How to build a world-class rock-paper-scissors bot

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dorothy wingrove

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Icons made by Freepik from www.flaticon.com CC 3.0 BY

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Greedy

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content

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sly

Icons made by Freepik from www.flaticon.com CC 3.0 BY

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Crystal ball

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Difficulty:

tattoo play

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Difficulty:

Ishikawa Watanabe Laboratory, the University of Tokyo (25th June 2012) Janken (rock-paper-scissors) Robot with 100% winning rate Retrieved from: https://www.youtube.com/watch?v=3nxjjztQKtY&feature=youtu.be

Full rights to Ishikawa Watanabe Laboratory

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imperfect information

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zero sum

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19

99

  # random bot

  my_move_history = []
  their_move_history = []

  def next_turn(their_last_move)
    ['r','p','s'].sample
  end

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  # always rock bot

  my_move_history = []
  their_move_history = []

  def next_turn(their_last_move)
    'r'
  end

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  # frequency counting bot

  their_move_history = {
    'r' => 0,
    'p' => 0,
    's' => 0
  }

  counter_moves = { 'r' => 'p', 'p' => 's', 's' => 'r' }

  def next_turn(their_last_move)  
    their_move_history[their_last_move] += 1

    their_move = their_move_history.max_by{ |_,v| v }[0]

    counter_moves[their_move]
  end

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  # Fixed string bot

  string = 'rrpspprss'
  current_position = -1

  def next_move(opp_prev_move)
    current_position =
      (current_position + 1) % string.length

    string[current_position]
  end

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De Bruijn

a de Bruijn sequence of order n on a size-k alphabet A is a cyclic sequence in which every possible length-n string on A occurs exactly once as a substring

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rrpspprss

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A = {0, 1}   B = (2, 3)

00010111

11101000

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A = {1,2,3,4}   B = (4, 4)

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0000100020003001100120013002100220023003100320033010102010301110112011301210122012301310132013302020302110212021302210222022302310232023303031103120313032103220323033103320333111121113112211231132113312121312221223123212331313221323133213332222322332323333

A = {r,p,s}   B = (3, 6)

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rrrrrrprrrrrsrrrrpprrrrpsrrrrsprrrrssrrrprprrrprsrrrppprrrppsrrrpsprrrpssrrrsrprrrsrsrrrspprrrspsrrrssprrrsssrrprrprrsrrprpprrprpsrrprsprrprssrrpprprrpprsrrpppprrpppsrrppsprrppssrrpsrprrpsrsrrpspprrpspsrrpssprrpsssrrsrrsrpprrsrpsrrsrsprrsrssrrsprprrsprsrrsppprrsppsrrspsprrspssrrssrprrssrsrrsspprrsspsrrsssprrssssrprprprsrprppprprppsrprpsprprpssrprsrsrprspprprspsrprssprprsssrpprpprpsrpprsprpprssrppprsrppppprppppsrpppsprpppssrppsrsrppspprppspsrppssprppsssrpsrpsrsprpsrssrpsprsrpsppprpsppsrpspsprpspssrpssrsrpsspprpsspsrpsssprpssssrsrsrspprsrspsrsrssprsrsssrsprsprssrspppprspppsrsppsprsppssrspspprspspsrspssprspsssrssrssppprssppsrsspsprsspssrssspprssspsrssssprsssssppppppsppppsspppspspppsssppsppspssppsspsppsssspspspssspsspssssss

### de Bruijn sequence for alphabet k and subsequences of length n.
def de_bruijn(k, n)
  @k, @n = k, n
  
  if @k.is_a?(String) # if k is a string, take k as the full alphabet
    @length = @k.length
    alphabet = @k
  else
    @length = @k
    alphabet = [*0..@length-1]
  end

  @a = [0] * @length * @n
  @sequence = []

  def db(t, p)
    if t > @n
      @sequence = *(@sequence + @a[1..p]) if @n % p == 0
    else
      @a[t] = @a[t - p]
      db(t + 1, p)
      ((@a[t - p] + 1)..@length-1).each do |j|
        @a[t] = j
        db(t + 1, t)
      end
    end
  end
  db(1, 1)

