When S2 first came, I regularly summon there every month using the coins and gems gathered and bought that time in 2018 and early 2019. In all summoning attempts at the S2 portal, it yielded me 3 Mitsukos, 2 Ariels, 1 Kageburado, 1 Inari, 1 Poseidon, and 1 Atomos as Atlantis legendaries, missing only badly wanted Tarlak and Ursena, and ignoring Mok-Arr and Misandra. As featured past HOTMs, I have gathered 2 Kunchens, 1 Ares, 1 Alberich, 1 Athena. The problem with summoning every month is that you may tend to get dupe legendaries. But due to the limited budget back then, I only have Mitsuko and Ariels in dupes, who are heroes some players wont mind maxing dupes of them.
When S3 commenced, my original plan was to collect as many valhalla coins possible from various free sources and only use them when all legendaries are summonable. I somewhat deviated a little, summoning a portion of my hoarded coins and use some of them every 3-4 months. So, for the those previous summoning at S3, due to the limited number of summon attempts, it was understandable not pulling a legendary (I still don’t have even Almur). When S3 was about to finish, Alfrike and Fenrir graced me their presence. Ratatoskr was from a previous summon attempt. The disadvantage I find in this strategy is that, as pointed out by others, you still have the same summoning odds (actually reduced for a specific hero because the pool is already inundated by more legendaries) and when you summon one, the new shiny toy is not that anymore new and shiny as players may have already been using them for quite some time. Though there are really good S3 legendaries that will last for quite some time, i.e. Alfrike, Frigg, Odin, Lord Loki, etc.
Going on to S4, I don’t know what would be my summoning schedules, whether to summon once I have the required number of coins, or hold on to them and only summon when I have enough for a 5x or 10x pull, or hold on to them until when all S4 legendaries are available at the portal. I wont be using gems to pull any hero from any portal, that’s for sure.