It's definitely rather selective and seems to have been designed by starting at one particular genre that it chose to feature at the bottom and working back up, but that's an entirely valid approach. I choose not to take it as a piece of propaganda suggesting that social media games are the ultimate evolutionary product of all games design ever; indeed, one might expect that soon enough, or even already, there could be arrows coming out of the big bottom box influencing game media that we are yet to experience.
There have been other game family trees in the past; I can remember having linked to one a year or two ago, and they all take different approaches because they all have different reasons behind them. This one seems to have taken the reasonable decision to prioritise clarity over comprehensiveness; I can think of all manner of interesting arrows that I'd like to draw linking boxes together, but I think the most important arrows are largely in place.
Nevertheless, as a paid-up member of the postal games party, while I am delighted to see play-by-mail games get their own box (for they are so often forgotten) I would like to root for them getting a couple of extra outgoing arrows as well. I'm hoping that some of you can help me make a convincing argument to this end. :-)
Many postal games are effectively RPGs played by post; while postal chess games were matches between two sides and postal Diplomacy games were matches between seven sides (or fewer after dropouts and eliminations, or more in some variants), commercial postal games could cater for hundreds (or, in a few cases, thousands) of players at the same time. I claim that it's not such a stretch to see postal games as proto-MMORPGs, with the O standing for offline. It would be interesting to know whether MMOnlineRPG designers have postal game experience and whether they claim them as an influence; if not, there's a definite case for postal games influencing MUDs, not least because one Richard Bartle ran his own postal games 'zine from 1977 onwards, a full year before, as referenced in his autobiography, his work on the original MUD.
I'm also tempted to wonder whether postal games can claim prior art for the existence of virtual economies. Bribery in postal Diplomacy is par for the course, but I wonder if there are substantiated precedents to (the local equivalent of) gold farming arising from postal games. I was all too young, innocent and broke at the time, but you may know otherwise...
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