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So I just found my copies of H3 and AB (I don't have SOD yet) and am replaying them, with the thought of speed running these games.  They're obviously runnable (in fact quite a few missions conveniently are built so that you can beat them most easily by rushing at the objective as soon as possible with your initial forces, since the enemy relies upon having a castle edge to compete against you and doesn't start with a prebuilt army). 

There are two questions that need to be answered before we can speedrun this game:
First:  How do we time runs?  We can do it by time, as we would other games, or we could do it in terms of total turns needed to win (presumably if the latter timing is used, we would try to do each turn as fast possible.  These may be one and the same in some missions, but not in others .  I'd lean toward turns if there is a conflict, personally because otherwsie for certain missions you might simply "press e" to end your turn repeatedly at times just to accumulate enough gold/minerals faster than going around the map during turns collecting. 

Second:  What type of runs are we doing?  ILs are simple enough although not my thing - they'd obviously involve having the best possible heroes for later missions in campaigns, which involves resetting and slowly playing prior missions in a campaign for setup.  Are single campaigns enough for an SDA submission?  For ROE and SOD I'd imagine not as they're short campaigns and the storyline goes across multiple campaigns.  For Armageddon's Blade however, each campaign is stand alone and 7-8 missions.  I imagine a full game run would be submittable, but are individual campaigns? 

Hopefully others are interested - this game is a classic and it's a shame the later iterations have been very hit or miss. 

Hope to have some strategies for the individual campaigns soon.
Thread title:  
Sure, individual campaigns can be submitted.
@Timing. Both variants are possible. But personally i think that for HoMM3 minimal amount in-game days/turns run would be a lot better and more interesting (even if in real time it will be a lot longer).
I like this game and its awesome soundtrack since I tried it back in the days, it's so much better than the last two games. So I'll happily follow your progress.

I too think a "minimal in-game turns" run would be more interesting since it would require more carefull planning.
Edit history:
LotBlind: 2014-08-18 10:57:17 am
Without being an authority on this (if you want an increased likelihood of an admin to answer, post in SDA Discussion), it seems it's pretty much against all SDA conventions to time by anything other than in-game timer time (meaning real time as measured by the game) or real time. There's no such thing as lowest number of moves/steps from an SDA point of view. I've never heard of a game that deviates from that but I might be wrong. So if you want an SDA run you'll probably have to go for real time. On the upside that means you can still do a separate turn-timed run and submit it under Casual Speedrunning or so.

There's no such thing as ILs for the campaigns because one mission affects the next one. Or at least if there is you'd have to, like you outlined, have to grind out the best starting scenario for usage at the start of each mission. Therefore it would be totally justified to do entire campaigns as segmented runs (you could even segment inside maps) or as one long SS if anyone is that bold... dunno how long that would make them. I feel ILs of the extra (but official) single-map scenarios would also be accepted. It seems to be something like playing through extra levels in whatever game has extra levels... should probably confirm that with someone else though. And with ILs there's the ruling that you'd have to submit an entire table at once, i.e. you normally can't just do one or two and submit them, however I'm not sure if that applies with extra missions like those. If it does, that'd be quite an arduous task I picture.

All in all you should get an official-er view on all such questions. Dunno who specifically out of SDA staff would know the game series. So you may have to explain how it works to them.
Btw here old thread:
https://forum.speeddemosarchive.com/post/heroes_of_might_and_magic_iii_roe_ab_sod.html

The same question about timing was discussed, but without final consensus too.
Quote from xsite:
If your goal is to submit to SDA you'll have to be able to classify the run in a category. I think that optimizing for in game days could count as low% per sda rules, but don't quote me on that.

Right I remember that discussion.  Problem is that unlike certain other games' low percent , lowest turns possible may not be objectively knowable without super extensive testing
I have an easy solution for that: if someone comes along and does the run with less turns used (if that was allowed as low% for this game) their run obsoletes the previous one even if it's slower in real-time or slightly more sloppy on average. No-one has commented on this (talking about the admins) despite it seeming like such a relevant issue for all games like this. There's more than one game where it's difficult to tell what's the absolute lowest (or sometimes absolute highest) percentage and that keeps changing over time anyway much in the way I described.

So yeah, do it like that and it's left to the runners to do the best they can.
Updating this a little, doing a casual run through atm to remember each campaign.  So far through 2 campaigns - First Castle and then Dungeon/Inferno campaign.  Both campaigns are set up similarly - two missions where you can (and it's best to) blitz through the enemies as fast as possible from the start (the dungeon/inferno ones require actual castle build up a little bit, but not very much, whereas the castle ones basically require no construction at all due to starting units) followed by a third that is longer and structured in a way to stall you out (garrisons). 

The Dungeon/Inferno one can apparently be bypassed - apparently either water walk or summon boat can get a way to sail around the garrison into the area where the final town is.  And the final town is guarded by an uber hero, who can be lured out his town if you use an extra hero (i'm not sure, but i suspect i need a hero with either stables access and/or logistics to sneak back into the castle before the uber hero can come back).  So that one can in theory be rushed. 

The castle one is trickier - there's a griffin conservatory that holds 5 angels that can boost your army faster that might give you a shot at taking the garrisons early - i just wonder if the fastest way might be taking extra time on mission 2 and getting dimension door from one of hte four inferno/dungeon castles' mage guilds.  Requires luck there.