In the test I did with a Julii campaign, the war declaration didn't change between playing continuously and reloading.
Julii imperial campaign, M/M difficulty, FOW false:
Start, 270 BC. Position the map so that you can see both Syracuse and Athens. Hit end turn.
Turn 1, 270 BC. Scipii sieges Syracuse which can hold 7 turns. This initial siege of Syracuse might be scripted. Hit end turn.
Turn 2, 270 BC. Decline the trade offer from Gaul. Syracuse can hold for 6 turns. Hit end turn.
Turn 3, 269 BC. Accept the marriage offer. Syracuse can hold for 5 turns. Hit end turn.
Turn 4, 269 BC. Syracuse can hold for 7 turns. (Perhaps an unsuccessful assault was made and the siege has been reinstated.) Macedonia sieges rebel owned Athens which can hold for 6 turns. Macedonia is at war with the rebels and no one else. Save the game. Hit end turn.
Turn 5, 268 BC. Syracuse can hold for 6 turns. Athens can hold for 5 turns. Hit end turn.
Turn 6, 268 BC. Syracuse can hold for 5 turns. Athens falls to Macedonia. Exit the game.
Load the savegame made on turn 4. The random number generator could introduce a difference at this point because after a reload the AI may not perform the exact same sequence of decisions requiring a random number. It's possible that a random number is used to weight the decision to break a siege, but I find this test to be very repeatable. Hit end turn.
Turn 5, 268 BC. Scipii lifts the siege on Syracuse and moves away. Macedonia lifts the siege on Athens and moves away. Macedonia is still at war with the rebles, and the Macedonian army which was sieging Athens moved north to an area where there are no rebel armies. There is in fact no observable threat to Macedonia anywhere on the map, and they are not at war with any other faction. Hit end turn.
Turn 6, 268 BC. Scipii sieges Syracuse which can hold for 7 turns. Macedonia sieges Athens which can hold for 6 turns with the same army as before. This is a futher indication that there are no other threats to Macedonia because the AI returned to the same strategy is was using before the save on turn 4.
End of test.
Conclusion:
Clearly, loading the game caused both sieges to be lifted because neither siege was lifted when play was not interrupted by the save/load cycle. The expansion by Scipii and Macedonian is set back by the lifting of these sieges. It's apparent that the AI reformulated it's siege strategy, and it took more than one turn to get the sieges back in place. It took the first turn (turn 5) to reassess the situation just as CA claims, and the second turn (turn 6) to reinstated the sieges. This reassessment was necessary only because the AI was not fully aware of the situation after the reload. The course of the campaign is altered by saving and loading because Macdonia should already be in possession of Athens on turn 5, and Scipii should be further along in it's conquest of Syracuse. This has a far reaching effect because a faction is set back economically for the rest of the campaign, it affects all AI factions and happens repeatedly as often as you reload.
It's true than not all sieges are necessarily lifted after a reload, but from observation with FOW off I would estimate that 90% are lifted. The AI may be moving these formerly sieging armies away from cities because it's programmed not to position them that close to cities that it isn't sieging.
Bromely's data is very nicely done, and it doesn't surprise me at all that it shows 4 continuous turns to be the level which allows expansion since the max siege length is typically 7 turns. I'll bet the average siege length is about 4 turns. I would say to get on a level footing with the AI you have to not only play at least 4 turns per sitting but also break off your own sieges and perform no diplomacy on the turn after a reload.
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