Some of them aren't so much a scam as they are taking advantage of people's inability to estimate probability. i.e. tossing a coin and having it land completely in the red circle. The circle is clearly larger than the coin, but people mistakenly believe that the relative area of the circle is their relative odds of winning. i.e. they think that since the circles make up about 1/30th of the total area, their odds are 1/30 of winning.. Also, because the circles are bright red against a background of white, they woefully overestimate the percentage of the surface that's actually red.
Here's the math for 1 1/2" diameter circles spaced only 6" apart (edge of the circle to edge of the circle). Of course, with a bunch of quarters scattered about, it's obvious that these circles are significantly larger than a quarter (15/16"). (Suckers!) From center to center, it's 7 inches, so if you draw a square connecting the 4 centers of circles, you end up with 49 square inches, of which you have 4 quarter-circles = a full circle. Of that, Pi * .75^2 is the area of the circle, 3.6% of the total area (49 square inches). And, even if people did this calculation, most would assume that it means that they have a 3.6% chance of winning; roughly 1 in 28.
But, if you calculate how much of the area where the quarter can actually land & win, it's significantly smaller, since the quarter has to be completely within the circle. The easiest way to calculate this (2nd easiest once someone posts an easier way 😛 ) is to figure out where the center of the circle can be. The center of the quarter has to be at least equal to its radius away from the edge of the red circle. That is, it has to be 1/2 of 15/16" away from the edge of the circle = at least 15/32" away from the edge of the circle. If you draw a circle inside the red circle, to denote the region where the center of the quarter can exist, you'll find that this new circle is 18/32" in diameter. (The entire circle is 48/32" wide; in 15/32" each from the left and right sides leaves 18/32" remaining). So, the actual area where the center of the quarter can be is
Pi * (15/64)^2 = .1726 square inches, out of that 49 square inches.
That makes the actual odds of winning 0.352% or 1 in about 284.
So, for every $71 spent by suckers, they average giving out about 1 prize that costs them $10 or less.
I don't know what the actual sizes of those circles are, and it varies, depending on what coin you're allowed to throw & the size of the prizes. But, I believe the probabilities I calculated here are in the ballpark (if not generously more in favor of the person playing the game than they actually are.)