I like practical statistics, for example when betting red/black in a casino, what is the chance that you would lose 10 times in a row ? Just keep doubling they say, but eventually you will get a bad streak and wont have enough money or you'll hit the limit.
If it landed on red 10 times in a row so far, the odds of landing another red on the next round are almost 50%. Gambler's fallacy is so much fun to observe at the tables though :)
In The Newtonian Casino (Might be called something else in the US) students who built computers in their shoes (in the 1970s!) to predict the outcome of roulette wheels discovered that lots of wheels had pretty severe tilts (which affected outcome) and that skilled croupiers had a "signature" -- they knew that particular wheel very well, and had practiced many times, and could increase their chance of hitting a particular number. (This is described in the chapter titled "Lady Luck").
It's supposedly possible to predict to a reasonable degree of accuracy where a roulette ball will land if you know its speed (ie time it hits the wheel, and time to pass a predefined marker).
I remember an experiment in high school math of some variety.
The teacher had us all "guess" what twenty coin flips would look like. The longest any streak any student wrote on their paper was maybe 4-ish in a row or something.
He then had us all actually flip the coins and record the results. One student had like 11 in a row, most hit a streak of somewhere between 5-8 of the same result.
Lesson learned, we're really bad at guessing 50/50 streaks.
To a rough approximation, 20 coin flips gives you 16 chances to get a 1/16 probability event of 5 in a row of heads or tails, so the average number of 5-streaks is 1 per student. With 32 kids a class, add 5 more to the streak length to expect to see.
