Curious as to what people think has the most replay potential.
Rules:
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The "desert island" aspect here is just to create an isolated environment. You don't have to worry about survival or anything along those lines, where playing the game would be problematic. This isn't about min-maxing your situation on the island outside of the game, or the time after leaving.
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No live service games unless the live service aspect is complete and it can be played offline -- that is, you can't just rely on the developer churning out new material during your time on the island. The game you get has to be in its complete form when you go to the island.
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No multiplayer games -- can't rely on the outside world in the form of people out there being a source of new material. The island is isolated from the rest of the world.
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You get existing DLC/mods/etc for a game. You don't get multiple games in a series, though.
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Cost isn't a factor. If you want The Sims 4 and all its DLC (currently looks like it's $1,300 on Steam, and I would guess that there's probably a lot more stuff on EA's store or whatever), DCS World and all DLC ($3,900), or something like that, you can have it as readily as a free game.
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No platform restrictions (within reason; you're limited to something that would be fairly mainstream). PC, console, phone, etc games are all fine. No "I want a game that can only run on a 10,000 node parallel compute cluster", though, even if you can find something like that.
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Accessories that would be reasonably within the mainstream are provided. If you're playing a light gun game, you can have a light gun. You can have a game controller, a VR headset and controllers, something like that. No "I want a $20 million 4DOF suspended flight sim cockpit to play my flight sim properly".
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You have available to you the tools to extend the game that an ordinary member of the public would have access to. If there are modding tools that exist, you have access to those, can spend time learning them. If it's an open-source game and you want to learn how to modify the game at a source level, you can do that. You don't have access to a video game studio's internal-only tools, though.
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You have available to you existing documentation and material related to the game that is generally publicly-available. Fandom wikis, howtos and guides, etc.
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You get the game in its present-day form. No updates to the game or new DLC being made available to you while you're on the island.
What three games do you choose to take with you?
Ah man this really is tough, your post details a lot of what's on my mind, but I think ultimately these three win out;
Minecraft - especially given the fact that we have access to the entire modding sphere, it's just plain silly how much creativity has been poured into this, and the game is pure nostalgia for me. I could get lost in it for aeons.
Dwarf fortress - wins out to CDDA because I'm a strategy nerd. What has ended up killing me in the past with this game is how much time it takes, but on a deserted Island? Well, time isn't an issue.
The last one is perhaps the most difficult, but assuming that I have access to a sufficiently high-end pc, I'd want KoboldAI (United) with all currently available local models downloaded. This is only borderline a "game", but I am able to modify the software, and the possibilities are simply endless for creativity. It'd definitely ease up the loneliness a fair bit.
I think that you can probably count KoboldAI as a game. Well, maybe more the "toy" category than "game" -- stuff like SimEarth, Conway's Game of Life or such might fall into that category. They don't have any real goals, are pretty much a pure sandbox, but "toys" like that are often-enough described as "games" to count.
The other day, I picked up something on Steam that was basically a spirograph, Zen Trails. That really falls into the "toy" category, but it's classified as a game on Steam, and I don't think that that'd be terribly-controversial for someone to call it a game.
I'll allow "toys".
Though I'm sure that there's some kind of line there. Like, thinking of the spirograph immediately brings to mind a class of software packages that are designed to let one play around with L-systems and suchlike, to make pretty pictures, stuff like that. Is Context Free a toy? Maaaybe. But I don't think I'd call Asymptote or Logo a toy, though both are certainly useful for making spirograph-like images and one can happily play around with them doing that. Somewhere a "toy" crosses the line from a "toy" to a "tool".