Around £110-120 AKG K701/702 (702 with detachable cable) are among absolute top headphones for gaming with huge binaural soundstage and neutral bass.
Bass actually reaches quite low if you listen for it, but it always takes back seat to details.
You simply don't get strong always present bass immersion, instead they give "god mode/wallhack" level details.
You could literally tell from sound that:
"Someone is coming from rear left... Now he stopped coming closer and is directly behind moving toward right" or
"Someone firing front right far away and is likely less dangerous, but there's someone firing closer rear right"
With more fun above neutral bass headphones (like Beyerdynamic DT990) those details aren't so easily distinguished when there are lower frequency sounds.
Of course if you have noisy environment to isolate then open headphones aren't good.
Binaural sound contains cues brain uses to process 360 directionality just from two input channels.
Good headphones also give sense of distance.
Like first minute of this tells instantly if headphones are good with those gunfiring sounds from different directions and distances:
With bad headphones those don't sound any special.
You likely have such headphones...
That budget would easily also fit sound card for binaural simulation.
Sad truth is that in average game sounds have stagnated to what they were 15 years ago and most games don't even have real own sound settings.
And even if there's some headphone mode it's usually just crossfeed to eliminate very artificial in one ear feel of 2.0/stereo speaker mix played back by headphones.
(with speakers sound from one channel reaches also other ear which doesn't happen with headphones)
Sound Blaster Z would be £50 at its cheapest:
https://www.overclockers.co.uk/crea...g-sound-card-oem-30sb150200000-sc-088-cl.html
Wouldn't exactly trust it to fully drive AKGs with high dynamic range classical music, but games don't have such low average signal level and lot louder transients.
Because such volume differences would simply make listening game sounds annoying.
Really shame most music is in stereo.
While you can pick up instruments and such you still know you're listening recording, but binaural recording with good headphones is like actually being in there:
Or how about virtual hair cut:
