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To get an idea about what chess variants people like to play, one can look
into statistics of running games at BrainKing.com
(http://brainking.com/en/Statistics?p=2):

3.	Chess	3128
11.	Dice Chess	1325
12.	Dice Chess 10x10	1316
26.	Loop Chess	385
27.	Japanese Chess	369
44.	Massacre Chess	207
45.	Chinese Chess	207
46.	Dark Chess	202
52.	Anti Chess	163
57.	Atomic Chess	151
59.	Embassy Chess	149
61.	Ice Age Chess	145
64.	Horde Chess	139
66.	Ambiguous Chess	132
67.	Grand Chess	132
70.	Fischer Random Chess	125
74.	Fortress Chess	112
76.	Amazon Chess	109
78.	Los Alamos Chess	109
87.	Extinction Chess	95
89.	Behemoth Chess	95
90.	Three Checks Chess	94
91.	Capablanca Random Chess	91
92.	Corner Chess	89
93.	Janus Chess	88
94.	Racing Kings	87
97.	Minishogi	83
99.	Cylinder Chess	82
100.	Recycle Chess	82
102.	Crazy Screen Chess	77
106.	Screen Chess	70
107.	Knight Relay Chess	68
110.	Legan Chess	66
116.	Knightmate Chess	59
122.	Berolina Chess	54
123.	Cheshire Cat Chess	53
126.	Maharajah Chess	44

Unfortunately statistics for finished games is not easily available at this
site. Still one can visit pages for particular variants and see the number
of total finished games, e.g. for 'Dice Chess':

Statistics of won games
white	33290 (51.71 %)
black	31028 (48.19 %)
Draws	60 (0.09 %)

No suprise, that such great games as 'Loop Chess' and 'Japanese Chess'
at the top of the list. However, it is amazing to see 'Dice Chess' as a
second most popular chess variant (after chess itself)!