This is the first in a series of posts on mathematics in the "real world."
Should you pay to play these games?
Aside from the obvious answer, that these games are fun, and so whether or not you win, the games have an intrinsic "fun" value, one wonders how fair these games are to play. It’s easy to deduce that the games are unfair (why would an organization trying to make money use them otherwise?) but how unfair are they?
This is essentially an expectation problem in the wild, and attempts to analyze games of chance like these by mathematicians led to the formation of probability theory itself.
One way to answer this question is to go to a carnival where there are a bunch of these games, and record some experimental data. You can either use your own money to play all of the games, or stand around surreptitously with a notebook and let other people do the experiment for you, while you record results.
Another way would be to set up your own versions of these games, then host a carnival at your school (or in your classroom), and have participants play the games (perhaps using monopoly money?). If they don’t record results, the activity is fun, but not very mathematical, so I strongly recommend some record keeping takes place during a school sponsored carnival event. You will also need some time at the end for people to analyze, then discuss their results. I recommend, if you do this as a school activity, checking in with your students about common misconceptions about probability that they have, and make sure their analysis of the results spends at least a bit of time debunking some of those misconceptions.