Man softcover from approved retailers is really hard (no sarcasm), so many good games only come in hardcover. If you give me more information about his preferences I could help you narrow the list down.
Lamentations of the Flame Princess(BX DnD) - this is the current hot stuff. Dark and Mature with a great ruleset. Lots of the best supplements coming out are based on this system. Veins of the Earth was built with this system in mind.
One of these don't stand out to you then i'd recommend Microscope. It's a timeline building RPG that makes worlds and histories. Lord of the rings was done with this one, you'd produce something like the silmirallion. If you don't know what to play, play this and get some inspiration going. once you have a better Idea of the style of game you want come back and we can give you a more focused RPG suggestion.
Someone suggested you might be looking for Video games. This is the wrong place for that but I'd recommend Divinity Original Sin , Pillars of Eternity, The Original Fallout, Planescape: tides of Numenera, Supergiant Games products (Bastion, Transistor, Pyre), Dark Souls, Shadowrun: Dragonfall, and Darkest Dungeon.
Play [Microscope] (http://www.amazon.com/gp/aw/d/0983277907/ref=mp_s_a_1_1?qid=1420205184&sr=8-1&pi=AC_SY200_QL40) with your players. I cannot reccomend this enough. It's an rpg where you build. A fictional history from scratch. Things get weird, unique, and awesome quickly. All you need are index cards and a pen. The book is pretty thin, and 2 quick read throughs will learn you the rules. The guys that made it deserve the money, though.
/u/pierec already mentioned Fiasco, which is great, plays fast, and requires very little setup -- and the setup is just as fun as the play.
Another option that I can't recommend highly enough is Microscope. Microscope tends to be less gonzo than Fiasco, and relies even less on external inputs for play (Fiasco games rely on free playsets you can get on the Bully Pulpit webside). Microscope also rewards (but does not require) a dedicated group coming back to the world they create over and over again.
Note that both of these are more like collaborative improv-fiction exercises than proper games, in that there's no winner or loser -- the point is to make an interesting story. But they're wonderful with the right group.
Indie Press Revolution is a great source for indie story games like this, if you want more.
One part where your friend is absolutely correct is in Skill and Power selection. 4E's tactical combat is really quite good, and the storytelling elements are not really supported by the rules. Therefore, when choosing a power on Level-up, you would be a fool to not pick the power that confers the best tactical advantage. Do you want the ability to add 15 to your athletics roll, or to be able to shift your speed and make 2 attacks? By taking powers that improve chances of good storytelling, you are actively weakening your character in combat. Ideally, you shouldn't have to choose.
Asside from that, 4E rules do not do anything to prevent or hinder storytelling. They just do absolutely NOTHING to assist in it. At it's heart, D&D is a tactical combat game. Look at the stories here, a lot of them are about noteable fights.
Unfortunately, the skill system in D&D encourages you to only do things you are good at, and kind of locks you in to a set path of expertise. If you wanted to become better at a certain thing, you would have to house rule it. People are extremely attached to their characters, and you only get experience for conquering challenges, so there is no rules supported incentive to have bad things happen to your character, which unfortunately makes for REALLY good storytelling.
If you're looking for games that encourage good storytelling, there is a genera called "Story Games". Check out Microscope. It's kind of a world building game where you go through a series of vignettes. Characters are really impermanent, which frees them up to be actual characters who are able to follow their hopes and dreams, instead of walking combat engines.
This is literally the perfect thing you are looking for. It's basically collaborative world history generator where you can zoom in and zoom out of various parts of history to see how things unfold. Matt Colville can vouch for it's usefulness.
Man softcover from approved retailers is really hard (no sarcasm), so many good games only come in hardcover. If you give me more information about his preferences I could help you narrow the list down.
https://www.amazon.com/Esoterrorists-RPG-2nd-Robin-Laws/dp/1908983523/ref=sr_1_1?s=books&ie=UTF8&qid=1494289945&sr=8-1&keywords=Esoterrorists
https://www.amazon.com/Blue-Rose-AGE-Romantic-Fantasy/dp/1934547743/ref=sr_1_2?ie=UTF8&qid=1494289980&sr=8-2&keywords=Blue+rose+rpg
https://www.amazon.com/Microscope-Ben-Robbins/dp/0983277907/ref=pd_rhf_dp_s_cp_9?_encoding=UTF8&pd_rd_i=0983277907&pd_rd_r=Z3RJ2JPXJQYDRYA06S2Y&pd_rd_w=hHGH4&pd_rd_wg=W5G5p&psc=1&refRID=Z3RJ2JPXJQYDRYA06S2Y
https://www.amazon.com/Bully-Pulpit-Games-BPG-005/dp/1934859397/ref=pd_sim_14_3?_encoding=UTF8&pd_rd_i=1934859397&pd_rd_r=JBAWXXB309ERX5KH0PXT&pd_rd_w=Eunmp&pd_rd_wg=OTd2y&psc=1&refRID=JBAWXXB309ERX5KH0PXT
https://www.amazon.com/Monster-of-the-Week-EHP0009/dp/1613170920/ref=pd_rhf_dp_s_cp_2?_encoding=UTF8&pd_rd_i=1613170920&pd_rd_r=WFVTZB7V8R3S7S8F462W&pd_rd_w=HYjgo&pd_rd_wg=K0zZT&psc=1&refRID=WFVTZB7V8R3S7S8F462W
https://www.amazon.com/Evil-Hat-Productions-EHP0002-Accelerated/dp/1613170475/ref=pd_sim_14_8?_encoding=UTF8&pd_rd_i=1613170475&pd_rd_r=JBAWXXB309ERX5KH0PXT&pd_rd_w=Eunmp&pd_rd_wg=OTd2y&psc=1&refRID=JBAWXXB309ERX5KH0PXT
https://www.amazon.com/Urban-Shadows-Softcover-MPG007-Truman/dp/1987916166/ref=pd_sim_21_2?_encoding=UTF8&pd_rd_i=1987916166&pd_rd_r=DKP8DTTM0N8MT2HDRFPZ&pd_rd_w=i0nmQ&pd_rd_wg=KPg28&psc=1&refRID=DKP8DTTM0N8MT2HDRFPZ
https://www.amazon.com/Kingdom-Ben-Robbins/dp/0983277915/ref=pd_rhf_dp_s_cp_13?_encoding=UTF8&pd_rd_i=0983277915&pd_rd_r=A9ZZTCT4BD1KY3DA9ZYW&pd_rd_w=jRFtT&pd_rd_wg=biDau&psc=1&refRID=A9ZZTCT4BD1KY3DA9ZYW
https://www.amazon.com/Bully-Pulpit-Games-Durance-Playing/dp/0988390906/ref=pd_sim_14_26?_encoding=UTF8&pd_rd_i=0988390906&pd_rd_r=T0HFDYG416QT8CZBM6C7&pd_rd_w=ljUZO&pd_rd_wg=hK410&psc=1&refRID=T0HFDYG416QT8CZBM6C7 (I think)
Character playbooks for pbta might be hard to print off.
