## Problem 37 of Monte Carlo solutions to Fifty Challenging Problems...

(This is another part of the Fifty Problems series, a set of example applications of Monte Carlo methods. In each post, I present source code which answers a probabilistic question using simulated models of the underlying system.)

Problem 37: We need $40 to get on the bus home from Vegas tomorrow, but are down to $20. The plan is to play evens in roulette (2:1 payout, 18/38 probability of winning), but we're missing one detail. Do we bet it all one time and walk away with $0 or $40, or do we bet it a dollar at a time?

#!/usr/bin/env ruby
# Bold play or cautious play? We need $40 to get on the
# bus home from Vegas tomorrow, but are down to $20. Do
# we bet it all at once on evens in roulette, or do we
# bet it a dollar at a time?
TRIALS=10000
P_WIN = 18.0/38.0 # 18 evens on a 38-slot roulette wheel
def play_bold()
return rand() < P_WIN
end
def play_cautious()
bank = 20
plays_remaining = 10000 # limit how long we can play
while (bank < 40 && bank > 0 && plays_remaining > 0)
if (rand() < P_WIN)
bank += 1
else
bank -= 1
end
plays_remaining -= 1
end
return bank == 40
end
win_bold = 0
win_cautious = 0
TRIALS.times {
win_bold += 1 if play_bold()
win_cautious += 1 if play_cautious()
}
puts "After #{TRIALS} times, wins:"
puts " bold: #{win_bold}"
puts " cautious: #{win_cautious}"

I've been coding my way through *Fifty Challenging Problems in Statistics with Solutions*. This post is a part of the *Fifty Challenging Problems* series.

*This was brought to you by Josh Myer.* He has other
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