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Station, come to Vegas and play in a typical game. If a player busts out or leaves after his small blind, the button remains in place in a CASH GAME only. That way the blinds are still in front of the button. This makes it so much less confusing for the players.

In a tournament, you may have a dead button but an incoming player make take the position in which they sit EXCEPT if that position is between the Small Blind and the button.