Wednesday, February 2, 2011

Skee Ball Game Theory

As a kid, I always wanted to win the stereo at the Dream Machine arcade in the North Dartmouth Mall.  The stereo was worth 10,000 tickets.1  How long would it take to win that many tickets and how much would it cost?

Anyone who's spent time in an arcade knows that the best way to get tickets is through skee ball.  In addition to giving out lots of tickets, you could steal−er−acquire even more by pulling the tickets out of the the slot very quickly.  Usually one skee ball game would net you about 5 tickets.  Back in the day, it cost 25¢ to play and you might get $2 allowance each week from mom. At this rate, it would take 

(10,000 tickets) / [ (5 tickets per 25¢) · ($2 per week)]
= 5 years,

and a total cost of

(10,000 tickets) / (5 tickets per 25¢)
= $500.

Given that it was at most a $100 stereo, I was probably better off spending the money on baseball cards.

[1] I was about 10 at the time, so my memory could be flawed on the exact number.


  1. I'm trying to follow the math here but I'm having trouble. Could somebody break down the math for me so I can do the calculations myself? Thanks, and I always enjoy the work you do on this blog.

  2. Hi Joey,

    I'm happy to help explain. Did you have a specific question? If not, let me try to break it down like this:

    If I get $2 of allowance each week, that means I can play 8 skee ball games since there are 8 quarters in $2. If each of those skee ball games earns me 5 tickets, then each week I'll get (5 tickets per game)*(8 games)=40 tickets. If I earn 40 tickets each week, then it will take 250 weeks or roughly 5 years to earn 10,000 tickets since (40 tickets each week)*(250 weeks)=10,000 tickets.

    If you have any other questions, free free to ask.


  3. Thanks! That did it. It's just when somebody put the problem in shorthand formula form I tend to get confused as to how to do the math.

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