\# Montecarlo.py \# This program uses a Monte Carlo approach to estimate the probability of winning the dice game "Approach" with different \# "hold" values. \# Recall that approach works like this: \# Both players agree on a limit n. * Player 1 rolls first. They go until they either exceed n or hold. * Then player 2 rolls. They go until they either exceed n or beat player 1 's score. \# The player who is closest to n without going over wins. \# We can reduce this to the problem of of player 1 choosing the best value at which to hold. \# We'll estimate this by simulating all possible hold values from n5:n \# This function should try each possible hold value 1000000 times. Once a hold value is set, \# play a random game and keep track of the number of wins for player 1. \# n is the limit. def monte_carlo_approach(n) : win_table ={} for i in range (n5,n+1) : win_table [i]=0 for i in range (1000000) : \#\# you do this part. My solution is under 20 lines of code. Yours can be longer, but if it's getting \#\# really big, take a step back and rethink. for item in win_table. keys () : print("\%d: \%f" \% (item, win_table[item]/1000b00))