does the exact opposite, and have pressing left/right while airborne give the character less horizontal velocity than they would on foot, but we're ignoring how people can move in real life: without something to push off, horizontal movement in air depends more on how you jumped than on what you do while airborne.
Say you jump at a 45dg angle (pi/4). Sin and cos of that angle are both 0.707, so that conveniently means we get the same value for horizontal and vertical velocity: our v0 of 4.9 × 0.707. Since I don't feel like multiplying that many digits, let's round to 5×0.7, which is 3.5.
Now, even if your run speed is 4m/s, and you only get 5m/s by jumping, your horizontal velocity is only 3.5m/s. And your airtime is reduced to 3.5/9.8 doubled, or a little more than 0.7s. That cuts your max height to 1/2×9.8×0.35^2, which is a little over 0.75m.
If you jump a at a lower angle, say 30dg (pi/6), your vertical velocity would be even lower (0.5 × 5 = 2.5), and your horizontal higher (0.866 × 5 = 4.33, which is slightly higher than our default run speed of 4m/s). Realistically, jumping like this requires a moment to crouch to build up the energy for that much velocity, but since when do games bother with jump animations anymore, especially audio games?
So if you can insta-jump while running, ok, this is how you'd exploit it for increased speed. Notice the airtime, though: we cut v0 in half, so airtime also gets cut in half. So our max height becomes 1/2×9.8×0.25×0.25, or 1/32×9.8, or 10/32 if we want to round. That's close to 1/3m. So this would be high enough to jump pits if the pit is no more than 2m across, and things under 0.3m high (you're on a curving path, though, so something that's 0.25m high directly in front of you still hits you), but anything higher than that (like most enemies, even dwarf-sized ones) are still in your way.
Or, to ditch the math for the Google bots who made it this far: you have a specific path that you follow based on the angle of your jump. The three that I went over can map neatly to vertical jump, walking-jump, and running jump. The last one gets you not even a foot off the ground, but does give you a burst of speed, if we ignore the crouch/windup.
So Psycho Strike's use of horizontal jumping as a dash makes some sense, but it shouldn't make the character basically invincible. It makes a little more sense in The Gate, but only for the smaller enemies and threats, like rats and slime-waves, not for zombies and vampires. If we're super-jumping at 6m/s, everything changes, and balance gets weird again.
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