Hello! I'm Frobei and I've been Challenger multiple sets in a row.
Headliners can be confusing so here's what you should remember to optimize your games and aim for the perfect headliner

GENERAL RULES
Before we get into the most important Headliner rules, it is important to talk about the general rules and I’m sure most of you know them already but it’s important to have everyone on the same page.
So here are the rules:
If you don't own a Headliner, you will be offered a HL at every shop. If you own a HL, you will have one offered every 4 shops.
It’s pretty simple and from now on we will call shops that include a headliner as “headliner shop”.
Then if you buy a headliner, it takes 3 units from the pool of champions.
It makes sense but it's best to be sure everyone knows this.
And then if there are not enough units in the pool, you can’t be offered a headliner.
This happens usually around 4 cost and 5 cost champions, if everyone plays Ezreal, there’s a chance there is not enough left in the pool for you if you wanted him as well.
Rule #1
Ok now let’s talk about the hidden rules and the rules that have been changed recently with patches.
The first rule concerns your ability to find 4-cost or 5-cost headliners.
“If you already own more than 4 copies of a 4-cost unit, you can’t find its Headliner. And if you already own more than 3 copies of a 5-cost unit, you can’t find its headliner.”
Basically, if you have already Ahri 2 and two other Ahri on your bench, you can roll as you want but you will never find her headliner.
If you played Set 10 since the beginning, you can completely forget about the former rule that counted the number of units from all the players before showing any headliners.
Rule #2
When you see a headliner, it won’t show the same +1 trait you saw as the last time you saw that headliner
This rule is one of the most important rules to know if you want to force a specific headliner with the correct +1 trait.
It means if you skip Champ A with +1 trait, and 10 shops later you see again Champ A in your headliner shop, it will NEVER have the same +1 trait as the one 10 shops before.
Here are two examples: Let's say you want to play Samira Executioner but the first Samira HL you find is Country. It means the next time you see a Samira HL in your shops (no matter when), she will be Executioner because she can't be Country again. However, if you skip her again, then the next Samira will be Country because she can't be Executioner as she was already before.
Now let's say you want to play Yone Crowd Diver but the first one you find is Heartsteel. So you decide to skip it and the next Yone can't be Heartsteel again, so it will be either Edgelord or Crowd Diver. Let's say the next one you find is Edgelord and you decide to skip it again. It means the 3rd Yone you will find can't be Edgelord but it can be either Heartsteel or Crowd Diver.
Rule #3
If you pass a champion, you won’t see that champion for 7/7/7/5/4 HL shops
This one is easy to understand. If you pass a HL champion that is 1-cost, 2-cost or 3-cost, you can't see it again before 7 Headliner Shops (normal shops don't count). If you skip a 4 cost, you can't see it again before 5 headliner shops. and if it's a 5 cost, you won't see it again before 4 headliner shops.
So if you are looking for a Samira Executioner but you found Samira Country, you will have to roll 7 times to have a chance to find the other Samira. So make sure you have enough gold if you are forcing a reroll comp because you might have to spend a lot of money just to find her.
Rule #4
If you pass on a highlighted trait, you won’t see that trait highlighted again for 4 headliner offerings
This is the newest rule and here's how it works.
Let's say you are level 8 and you are rolling to find specifically Karthus Executioner but your first shop offers you Vex Executioner. It means for 4 HL shops you cannot find any +1 Executioner. So you will not have Karthus Executioner or Akali Executioner. However, this doesn't prevent you from finding Akali KDA (or True Damage) or Karthus Pentakill in these 4 HL shops.
Also it became impossible to affect this rule because of patch 14.2 which removes the ability to "reset the HL count" by buying and selling the headliners. So there is no longer any benefit from buying / selling headliners like we used to.