In order to modify the map (and gain the benefit of cave provinces) you will need to use the SemiRandomize button. 'Execute' generates a random map and 'Semi Randomize' creates a modified version of the map file with '_SR' appended to it. The modified map file can be found in the dominions3\SemiRandom folder. Copy & paste this map file into your dominions3\maps directory and you should be good to go.
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...bizare connections, where some provinces have zero connections ,or the connected province is several provinces away.
Also the map I see when creating the game(picking the map from the list)is always different than the one that loads in for the game. On one map the names of several provinces where clumped together in the water.
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That is bizarre. I have never seen or heard of anything like that. The only thing that I can think of is if the map file and the image are mismatched. When you use the execute button, RanDom just calls dominions3 via the command line and feeds it the settings (colors, terrain info, map name, etc) and then lets dom3 generate the initial map file and image. Then when you use the SemiRandomize button, a 2nd application (written in Yabasic) modifies the map file (the text one, not the image). In order for this to work properly, the map file named must be located in the dominions3\maps folder. The original map file is left untouched, and the modified "_SR" version then needs to be moved into the dominions3\maps folder. You can tell which one is SemiRandomized from within the game by reading the description.
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I haven't seen any sign of cave formation yet, could you supply some good settings that would result in caves?
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To increase the odds of getting some cave provinces, you will need to include plenty of border mountains. To do this, make sure that the "Normal Mount" checkbox is unchecked (as I believe it is by default) and increase the "Mountain" slider to a level you are comfortable with. The sample map that you uploaded appears to have plenty of potential provinces. Did you make the dimensions so small just for testing or are you using those dimensions in game? I wonder if using such a small image is causing dom3 to go bonkers. Just a thought.
Good luck and let me know if you continue to have trouble.