Both situations are possible, I think.
Ah, cool, so it's a mix of things, and not any one in particular then?
If the developer can sell it to me in words and a few pictures, often I will buy it. A good quick to read site is important for the most part, especially if it's relied on to sell copies. It doesn't even have to be fancy, even just a wordpress or tumblr, as long as the relevant information is there and easy to find. A poor site design can really harm interest.
If I like a demo enough to play it again, and I can see what it has to offer, sometimes that's all it takes.
Ah, so a demo *helps*, but it's not required; sometimes the way the developer sells it to you is enough.
Dear Esther is quite hard to define really as a game, opinion is probably quite divided. Chapters or acts is a good way to split a game up, as long as it makes sense to end the chapter. A prologue chapter could be an excellent way to use a demo, I think Portal did something similar and it's been a while but I think Darwinia did too, that had a prologue. A demo in that sense is quite a good idea in my opinion. Now between an actual chapter that is included in the game, or something extra that is separate, it's down to the developer. If I have to replay something again in the full version, it should be short and snappy enough to get through without a feeling of 'GET ON WITH IT ALREADY I KNOW THIS.'
If the developer chose not to release a demo, even though there seems to be a logical point that could be used as a demo, well that's their own decision. It depends on how they want their product to be played or what the demo would lead up to. A demo should end on some sort of cliffhanger or introduction of something important to the story/gameplay.
Cheers for that. Ending on a logical break in the story of some sort seems to make the most sense.
Personally I seldom download demos since I usually know before hand if I want a game or not.
Is that due to word of mouth (ie. your friends like the game), or you having heard of and already researched the game, or a bit of both? Or something else?
I think demo size isn't that big deal anymore since most of people have relatively fast internet connection. Especially if one can just insert license code to demo and avoid second download.
Perhaps that is shifting a bit. As mentioned, it used to matter a lot. It'd definitely impact people with slow connections, of course, but maybe this is shifting as so many more people have faster and less limited connections.
If a game cost $15 or more, I would want a demo. Not to mention a game that cost $60(though I think there arn't any Indie games costing $60?).
Like Paul mentioned, if a game is cheap, it would be easier for me to just buy it rather than be bothered with a few more clicks and momments to install a demo.
And as mentioned, a demo is good to test if the game works on your machine or not. It's usually more relevant for 3D games, unless the developer has buggy software.
I agree that there is some kind of annoyance to replay a game bit you played in the demo, or even to have to stop playing to download the full version and only then continue your game.
I can think of several solutions to these issues. First, you can have the demo only play the tutorial levels, so you won't have to replay it in the full version. You can also save the game in the demo, and load it in the full version. And to not stop you from playing, you can make it a shareware, basically.
I am wondering what kind of demo I will make for my game, I might just have single player that lets you play 20 turns of a match or something like that.
Cool, thanks for that. Wanting to avoid intro level replay seems a popular theme, as does using a demo to see if your machine can run the game. This is in line with my thoughts on the subject as well. It would appear that there is also a threshold, which varies by the person, under which it doesn't matter much if there isn't a demo or not. This isn't as much in line with my thoughts, but I think I'm in the minority here. Good to know.

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One thing I am wondering, in general, is whether the availability of game demos has changed recently. In everyone's personal opinion (ie. no right or wrong here), are they perhaps more frequently used and available, less so, or something in between? Is there a trend, and if so, what is it, and possibly, why do you think it is occurring?