I don't know if it's illegal or not, but it's certainly taboo in some corners to teach about gambling in schools. I looked but cannot find the words or phrases "gamble", "gambling", or "games of chance" anywhere in California education code (search here), but I'm not sure.
This is remarkable to me. Our state has a lottery system, some of the proceeds of which fund public education. The odds of winning are printed on each ticket!
The entire field of probability was jump-started when some enterprising individuals tried to determine probabilities for winning at games of chance! I can't tell you how many students ask me about Texas Hold'em, tournaments of which they watch on television but about which I know nothing.
Just as it's against the law in California to teach about communism with the intent to instill in the minds of students a preference for communism over our representative form of government, I decided that if I teach about gambling I must do so without glorifying it or instilling a preference for it. I assume that this is how sex, drugs, and alcohol are also addressed in the appropriate classes.
As my Algebra II students have been learning about probability, permutations, and combinations recently, games of chance are very relevant to the subject matter. Many of the problems in our textbook have dealt with probabilities of drawing certain cards from a deck, so I've extended that to other probabilities--for instance, the probability of being dealt a royal flush in 5-card stud (or 5-card Darren, same thing).
And then there's Keno.
Keno is similar to the state lottery in that balls are drawn from a hopper, but more interesting. Players mark numbers from 1-80 on a Keno ticket, and then 20 numbers are drawn from the hopper. If a certain number of the players numbers are drawn, the player wins! Keeping with the "don't glorify it" theme, we calculated the probabilities of the player's choosing only 1 number and having that number chosen. Turns out there's a 1/4 chance, meaning that if the player chooses only one number (say, 25), that number will be drawn on average only once in four games. Since Keno is generally $1 a game, the player would have to play 4 games at a cost of $4 in order to win one. According to my Circus Circus Reno Keno payout sheet, a player would win $3 for getting one number drawn out of one.
Did you get that? Mathematically, you pay $4 in order to win $3. Those casinos weren't built because all the players were winning, you know!
But no one picks only one number--birthdays are a favorite. So we calculated the probability of choosing two numbers and having both of them drawn. Skipping all the math here, the probability is about 1/17. In other words, you'd have to play 17 games (costing $17) to win one--and the payout would be only $14 according to the Circus Circus booklet.
We did the same for 3 numbers--probability of 1/72, for a payout of only $42.
The students seemed to enjoy the "practical" lesson and I taught much about counting principles and probability. Additionally, no one could say I was glorifying gambling at all. Sounds like a win-win to me.
What's the probability of that?