What you fail to understand is that the djinn system would cease to be fun with the nerfs you're proposing. Djinn and summons were designed to work in a cadence, where the player expends an ammo-based system to steadily weaken themselves, with the promise of being able to pull off a strong attack later in the battle and recover their spent resources. After a certain point, it reaches an equilibrium where the player is getting back djinn at the same rate they're spending them. That is how this system was designed. If you make djinn take longer in recovery, this cadence is lost; the player is made weaker and weaker with no equilibrium in sight, until they finally run completely dry. Djinn would lose their intended use, and just become a watered down mechanic to fix a non-existent problem.
Did I say non-existent? Yes, I mean it. The loop you mentioned is end-game only. In GS1, you only have Flash available for the final battle. The designers knew it was broken. It exists so that players who are underleveled (or bad at the game) can still beat it. Remember that games are meant to be beaten, so it's okay for this kind of thing to exist sometimes. Can you use it to trivialize the Fusion Dragon? Yes. Does it make the battle take forever because you're doing practically no damage with this strat? Also yes. Is it fun? Not after the first 20 times you do it. There are sustainable ways to take down the Fusion Dragon that don't involve stalling out the battle. Players will naturally gravitate toward using the most damaging method available to them that can consistently win, and if they're underleveled to the point of having to rely on Flash+Granite spam, it's probably a good thing the option is there for them.
For future reference, there is actually a better loop in GS2 that makes use of lull and eddy:
Do stuff -> lull
Flash -> summon magaera -> unleash eddy -> summon mercury
Do stuff -> lull
...you get the idea. There's a few other variants, and it requires a very deliberate turn order to make the second turn work, but if your lull user is faster than the boss, you get to completely skip its turn half the time, and receive 10% damage the other half. In the absence of djinn interference moves (like djinn storm) or status (such as stun or instant death), it's effectively impossible to lose. Except... it turns out that Dullahan, Doom Dragon, Valukar, and even the Flame Dragons all have djinn interference attacks! Only Sentinel and Star Magician lack any form of djinn interference, both of which will take excruciatingly long to kill using this strat.
Naturally, this is boring as hell and requires intricate setup ahead of time, so most players don't do it. And why would they? They could summon rush instead and KO even Dullahan in 3-4 turns. There is no fight in the game that is difficult enough to warrant such a strategy, with the most difficult fights even having something specifically to dissuade it, so players will instead trend toward using a setup that inflicts more damage.
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As for the other "problem" you mentioned, of players spamming summons in normal battles: This isn't a problem in and of itself, but rather a symptom of a different problem. Players use summons on normal battles not because it's "broken," but because they're lazy. They don't actually want to fight battles, so they use the quickest, most efficient, and most consistent method available to them so they don't have to. That last one is important. Fleeing battles is actually faster than summon rushing them - if it succeeds. Fleeing often fails, however, so players get into the habit of fighting everything they come across, which means they have to resort to other means to clear it quickly. If flee consistently worked, players wouldn't feel the need to summon rush to clear encounters.
Another thing to note is that this "broken" strat involves the monotony of going into the djinn menu after every single battle to set up for the next one. If the player is willing to go to such extents to circumvent the expected gameplay pattern, may as well let them. Even if you did double recovery time, players would just shift to using djinn unleashes to kill enemies and then set them back after battle, which is just as sustainable as summon rushing, albeit slightly more involved and may not one-round.
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As for your multiple health bar solution... this is effectively identical to simply reducing the percent HP modifier on summons. If you wanted to split a boss's health bar into two, it would be equivalent to halving the percent HP modifier. May as well cut to the chase and reduce the HP percent damage itself, rather than trying to do some fancy workaround for bosses.
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And finally, the HP/PP cost proposal: this is highly problematic. Keeping psynergy and summon resources distinct is important for preserving both of their usefulness. If summons cost PP, it would just crowd out psynergy, rather than meaningfully limit summons. And making it cost HP would just feel bad. The cost would either be so low that you wonder why it's there in the first place, or it would be so high that you'd frequently kill yourself when trying to use it in a boss fight. There's no middle ground.
