“Teaching and learning are not the simple transmission of a set body of knowledge from an authoritarian teacher and to a passive classroom of students.” -Bill Gates on Education Reform
Whether or not you like or agree with Bill Gates, you have to acknowledge his business and individual successes, and his passion for education reform. One thing that we should all agree upon is that the status quo is not acceptable. We need to find new ways to engage students at critical points in their development to insure that FUNDAMENTALS are not just learned and understood, but become second nature to them. Back before calculator were invented, students had to memorize multiplication tables. How many 5th graders today can rip out the multiplication tables as well as their parents?
Some private schools and even charter schools that do not have their hands tied by the same constraints as general public schools have implemented new techniques designed to engage their students by introducing practical applications to fundamental mathematics and statistics. One of these techniques is the use of casino games.
Games of most any type capture the attention of students and adults alike. Take the game of Monopoly for example…the rule are laid out, the players each formulate their own individual strategy based upon the rules, there is an element of chance with the dice and the cards, and there is ultimately a winner. These are the primary element of just about any ‘game’, and games that help teach while in the process of playing them are a Win-Win for everyone. The one feature of all casino games is that they have all been developed by mathematicians and time tested to produce a statistical advantage for the casino, otherwise places like Las Vegas and Atlantic City wouldn’t exist. The fun part for the students is in learning and playing the games (not for real money of course), and CRACKING THE CODE of the statistical house advantage. Besides for learning mathematics and statistics, they will also learn that they CAN’T WIN in the long run!
Examples of Casino Game Math
Roulette is a popular casino game and probably the easiest example for illustrating mathematics and statistics. The roulette wheel has the numbers 1-36 plus 0 and 00 making for a total of 38 possible outcomes from a single spin. If you place a bet on a single number on the board and win, the casino will pay you 35-1. In this example, the casino has a statistical advantage of 5.26%. How did we get that? There is a probability of 1/38 that the player wins 35 times the bet, and a 37/38 chance that the player loses their bet. The expected value is:
−137⁄38 + 351⁄38 = −0.0526 (5.26% house edge)
The ‘House Edge’ is what keeps casinos alive and well. It means that for every $1 bet the casino will statistically make 5.26 cents on this particular bet.
Another bet in the game of roulette is called the “Top Line” where the player places a single wager which covers 1,2,3,0,00 (five numbers) and will pay 6-1 if any of those numbers are spun. In this case, the expected value is: 카지노사이트
-1x 33⁄38 + 65⁄38 = −0.0789 (7.89% house edge)
Which bet will cost the player the most money in the long run?
Every bet on the roulette wheel (and on virtually every bet on every game in a casino) has a house edge, so more than others as you can see.
Another example is the game of Craps where 2-dice are used. Understanding the probabilities of rolling a given number using a pair of dice is critical to being able to calculate the house edge on any given bet.
2 (1): 1-1
3 (2): 1-2, 2-1
4 (3): 1-3, 2-2, 3-1
5 (4): 1-4, 2-3, 3-2, 4-1
6 (5): 1-5, 2-4, 3-3, 4-2, 5-1
7 (6): 1-6, 2-5, 3-4, 4-3, 5-2, 6-1
8 (5): 2-6, 3-5, 4-4, 5-3, 6-2
9 (4): 3-6, 4-5, 5-4, 6-3
10 (3): 4-6, 5-5, 6-4
11 (2): 5-6, 6-5
12 (1): 6-6
Two dice with six sides each which produces 6×6=36 possible combinations with symmetrical distribution of the numbers. For a one roll bet on the number 12 the casino will pay 30-1. What is the probability of rolling a 12? How do you calculate the house edge on this bet?