As I said earlier:
Of course it can still fail, but the chance to fail 4
times in a row with 50% success chance is very low, and if it happens
you can’t really do much about it, at least 2~3 fails were on something
that doesn’t matter much.
You’re not cheating the system by following this, the success chance to enhance afterwards is still 51%, but theorycrafting, if you want to be “less likely to fail on something that cost a lot”, you’d rather fail on something that doesn’t cost a lot.
The chance to get head head head is the same as any other sequence true, but the chance to get head head head is not the same chance as getting (head+tail+head and head+tail+tail and tail+tail+tail etc…) combined.
And I know what I’m saying, I read that site I linked years ago, this is not a magical solution or cheating the game’s mechanics, but we all know the chance to get head+head+head+head from the start is not 50%, and you can result in other sequences that include tail, which in our case equals failure.
As we know that the chance to get head+head+head+head is 6.25%, if you end up reaching head+head+head, you would know you are less likely overall to get tails, but in reality we know that the chance is independent and is actually still 50% to get heads, but if you are realistic enough, you would believe that you cannot keep getting the same result forever in a 50% chance coin toss, in which case I would rather try enhancing something else until I fail twice consecutively with the same odds then try again.
As I said, this doesn’t change the odds to succeed in one enhancement, it is still RNG, and it will forever be, but it is still somewhat safer in this game, coming from facts, but you can call it a way to “feel better about yourself”, I personally wouldn’t risk enhancing once again after succeeding 3~5 times in a row still .
TL;DR: It doesn’t boost your luck, but it evens the odds of a normal 100 coin toss that should result in an average of 50 head 50 tail result.