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@Sala: I completely disagree with making multi-elemental summons more expensive. They're already weaker per djinni used than their mono-elemental counterparts. All of the multi-elementals of 6 cost or lower are pretty well balanced imo. It's only the 7+ djinn summons that are problematic, since they give a disproportionate amount of burst damage for summon rushing the bonus bosses. Essentially, these summons only exist to be abused by summon rushing, while the 6 and below summons are all plenty feasible for a conventional party to make use of. Even if they were made more expensive, it still wouldn't solve the issue of how much burst they can put out.
Did I say non-existent? Yes, I mean it. The loop you mentioned is end-game only. In GS1, you only have Flash available for the final battle. The designers knew it was broken. It exists so that players who are underleveled (or bad at the game) can still beat it. Remember that games are meant to be beaten, so it's okay for this kind of thing to exist sometimes. Can you use it to trivialize the Fusion Dragon? Yes. Does it make the battle take forever because you're doing practically no damage with this strat? Also yes. Is it fun? Not after the first 20 times you do it. There are sustainable ways to take down the Fusion Dragon that don't involve stalling out the battle. Players will naturally gravitate toward using the most damaging method available to them that can consistently win, and if they're underleveled to the point of having to rely on Flash+Granite spam, it's probably a good thing the option is there for them.
For future reference, there is actually a better loop in GS2 that makes use of lull and eddy:
Do stuff -> lull
Flash -> summon magaera -> unleash eddy -> summon mercury
Do stuff -> lull
...you get the idea. There's a few other variants, and it requires a very deliberate turn order to make the second turn work, but if your lull user is faster than the boss, you get to completely skip its turn half the time, and receive 10% damage the other half. In the absence of djinn interference moves (like djinn storm) or status (such as stun or instant death), it's effectively impossible to lose. Except... it turns out that Dullahan, Doom Dragon, Valukar, and even the Flame Dragons all have djinn interference attacks! Only Sentinel and Star Magician lack any form of djinn interference, both of which will take excruciatingly long to kill using this strat.
Naturally, this is boring as hell and requires intricate setup ahead of time, so most players don't do it. And why would they? They could summon rush instead and KO even Dullahan in 3-4 turns. There is no fight in the game that is difficult enough to warrant such a strategy, with the most difficult fights even having something specifically to dissuade it, so players will instead trend toward using a setup that inflicts more damage.
---
As for the other "problem" you mentioned, of players spamming summons in normal battles: This isn't a problem in and of itself, but rather a symptom of a different problem. Players use summons on normal battles not because it's "broken," but because they're lazy. They don't actually want to fight battles, so they use the quickest, most efficient, and most consistent method available to them so they don't have to. That last one is important. Fleeing battles is actually faster than summon rushing them - if it succeeds. Fleeing often fails, however, so players get into the habit of fighting everything they come across, which means they have to resort to other means to clear it quickly. If flee consistently worked, players wouldn't feel the need to summon rush to clear encounters.
Another thing to note is that this "broken" strat involves the monotony of going into the djinn menu after every single battle to set up for the next one. If the player is willing to go to such extents to circumvent the expected gameplay pattern, may as well let them. Even if you did double recovery time, players would just shift to using djinn unleashes to kill enemies and then set them back after battle, which is just as sustainable as summon rushing, albeit slightly more involved and may not one-round.
---
As for your multiple health bar solution... this is effectively identical to simply reducing the percent HP modifier on summons. If you wanted to split a boss's health bar into two, it would be equivalent to halving the percent HP modifier. May as well cut to the chase and reduce the HP percent damage itself, rather than trying to do some fancy workaround for bosses.
---
And finally, the HP/PP cost proposal: this is highly problematic. Keeping psynergy and summon resources distinct is important for preserving both of their usefulness. If summons cost PP, it would just crowd out psynergy, rather than meaningfully limit summons. And making it cost HP would just feel bad. The cost would either be so low that you wonder why it's there in the first place, or it would be so high that you'd frequently kill yourself when trying to use it in a boss fight. There's no middle ground.
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@Sala: I completely disagree with making multi-elemental summons more expensive. They're already weaker per djinni used than their mono-elemental counterparts. All of the multi-elementals of 6 cost or lower are pretty well balanced imo. It's only the 7+ djinn summons that are problematic, since they give a disproportionate amount of burst damage for summon rushing the bonus bosses. Essentially, these summons only exist to be abused by summon rushing, while the 6 and below summons are all plenty feasible for a conventional party to make use of. Even if they were made more expensive, it still wouldn't solve the issue of how much burst they can put out.