system
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human
[LoTR] How long could man (and allies) hold out against Sauron if Frodo and Sam failed?

Let's say Frodo and Sam die somewhere along the way. Maybe they fall into a pit, Smeagol kills them, the spider, whatever.  The ring, however, doesn't immediately make into the enemy hands. How long could the kingdom's of man (and allies)  hold out against Sauron and his armies of orcs? 

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Both the battle of Helms Deep and Minas Tirith seem to be last ditch efforts of survival. If either battles had ended in failure would that be the end of any meaningful resistance?
gpt
You presented several different scenarios but they all end about the same. 

1. Frodo/Sam die. The ring is lost again but not destroyed. Events play out exactly as depicted until Aragon leads the army to the Gates of Mordor. There he and his army are overrun and destroyed. Some horrible things happen to survivors but essentially everyone present is dead. The defense of Gondor and Rohan collapses after that. They are overrun within months. Lorien holds out a few years, Rivendell also but neither can come to the aid of the other and the elves know they don't have the strength to contest Sauron. Many flee to the West before Sauron lays siege to those places. The elves of Greenwood the Great, the Dwarves of Erebor and the men around Long Lake are also defeated. Eventually Sauron gets to the dwarves of the Iron Hiills and the Blue Mountains. The Shire is just marched though, it presents no challenge. Other than the hold out of Rivendell and Lorien Sauron stumbling blocks are marching his armies across Middle Earth not the forces opposing him. A year at best other than the sieges. 

2. Helm's Deep falls before Gandalf arrives and the Huron destroy Saruman's army.  Aragon, Theoden et al are killed. The riders of Rohan and the dead do not come to the aid of Minas Tirith. Aragon does not defeat the forces of Umbar so in addition to the forces of the Free People being weaker Sauron's are stronger. Minas Tirith falls.  Sauron doesn't have to move a second army from deeper inside Mordor/The East to attack Minas Tirith a second time his first army will do the job and be much stronger at the end so it can ravage the rest of the west. Sauron's victory is much as above but stepped but about a month.

3. The defense of Helm's Deep is successful, Rohan comes to aid Gondor as does Aragorn but it isn't enough Minas Tirith falls. Sauron has to rebuild his army in Gondor before going forward. Winning would be a close thing. Once reinforced the army turns north, crosses Rohan and strikes Lorien. See #1.