If you are skipped to the end of floor 8, as was done now, you missed exactly 1 Luck scroll due to how Luck scroll distribution works. Those that bought the offer need 18 dooms as their starting score, not 16. Also, nobody would have encountered a Heroism scroll by this point because they are clamped to 12 floor pools starting at floor 13. Edit: Fireball scrolls are 1 per 6 floor starting at floor 7, so clearing floor 8 from the deal would have had a 1/3 chance to miss a fireball scroll.(as noted before, fireball scrolls matter very little overall though by comparison) Without you having this knowledge yourself, I urge you to check with the team that this has been how it worked since patch 4.3. It will be nearly impossible for me to “prove” to you that these are the exact thresholds despite having charted this out over and over and over no matter how much evidence I provide, as the only official source links I could find were here, which don’t exactly specific how they are clamped:
Although the patch notes only mention Fireball and Heroism, Luck scrolls are definitely clamped. We’ve had dozens of tower events since this point and they always follow the “1 every 4 floor set, starting at floor 5” pattern.
Surely there has to be someone around that knows the ins and outs of how Tower of Doom works and can design an offer that, bare minimum, does not shortchange on the event score? Boons and scouting have nebulous value, clamped luck scrolls don’t.
On a related note, if you are going to keep the headstart offer as is I’d recommend just having it clear past stage 8 on purpose and giving 18 dooms, as I’m pretty sure the offer can’t calculate whether or not the luck scroll will be on floor 8 that far ahead of time and you run into murky waters if you clear to stage 8 where you simply had a high chance of the luck scroll being passed over (as the scroll for 5-8 could still be on stage 8).