  @sequence.map { |i| alphabet[i].to_s }.join('')
end

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first move

latest move

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Count: 2

first move

latest move

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Count: 2

first move

latest move

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  # basic direct history bot

  their_move_history = ""
  
  counter_moves = { 'r' => 'p', 'p' => 's', 's' => 'r' }

  def next_turn(their_last_move)
    their_move_history << their_last_move
    
    regexp = /([rps]{3})([rps])[rps]*\1$/
    matches = regexp.match(their_move_str)
    their_move = matches.captures[1]

    counter_moves[their_move]
  end

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spsrrrspssssrrr

([rps]{3})([rps])[rps]*\1$

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([rps]{3})([rps])[rps]*\1$

spsrrrspssssrrr

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spsrrrspssssrrr

([rps]{3})([rps])[rps]*\1$

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([rps]{3})([rps])[rps]*\1$

spsrrrspssssrrr

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biggest window size

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  # direct history bot, biggest window size

  @their_move_history = "ssrssrpssprrps"

  @counter_moves = { 'r' => 'p', 'p' => 's', 's' => 'r' }

  def next_turn(their_last_move)
    @their_move_history << their_last_move
    their_move = nil

    5.downto(2).each do |i|
      regexp = /([rps]{#{i}})([rps])[rps]*\1$/
      matches = regexp.match(@their_move_history)
      (their_move = matches.captures[1] and break) if matches
    end

    their_move = fallback_method unless their_move

    @counter_moves[their_move]
  end

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greatest number of matches

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  # direct history bot, greatest number of matches

  @their_move_history = "ssrssrpssprrps"
  @counter_moves = { 'r' => 'p', 'p' => 's', 's' => 'r' }

  def next_turn(their_last_move)
    @their_move_history << their_last_move
    possible_moves = {}

    5.downto(2).each do |x|
      str = @their_move_history[-x..-1]
      matches = @their_move_history.scan(/(?=#{str}([rps]))/)
      match_counts = matches.count

      if match_counts > 0
        possible_moves[i] = { count: match_counts, following_move: matches[0][0] }
      end
    end

    if possible_moves.length > 0
      their_move = possible_moves.max_by { |k, v| v[:count] }[1][:following_move] 
    else
      their_move = fallback_method
    end

    @counter_moves[their_move]
  end

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frequency of following move

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  # direct history bot, frequency of following move

  @their_move_history = "ssrssrpssprrps"
  @counter_moves = { 'r' => 'p', 'p' => 's', 's' => 'r' }

  def next_turn(their_last_move)
    @their_move_history << their_last_move
    possible_moves = { 'r' => 0, 'p' => 0, 's' => 0 }

    (2..5).each do |i|
      regexp = /([rps]{#{i}})([rps])[rps]*\1$/
      matches = regexp.match(@their_move_history)
      possible_moves[matches.captures[1]] += 1 if matches
    end

    their_move = possible_moves.max_by{ |k,v| v }[0]

    @counter_moves[their_move]
  end

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A

B

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A

B

A'

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A'

B'

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A

B

A'

B'

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B

A'

B'

A''

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Iocaine powder

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https://rps-slackbot.herokuapp.com/

https://github.com/notthepoint/rps_slackbot

thank you

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https://webdocs.cs.ualberta.ca/~darse/rsbpc1.html

http://web.archive.org/web/20061202004212/http://www.ofb.net/~egnor/iocaine.html

https://pdfs.semanticscholar.org/5bae/79f4eb6fab8c8106736cf94a255d1535bf34.pdf

http://www.ijiris.com/volumes/volume1/issue5/11.NVIS10093.pdf

http://worldrps.com/

http://www.samkass.com/theories/RPSSL.html

https://fortheloveofplay.wordpress.com/2010/11/16/after-another-short-break-not-much-equipment-games-returns-bear-hunter-ninja/

https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/psr.html

https://en.wikipedia.org/wiki/Side-blotched_lizard

Darse Billings (2000). Thoughts on RoShamBo. ICGA Journal Vol. 23, No. 1

http://www.umop.com/rps.htm