So about Hashirama’s gambling problem
I’m pretty sure that at least part of Hashirama's thing is just impulse control (this is where he gives himself permission to be impulsive, everybody needs an outlet and this one seems safe enough for him, etc etc), but the root of it is the fear of missing an opportunity that won't come again.
This reads to me like maladaptive grief, actually, that his losses young in life primed him to take a chance, any chance, because you can keep pushing back the finality of loss if only you keep trying (so he will keep jumping after false hope as long as there is someone to dangle it in front of him, because he can't accept that the pursuit of something he wants is hopeless).
Dude got stuck in the bargaining phase of grieving and... never really left.
So this manifests as a gambling addiction - he is extremely susceptible to sunk cost fallacy and will keep throwing good money after bad rather than cut his losses and try a different tactic, because giving up means accepting he’s lost.
(And both of the surviving Senju brothers are awful at accepting loss - Edo Tensei is not a jutsu that comes from a person who is able to move on instead of obsessing over their mistakes and how to correct them, but this isn’t about Tobirama.)
Hashirama’s refusal to just fucking quit is a strength in cases where that sincerity and commitment have the chance to sway a person, but when it comes to games of chance, or people who have already made up their minds and won't be turned from their decisions, it means that he will keep taking the stupid chance in the hopes that things turn out differently this time. (So yes, his weakness and his strength are both hope, go fucking figure.)
Compounding the problem, if the consequence of his repeated attempts is only harm to himself, he’ll laugh it off. He hasn't had to be careful for his own sake since he was a child. The losses he fears are for those around him, which is why he's so obsessed with large scale, sweeping change - he wants to create a world that can't threaten them. The difference between his vision of peace and Madara's is ultimately less about selfishness vs. selflessness, I think, and more about how much of a margin of safety they will accept as safe enough, because Hashirama can’t quit.
Hashirama won’t cut his losses and give up on things even when it would be reasonable to do so, and it means he grows into exactly the kind of person that lets the perfect become the enemy of the good. He becomes increasingly all or nothing in his mindset as he gets older - see his speech to Madara in their last fight- and all of this to my mind boils down to his complete inability to leave well enough alone.
