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?
Tetris, MarioKart 8, and Solitaire.
Dude you can just make cards.
I'm kind of getting away from the point of the post, but honestly, I'm not actually sure that you could, on a desert island. I mean, the hardware is simple compared to what a video game uses, sure. But a fundamental element of the great majority of solitaire games is some face-down cards that are unknown, which means that you have to have some kind of manufacturing process that makes the card backs indistinguishable even for someone who has been playing with them for five years. I...don't know how I'd do that, on a desert island. Honestly, I'm not even sure that a standard pack of cards would continue to be usable for that long -- I think that they'd develop creases and folds and wear that you'd start to recognize.
You might be able to make a reasonably-usable set of dice, play games that use that. That's a way to introduce hidden information, though I'm sure that they wouldn't be as fair as a commercial set today. If you have hidden information, you don't need indistinguishable cards -- you can just keep all the face-down cards face-up off to the side, and use that information to pick one of the face up cards from your when you would have flipped a face-down card in solitaire as it's traditionally played.
If you think about it, there are a lot of older games that people used to play, but it took a long time for card games to show up, and that makes me suspicious that the manufacturing maybe isn't easy.
kagis
https://www.britishmuseum.org/blog/top-10-historical-board-games
Here's a list of old board games.
Looking at this, you do have Mahjong, and that requires making tiles that have indistinguishable backs. But...I'm not even sure that I could reasonably get together an industry capable of making indistinguishable tiles on my lonesome in five years. Not sure what they're made of. Porcelain?
kagis
Apparently bone.
https://en.wikipedia.org/wiki/Mahjong_tiles
There are a number of dice games listed.
I think that a simpler way to handle a "hidden information" aspect to games using primitive technology would be to create physically-similar things that go into a container, where you reach into the container and pull one out.
Face-up solitaire is not that different, as a game. It's still a puzzle you can fuck up.
If nothing else - pick a video game that has solitaire in it.
For the wider faff about actual desert-island manufacturing, consider a spinner instead of dice. Marking sixths on a circle is dead easy and then all you need is one stick kinda balanced on another. Yahtzee might take a while... but who are you gonna play against?