From a purely programming point of view, I highly doubt that the chances would be different when you do another gacha. It's just unnecessary work for the programmer. Why would they do that?
Programming different % with different time makes a bit more sense, but still, it's just extra work, and it doesn't improve the UX in any way. So there's no point in wasting effort on it.
I think better chances on gacha (if it's true) is not due to programmed different % but more due to unperfect random algorythm. Random is never truly 100% random and I think some values are more frequent at certain times for certain reasons. I'm absolutly not sure about that and it's just suppositions but I already heared about similar case of random affected by time.
I started playing on Nutaku and wanted to try the japanese DMM Version, played the tutorial, made the first 10+1 Gacha and got this little beauty, and I was like:"WTF, why here, why now?"
But well she is really nice, and has at least a pleasent voice