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Pro Easy to learn
GameMaker: Studio is incredibly easy to learn. It requires almost no programming knowledge which means that those without the technical experience, such as designers or artists, can get create their projects without the help of a programmer.
Pro It has an IDE used for loading all of the assets
It is very easy to manage all these resources you want to put in your game, the UI widgets for each assets (sprites, sounds, backgrounds, rooms, objects and shaders) are intuitive enough for when adding or even editing the properties of each your assets. The included editors are also good and easy to use (sprite/image editors, shader editor and room editor).
Pro Has a free version that still allows for creative game development
Game Maker Studio uses a tiered service beginning with its free option. This standard edition of GM Studio has all of the features of the professional edition, minus the additional export modules for cross platform releases. The free standard edition also comes with a non-removable "Made with Game-Maker" splash screen. All other features are unhindered by the free version.
Pro Access to the GML scripting language
Game Maker Language (GML) is the primary scripting language that is interpreted similarly to Java's Just-In-Time compilation used in GameMaker. It is used to further enhance and control the design of a game through more conventional programming, as opposed to the drag and drop system.
Pro Has a Marketplace
Yoyogames website has a marketplace which opens up an opportunity for people to sell or giveaway created assets and resources (sprites, scripts, sounds, extensions, full source codes, etc.) for use in GameMaker. This benefits people who needs quality assets for their games, and for creative people to provide these assets for extra income. The Marketplace has a rating system so it can eventually increase the quality and competitiveness of the assets submitted.
GameMaker: Studio projects can be deployed to: HTML5, Linux, Windows, OS X, Windows Phone, Android, iOS and PS3/4/Vita.
It's been around since 1999.
Pro Cross-platform multiplayer support
There is the possibility of creating games that interact with different platforms and is not that hard.
Pro Easy cross-platform shader support
Write your own shaders in one shader language and have it automatically ported to all platforms. You can even choose a specific shader language to wield the full power of the target device.
Pro Easy to use
Game Maker Studios simple interface allows for rapid prototyping, and easy development.
Pro Easy to find resources/tutorials/assistance
GameMaker: Studio has a huge following, tons of people put up tutorial videos, and it's just generally easy to find help. It has a huge community.
Pro Supports 3D
There is also 3D support that doesn't interfere with the primary 2D focus.
Con Exporting to some formats costs extra
You need to buy extra modules to be able to export to platforms like Android, iOS, HTML5 and others.
Con The scripting language used is quite limited
Language does not support actual objects, structs, real data types, functions, overloading, even argument naming. Developers generally have to code around the lack of these features in very tricky ways.
Con Poor level editor
No marquee select, no layers, only one undo, glitchy, poor manipulation of scale/rotation, can't manipulate draw order, no grouping, etc.
Con Lacks a cross-platform dev environment
The dev environment only runs on Windows.
Con No built-in refactoring tools
There are no built-in refactoring tools - for example, you can rename a resource, but GM:S will not automatically change the mentions of it across the code to the new name. At the same time, however, all file formats are text-based, meaning that the effect can be achieved by simply doing "find & replace in files", which is a feature offered by pretty much every external code editor nowadays.
Con Destructive DRM
In late 2012/early 2013, YoYo Games released a version of their new Studio IDE for cross-platform development that would import games and destroy all of the image type resources for some legitimate purchasers of the software by superimposing a pirate symbol on top of the image. This was due to a fault in their digital rights management software implementation which they use as a method of combating pirated copies of the software. Though the false positives bug is reported to be fixed, the DRM is still in place and may affect placeholder graphics, etc. YoYoGames publicly stated they would remove the DRM at a later point in time, but that other less-invasive DRM techniques would remain.
Con Tends to crash or not compile games properly
Con Expensive for what it offers
There are several options with more flexibility, better learning resources, and a lower price point.
Con This is very flat for games
They are not beautiful, for example, Undertale.