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Monte Carlo simulation of the Memory Game
#=
Card matching game simulation
using Revise
Load with: includet("matchGame.jl")
Analysis of Jan De Wilde's Shinkei-Suijaku Memory Game
https://jandw.github.io/memory-puzzle/
=#
using Random
"""
matchMC(nPairs::Integer,nMC::Integer)
Monte Carlo experiment of the Match Game.
# Parameters
nPairs: Number of pairs of matching cards in the game
nMC: Number of Monte Carlo iterations
# Returns
expTurns: Expected number of turns required
# Example
matchMC(8,1e6)
12.515998
"""
function matchMC(nPairs::Integer,nMC::Integer)
# Count total number of plays
playCount = 0
# Card numbers
cardVec = Vector(1:nPairs)
# Initialize random number generator
rng = MersenneTwister(1234)
# Monte Carlo iterations
for play = 1:nMC
# Game vector
cards = shuffle(rng,[cardVec;cardVec])
# Add the number of turns to the playCount
playCount += playGame(cards)
end
# Divide playCount by the number of Monte Carlo iterations
expTurns = playCount / nMC
return expTurns
end
"""
playGame(cards::Vector)
Simulate play of a single game.
# Parameters
cards: Vector of cards in the game
# Returns
turns: Number of turns required
# Example
cards = [4, 3, 5, 8, 5, 6, 1, 8, 1, 2, 7, 6, 7, 2, 3, 4]
playGame(cards) = 12
"""
function playGame(cards::Vector)
# Number of cards
nCards = length(cards)
# On the first turn, check the first two cards. Move to the third card
k = 3
turns = 1
while k < nCards - 1
# Does kth card match one of the previous (k-1) cards?
if cards[k] cards[1:k-1]
turns += 1
k += 1
# Otherwise, compare the kth and (k+1)th cards, taking one turn and jumping ahead two cards
else
turns += 1
# If (k+1)th card matches an earlier card, take another turn
if cards[k+1] cards[1:k-1]
turns += 1
end
k += 2
end
end
# Compare last two cards. If they match take one turn, otherwise take two.
if nCards > 2
if cards[nCards-1] == cards[nCards]
turns += 1
else
turns += 2
end
end
# Return the number of turns required
return turns
end
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