easter_egg.rb

require 'rspec/autorun'
require 'json'
require 'httparty'
require 'pp'

GuessResult = Struct.new :x, :y, :count

class FakeGame
  def initialize(x=random_num, y=random_num)
    @x = x
    @y = y
    @count = 0
  end

  @@results = [:right, :higher, :lower]

  def guess(x, y)
    @count += 1
    GuessResult.new(@@results[@x <=> x], @@results[@y <=> y], @count)
  end

  def id
    :fake
  end

  def random_num
    rand(100) + 1
  end
end

class RealGame
  def initialize
    response = HTTParty.get('http://easter_egg_hunt.andrewfaraday.com/new_game')
    j = JSON.parse(response.body)
    @id = j['game_id']
  end

  def guess(x, y)
    response = HTTParty.get("http://easter_egg_hunt.andrewfaraday.com/guess/#{id}/#{x}/#{y}")
    j = JSON.parse(response.body)
    x_result = j['x'].to_sym
    y_result = j['y'].to_sym
    count = (j['turns']||0).to_i
    GuessResult.new(x_result, y_result, count)
  end

  def id
    @id
  end
end


class BinarySearch
  def initialize(min, max)
    @min = min
    @max = max
    @guessed = false
    update_next_guess
  end

  attr_reader :next_guess, :guessed

  def go(result)
    return if @guessed
    case result
    when :right
      @guessed = true
    when :lower
      @max = @next_guess - 1
      update_next_guess
    when :higher
      @min = @next_guess + 1
      update_next_guess
    end
  end

  private

  def update_next_guess
    @next_guess = (@max + @min) / 2
  end

end

def play(game)
  x_search = BinarySearch.new(1, 100)
  y_search = BinarySearch.new(1, 100)

  until x_search.guessed && y_search.guessed
    puts ?.
    result = game.guess(x_search.next_guess, y_search.next_guess)
    x_search.go(result.x)
    y_search.go(result.y)
  end

  {
    x: x_search.next_guess,
    y: y_search.next_guess,
    game_id: game.id,
    count: result.count
  }
end


def game_controller(game_constructor, game_count)
  (1..game_count).map do |i|
    game = game_constructor.call
    puts "Starting game #{game.id}..."
    play(game)
  end
end


def main
  # pp game_controller(->{ FakeGame.new }, 10)
  pp game_controller(->{ RealGame.new }, 10)
end

main


# tests

describe :FakeGame do

  it "returns right results" do
    game = FakeGame.new 4, 4

    result = game.guess(2, 5)
    expect(result.x).to eql :higher
    expect(result.y).to eql :lower
    expect(result.count).to eql 1

    result = game.guess(5, 3)
    expect(result.x).to eql :lower
    expect(result.y).to eql :higher
    expect(result.count).to eql 2

    result = game.guess(4, 4)
    expect(result.x).to eql :right
    expect(result.y).to eql :right
    expect(result.count).to eql 3

  end

end

describe :binary_search do
  let(:search) { BinarySearch.new 1, 100 }

  it "makes optimal guesses" do
    # aiming for 34
    expect(search.next_guess).to eql 50
    expect(search.guessed).to be_falsey
    search.go(:lower)
    expect(search.next_guess).to eql 25
    search.go(:higher)
    expect(search.next_guess).to eql 37
    search.go(:lower)
    expect(search.next_guess).to eql 31
    search.go(:higher)
    expect(search.next_guess).to eql 34
    search.go(:right)
    expect(search.next_guess).to eql 34
    expect(search.guessed).to be_truthy
  end

end

describe '#play' do

  it "guesses correctly" do
    game = FakeGame.new(34, 77)
    result = play(game)
    expect(result.y).to eql :lower
    expect(result.count).to eql 1

    result = game.guess(5, 3)
    expect(result.x).to eql :lower
    expect(result.y).to eql :higher
    expect(result.count).to eql 2

    result = game.guess(4, 4)
    expect(result.x).to eql :right
    expect(result.y).to eql :right
    expect(result.count).to eql 3

  end

end

describe :binary_search do
  let(:search) { BinarySearch.new 1, 100 }

  it "makes optimal guesses" do
    # aiming for 34
    expect(search.next_guess).to eql 50
    expect(search.guessed).to be_falsey
    search.go(:lower)
    expect(search.next_guess).to eql 25
    search.go(:higher)
    expect(search.next_guess).to eql 37
    search.go(:lower)
    expect(search.next_guess).to eql 31
    search.go(:higher)
    expect(search.next_guess).to eql 34
    search.go(:right)
    expect(search.next_guess).to eql 34
    expect(search.guessed).to be_truthy
  end

end

describe '#play' do

  it "guesses correctly" do
    game = FakeGame.new(34, 77)
    result = play(game)
    expect(result[:x]).to eql 34
    expect(result[:y]).to eql 77
    expect(result[:count]).to eql 7
    expect(result[:game_id]).to eql :fake
  end

end

Line 39 includes a hard-coded game id. This is why you were seeing the same result every time, and an ever-increasing turn count.
I've updated the SO question to correct this issue.
Thanks for playing (I enjoyed the idea of this challenge so much more than how it's gone)