As far as I know, they do not all generate with melon seeds. To find Mineshafts, I would recommend exploring mineshafts, and branch mining can help as well (exploring caves as well works). But otherwise, there's not much you can do to find them.
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"A sword yields no power if the person who wields it holds no courage."
I can say that pretty much every seed I have generated since mineshafts were first introduced into the Xbox edition has had 2 or more mineshafts in it and melon seeds somewhere within one of those mineshafts. So, even though it might be mathematically possible to have a world generate without a mineshaft and/or without melon seeds, I would think it would be extremely rare.
As for finding them if you're intent on staying pure in survival, the best way is to do a lot of exploring of deep caves and look for faint signs of light or wood or cobwebs. If you don't mind creating a duplicate of your seed and/or exploring around in creative mode, then the best way is to dig tunnels around layer Y25 and X-ray glitch every 50 to 100 blocks... again looking for signs of either cobwebs or wood.
To find Mineshafts, I would recommend exploring mineshafts
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OP: As Up said, it may be rare to have a world without mineshafts, or melon seeds. Every world I have made has had either/both. . .. however, the world I am on now may be an exception. I have been exploring for a while and cannot find a mineshaft, or stronghold or even a friggin ravine! . . . lots of cave systems though.
I may post the seed number if anyone fancies looking around it, or just msg me when I'm on, and you can come look for yourself. lol
When looking for mineshafts specifically I like to explore the surface entering all open caves and looking for ravines. Ravines reveal alot of area, are deep enough to cross a mineshaft and mineshafts can often be disected by them. All you need to see is that one small piece of fence or block of wood and you know your good.
After a mineshaft has been found on the seed to find another one I go to the opposite side of the map to look there.
Is it rare to have a melon seed in the world or is it more rare to NOT have melon?
As for finding them if you're intent on staying pure in survival, the best way is to do a lot of exploring of deep caves and look for faint signs of light or wood or cobwebs. If you don't mind creating a duplicate of your seed and/or exploring around in creative mode, then the best way is to dig tunnels around layer Y25 and X-ray glitch every 50 to 100 blocks... again looking for signs of either cobwebs or wood.
???
OP: As Up said, it may be rare to have a world without mineshafts, or melon seeds. Every world I have made has had either/both. . .. however, the world I am on now may be an exception. I have been exploring for a while and cannot find a mineshaft, or stronghold or even a friggin ravine! . . . lots of cave systems though.
I may post the seed number if anyone fancies looking around it, or just msg me when I'm on, and you can come look for yourself. lol
After a mineshaft has been found on the seed to find another one I go to the opposite side of the map to look there.