Probability and statistics blog

Maybe you remember playing this one as a kid. If you are about my age, you may have even created a version of this game as one of your first computer programs. You guess a number, the computer tells you if you if you are too low or high. I’ve limited the number of maximum guesses, and randomized the computer’s choice based on the Poisson distribution (more on that later).

Here’s the code. This was part of my attempt to understand how R reads input from the command line. One of the things I learned: you may need to save this to a file and run it with “source()”, instead of running it directly from the console, line by line.

# Classic guessing game with twist
x = 0
gotRight = 0
failed = 0

# Initial lambda for our random var
correct = 2000
initial = correct

# How many guesses should we allow per number
maxGuesses = 7
	
while(x != Inf) {
	# The +1 part makes sure we never get zero, which would trigger 0's forever
	correct = rpois(1,correct) + 1
	
	# The advantage of using "cat" instead of "print" is that you remove those pesky quotation marks
	cat("I am thinking of a number between 1 and infinity. What is it? (Type Inf to quit)\n")
	
	# Solicit input from the user
	x = scan(n=1) # Just one item in this vector
	
	# Be nice and let the user quit. 
	if(x == Inf) {
		cat("The correct answer was", correct, "\n")
		cat("You got", gotRight, "right and failed", failed, "times. Maximum allowed guesses was", maxGuesses, "and initial lambda was", initial, ". Goodbye.\n")
		cat("Post your score to http://www.statisticsblog.com/2010/05/the-guessing-game-in-r-with-a-twist-of-course/#comments \n")
		break
	}
	
	for(i in 1:maxGuesses) {
		if(x == correct) {
			print("You rock!")
			gotRight = gotRight + 1
			break
		} else {		
			if(i == maxGuesses) {
				cat("You ran out of guesses. I will pick a new random number based on the last one.\n")
				failed = failed + 1
			} else {
				if(x < correct) {
					cat("You are too low. Guess again.\n")
				} else {
					cat("You are too high. Guess again.\n")
				}
				
				x = scan(n=1)
			}			
		}
	}
}

Note 1: My code makes a couple uses of the aparently controversial "break" function. I can still recall a heated debate I had with a CS professor who believed that calling "break" (in Python) was as bad as crossing the streams of your Proton Pack. That said, I have sucessfully used it on several occasions now without any appearance by Stay Puft Marshmallow Man or changing the natural order between dogs and cats. In R, the biggest problem with using constructs like "break" and "while" is that, for reasons clear only to readers of this blog but not myself, if you ask R for help about either of these tokens using

?term

you get an sent an error or to purgatory, respectively.

Hint: Because the random guesses are Poisson based, using a "half the distance" strategy for guessing may not be the best way to go. The hardcore amongst yourselves might want to calculate the median of the expected value conditional on having guessed too low or high.

Note 2: The Poisson isn't a very good distribution for for this. Maybe you can find a better one, or at least jack up the dispersion like an overzealous offroader tweaking the suspension of his 4Runner.