Simulating a Fun Probability Problem in Python
At school right now, I am taking a course in discrete mathematics. The topic we are on right now is probability. For one of our homeworks, we got the following problem:
We are to choose between two games A, and B. In game A you roll a fair die once and you receive the number of dollars on the top face. In game B you roll two fair dice and you receive the maximum of the two values shown on the top face. It cost $3 dollars to play game A, and $4 to play game B. Which game should we choose?
Now, if I was a better student, I would jump right into the textbook or notes and try to figure out this problem in elegant, mathematical way. Instead of taking that boring route, I wrote a little Python script to simulate this problem. Haters, don't worry. I do know enough about statistics to be confident that if I run these games a whole bunch of times (let's go with 100,000 times) that I will be able to confidently see which of the two games is more profitable.
First I needed a random number generator. Python's standard library includes this and countless other useful libraries that I could drone on about for hours.
Now I need to write a function I can call over and over and over to simulate playing the two games repeatedly. I want to play the two games the same number of times, so let's toss them into a single function called
test(), which will return the net profit of both games for that specific round.
def test(): # game A # we get the value of the dice but we have to subtract the cost of the game profitA = random.randint(1, 6) - 3 #game B # we get the maximum of the two dice but, again, we have to subtract the cost of the game profitB = max(random.randint(1, 6), random.randint(1, 6)) - 4 return profitA, profitB
That looks good. Now we need a function that will loop the test over and over and accumulate the total net profit. This function should take the number of times I want to repeat the test as a parameter.
def runTests(repititions): sumA = 0 sumB = 0 for i in range(repititions): profitA, profitB = test() sumA += profitA sumB += profitB return sumA, sumB
Perfect! Now all we need to do is take the user input asking how many repetitions, run the tests, and report the outcome.
repititions = int(raw_input("Repititions: ")) sumA, sumB = runTests(repititions) print print "Game A net profit: $"+str(sumA)+".00 ($"+str(sumA / float(repititions))+" per game)" print "Game B net profit: $"+str(sumB)+".00 ($"+str(sumB / float(repititions))+" per game)" print print "Based off of these tests, game "+("A" if sumA > sumB else "B")+" is more profitable."
Awesome! All done. Here is the output of the program.
Repititions: 500000 Game A net profit: $249316.00 ($0.498632 per game) Game B net profit: $238126.00 ($0.476252 per game) Based off of these tests, game A is more profitable.
As you can see, it's really easy to get a hack-job answer to a non-obvious probability problem. All you need is a working knowledge of programming, and you're good to go! Python is especially nice for this task because it doesn't require compilation and is, syntactically, very easy to read and write.