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From this note:

Some projects try to do the right thing by using namespaces, but end up doing so in a somewhat brittle way. The typical code smell starts in the entry point to the library, where a bare module is defined

So I think you should remove https://github.com/wicz/s10-edu/blob/fe84615fa789d4a55c005fbc8d70d5c5f698b319/lib/rps.rb#L4-5

In some places you use the Ruby 1.9 key: value syntax, in others the "old" :key => value syntax (Guardfile, Rakefile, game_spec.rb).

Just for the sake of picky consistency it might be worth using only one of those syntaxes.

Game#check_win does 2 things:

1. find the winner
2. build the strings that announce the result to the player

Maybe it could be renamed and simplified in something like:

def get_winner(opponent_hand, my_hand)
  case opponent_hand
  when my_hand then :draw
  when BEATS[my_hand] then :me
  else :you
  end
end

And move the result string building in the format_output method?

Currently quitting a game is not possible. Let's refactor bin/rps to allow quitting.

#!/usr/bin/env ruby

require_relative '../lib/rps'

game = Rps::Game.new
loop do
  print "Your turn. Choose one of [r, p, s] or q to quit: "
  action = gets.strip.to_sym
  case action
  when :r, :p, :s
    puts game.turn(action)
  when :q
    puts game.statistics
    exit
  else
    puts "Invalid hand!"
  end
end

For me

HANDS = %w{ r p s }.map(&:to_sym)

is simpler if written

HANDS = [:r, :p, :s]

instead of writing this:

def foo bar, baz
  # ...
end

It is more idiomatic to write

def foo(bar, baz)
  # ...
end

There isn't an absolute consensus in the community, but the latter is much, much more widely accepted. For this reason, we ask that students use the latter style for MU related projects. (NOTE: This and similar points are covered by the MU Style Guide, which we expect you to be familiar with)