The image shows hemispherical holes cut into wood, what tool can I use to do that? I could have bought that mancala game from toysrus but I need holes a bit deeper and wider to hold more stuff. Also I need 8 or 9 on each side.
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A 2" ball end router bit, and a plunge router with adequate power to run it, and which can run slowly enough to run it safely (large diameter bits must not spin too fast.)
Or (these days) a CNC router with a considerably smaller bit (round-nose would still be best for the end result) programmed to go around in circles and cut the shape.
For only a few, possibly a 2" spade bit reground to round-nose and used in a drill press.
For more capacious holes without sharp bottom corners, but not hemispherical, a tray bit in a router.