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

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imperfect information

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zero sum

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Crystal ball

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Difficulty:

tattoo play

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Difficulty:

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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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r	r	r	p	s	p	p	r	s	s

Count: 1

s	s	p	p	s	p	r	s	s	r

s	r	r	r	r	p	s	p	p	r

first move

latest move

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Count: 1

first move

latest move

s	r	r	r	r	p	s	p	p	r

s	s	p	p	s	p	r	s	s	r

r	r	r	p	s	p	p	r	s	s

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Count: 2

first move

latest move

s	r	r	r	r	p	s	p	p	r

s	s	p	p	s	p	r	s	s	r

r	r	r	p	s	p	p	r	s	s

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Count: 2

first move

latest move

s	r	r	r	r	p	s	p	p	r

s	s	p	p	s	p	r	s	s	r

r	r	r	p	s	p	p	r	s	s

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WINDOW SIZE	COUNT	FOLLOWING MOVES
10	1	p
9	1	p
8	1	p
7	1	p
6	1	p
5	1	p
4	2	p, r
3	2	p, r
2	2	p, r

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  # 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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end of the line

get first capture

spsrrrspssssrrr

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

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

exactly 3

spsrrrspssssrrr

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spsrrrspssssrrr

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

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0 or more

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

spsrrrspssssrrr

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STRATEGIES
Random
Frequency counting
Direct history - fixed 'window' size
Direct history - highest frequency of matches
Direct history - highest frequency of following move
Direct history - longest repeating pattern

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A''

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A''

B''

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	No bluff	Bluff	Double bluff
Random
Frequency counter
Direct history - fixed window size
Direct history - highest frequency of matches
Direct history - highest frequency of following move
Direct history - longest repeating pattern

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	No bluff	Bluff	Double bluff
Random	0	0	0
Frequency counter	0	0	0
Direct history - fixed window size	0	0	0
Direct history - highest frequency of matches	0	0	0
Direct history - highest frequency of following move	0	0	0
Direct history - longest repeating pattern	0	0	0

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	No bluff	Bluff	Double bluff
Random	0	0	0
Frequency counter	0	0	0
Direct history - fixed window size	1	0	0
Direct history - highest frequency of matches	0	0	0
Direct history - highest frequency of following move	0	0	0
Direct history - longest repeating pattern	0	0	0

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	No bluff	Double bluff
Random	0	0
Frequency counter	0	0
Direct history - fixed window size	1	0
Direct history - highest frequency of matches	0	-1
Direct history - highest frequency of following move	0	0
Direct history - longest repeating pattern	0	0

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	No bluff	Bluff	Double bluff
Random, over last 10 rounds	0	0	0
Frequency counter, last 10 rounds	0	0	0
Direct history - fixed window size, over last 10 rounds	0	0	0
Direct history - highest frequency of matches, over last 10 rounds	0	0	0
Direct history - highest frequency of following move, over last 10 rounds	0	0	0
Direct history - longest repeating pattern, over last 10 rounds	0	0	0
Random, over last 100 rounds	0	0	0
Frequency counter, last 100 rounds	0	0	0
Direct history - fixed window size, over last 100 rounds	0	0	0
Direct history - highest frequency of matches, over last 100 rounds	0	0	0
Direct history - highest frequency of following move, over last 100 rounds	0	0	0
Direct history - longest repeating pattern, over last 100 rounds	0	0	0

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	No bluff	Bluff	Double bluff
Random, over last 10 rounds	0	0	0
Frequency counter, last 10 rounds	0	0	0
Direct history - fixed window size, over last 10 rounds	0	0	0
Direct history - highest frequency of matches, over last 10 rounds	0	0	0
Direct history - highest frequency of following move, over last 10 rounds	0	0	0
Direct history - longest repeating pattern, over last 10 rounds	0	0	0
Random, over last 100 rounds	0	0	0
Frequency counter, last 100 rounds	0	0	0
Direct history - fixed window size, over last 100 rounds	0	0	0
Direct history - highest frequency of matches, over last 100 rounds	0	0	0
Direct history - highest frequency of following move, over last 100 rounds	0	0	0
Direct history - longest repeating pattern, over last 100 rounds	0	0	0

	No bluff	Bluff	Double bluff
Random, over last 10 rounds	0	0	0
Frequency counter, last 10 rounds	0	0	0
Direct history - fixed window size, over last 10 rounds	0	0	0
Direct history - highest frequency of matches, over last 10 rounds	0	0	0
Direct history - highest frequency of following move, over last 10 rounds	0	0	0
Direct history - longest repeating pattern, over last 10 rounds	0	0	0
Random, over last 100 rounds	0	0	0
Frequency counter, last 100 rounds	0	0	0
Direct history - fixed window size, over last 100 rounds	0	0	0
Direct history - highest frequency of matches, over last 100 rounds	0	0	0
Direct history - highest frequency of following move, over last 100 rounds	0	0	0
Direct history - longest repeating pattern, over last 100 rounds	0	0	0