https://www.amazon.com/Havenshield-Complete-RPG-Rulebook-Myers/dp/154258356X/ref=sr_1_7?s=books&ie=UTF8&qid=1494291018&sr=1-7&keywords=Rpg (this seems like its worth a look)
That kind of sounds like Microscope (http://www.amazon.com/gp/product/0983277907/ref=s9_simh_gw_g14_i2_r?ie=UTF8&fpl=fresh&pf_rd_m=ATVPDKIKX0DER&pf_rd_s=desktop-1&pf_rd_r=15EKZT6HT67DQBPD8JQ8&pf_rd_t=36701&pf_rd_p=2437869742&pf_rd_i=desktop)
My typical List of OSR style Fantasy games
----------------
Retro Clones
All of these have complete free versions on their websites(usually minus art)
New Stuff
------------
One of these don't stand out to you then i'd recommend Microscope. It's a timeline building RPG that makes worlds and histories. Lord of the rings was done with this one, you'd produce something like the silmirallion. If you don't know what to play, play this and get some inspiration going. once you have a better Idea of the style of game you want come back and we can give you a more focused RPG suggestion.
Someone also suggested Chuubo's Marvelous Wish Granting Engine. If the idea of playing in a Ghibli film excites you, this is the way to go.
Someone suggested you might be looking for Video games. This is the wrong place for that but I'd recommend Divinity Original Sin , Pillars of Eternity, The Original Fallout, Planescape: tides of Numenera, Supergiant Games products (Bastion, Transistor, Pyre), Dark Souls, Shadowrun: Dragonfall, and Darkest Dungeon.
Official website: http://www.lamemage.com/microscope/
Amazon: http://www.amazon.com/Microscope-Ben-Robbins/dp/0983277907
microscope
https://www.amazon.com/Microscope-Ben-Robbins/dp/0983277907
Play [Microscope] (http://www.amazon.com/gp/aw/d/0983277907/ref=mp_s_a_1_1?qid=1420205184&sr=8-1&pi=AC_SY200_QL40) with your players. I cannot reccomend this enough. It's an rpg where you build. A fictional history from scratch. Things get weird, unique, and awesome quickly. All you need are index cards and a pen. The book is pretty thin, and 2 quick read throughs will learn you the rules. The guys that made it deserve the money, though.
Here is the desktop version of your link
/u/pierec already mentioned Fiasco, which is great, plays fast, and requires very little setup -- and the setup is just as fun as the play.
Another option that I can't recommend highly enough is Microscope. Microscope tends to be less gonzo than Fiasco, and relies even less on external inputs for play (Fiasco games rely on free playsets you can get on the Bully Pulpit webside). Microscope also rewards (but does not require) a dedicated group coming back to the world they create over and over again.
Note that both of these are more like collaborative improv-fiction exercises than proper games, in that there's no winner or loser -- the point is to make an interesting story. But they're wonderful with the right group.
Indie Press Revolution is a great source for indie story games like this, if you want more.
One part where your friend is absolutely correct is in Skill and Power selection. 4E's tactical combat is really quite good, and the storytelling elements are not really supported by the rules. Therefore, when choosing a power on Level-up, you would be a fool to not pick the power that confers the best tactical advantage. Do you want the ability to add 15 to your athletics roll, or to be able to shift your speed and make 2 attacks? By taking powers that improve chances of good storytelling, you are actively weakening your character in combat. Ideally, you shouldn't have to choose.
Asside from that, 4E rules do not do anything to prevent or hinder storytelling. They just do absolutely NOTHING to assist in it. At it's heart, D&D is a tactical combat game. Look at the stories here, a lot of them are about noteable fights.
Unfortunately, the skill system in D&D encourages you to only do things you are good at, and kind of locks you in to a set path of expertise. If you wanted to become better at a certain thing, you would have to house rule it. People are extremely attached to their characters, and you only get experience for conquering challenges, so there is no rules supported incentive to have bad things happen to your character, which unfortunately makes for REALLY good storytelling.
If you're looking for games that encourage good storytelling, there is a genera called "Story Games". Check out Microscope. It's kind of a world building game where you go through a series of vignettes. Characters are really impermanent, which frees them up to be actual characters who are able to follow their hopes and dreams, instead of walking combat engines.
Ben Robbins - Microscope
This is literally the perfect thing you are looking for. It's basically collaborative world history generator where you can zoom in and zoom out of various parts of history to see how things unfold. Matt Colville can vouch for it's usefulness.