as t--->∞, p(something getting shot down)--->1.
in that sense, trump's stubbornness in trying to force the iranians to sign an agreement rather than enforce regime change with violence is making the same mistake that putin has been making in ukraine for years. the russians have overwhelming dominance and should have won years ago, but they are refusing to win the war because they fear the outcome and, by refusing to win the war, they are guaranteeing they will eventually lose. the barbarian management strategy made sense for byzantium, precisely because they were in a position of structural weakness. it's a losing strategy in the long run, but it drags the process on and, in byzantium's case, bought them centuries of life past their death. there was always some possibility that the east would suffer a bought of the plague, or the west would slowly hellenize. it didn't happen. it could have happened; it was their only chance. they had to literally hold the fort and wait it out, but their chance never came (but, you might note that this is what the crusades were about). they really ought to have collapsed some time around the year 750, but the barbarian management strategy kept them going until the mid fifteenth century. russia may fear the outcome of winning the war in ukraine more than it fears the consequences of prolonging it into perpetuity, but it is not in a position of structural weakness. it's a strategy rooted in cultural association with orthodox christianity, rather than in an accurate analysis of the facts on the ground. i hate sports, but it's the most intuitive way i know to explain this probabilistic argument: the more often a team plays, the more likely they are to lose a game (because they are not truly independent events). if you keep playing over and over, you're eventually going to lose a few games. i actually won my dad's office football pool in 2007 by picking the giants, on the argument that the patriots were extremely unlikely to win, because they hadn't lost a game in months; the patriots would have been more likely to win the super bowl if they had lost a game in the regular season. my smart mathematical analysis won me almost $1000 that spring, along with snickers and guffaws from my dad's friends for years afterwards. because everybody else picked the patriots.
do you get it? do you understand the mathematical argument? even if you're overwhelmingly favoured, the math says that, the longer you fight the war, the more likely you eventually lose. you can't win repeatedly indefinitely, no matter how dominant you are.
"that's why they play the games."
another intuitive argument comes from legal litigation. if you ask the average lawyer, they'll tell you they hate going to court. smart lawyers do everything they can to avoid getting things in front of judges, because they know that all bets are off once you actually put it in front of a judge. even if you have the best argument, and your opponent has no chance, you still try to settle, because you just never know what judicial whim of fancy you'll have thrust on you. and, the more cases you fight, the more often you are to lose. lawyers understand this; they're taught this, and they learn it the hard way if they don't listen.
by using a tactic intended for a position of weakness to fight a war from a position of strength, putin is doing tremendous long term damage to the russian state. he understands that, but has calculated it's less bad than the alternative. we can't truly know if he's right or wrong, we can only see the conseqeunces of refusing to win the war, and insisting on dragging it on, instead.
trump's stubbornness in refusing to fight and win in iran is causing similar damage to the united states, but it's in terms of it's reputation rather than it's strategic dominance. trump has never really appeared to understand the importance of american projection. he's gone on the news and stubbornly insisted that he'll take his time, he won't be rushed in, etc. because this is about him, apparently, rather than about the united states.
if the americans continue to drag the process on by insisting on signing an agreement with a psychotic and delusionally insane terrorist death cult without carrying out the necessary regime change action first, more and more things are going to get shot down. it will not change america's dominance in the region, but it will embolden the lunatics in iran to deny it. and, it's important to remember a dictate of the last war: it doesn't matter what the truth is, it matter what people think the truth is. the americans need to be refocusing on their projection of power by hurrying up and getting this job done, in addition to enforcing the reality of it. otherwise, they're eventually going to lose, and be left with their dick in their hand, like a divorced tom brady in the boston cold.