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Reasoning With Mathematics

Lesson 9 - Making Bets and Decisions: The Statistics of Gambling

We've been discussing the way numerical patterns can help us to make decisions in a wide variety ofsituations where human beings want to predict what will happen. Humans are so interested in suchprediciting that it is the basis one of the oldest forms of human play. When anthropologists try todistinguish what makes us different from other animals, they argue about language, opposable thumbs,weapons making, child rearing and a variety of other human characteristics or behaviors, as definingcharacteristics of the species. Perhaps they should add guessing to their list, and guessing's closecousin, gambling. We're going to spend some time studying gambling, or gaming as it is sometimescalled, to understand how patterns enable skilled gamblers to make better bets and enable all casinos,lotteries, bingo games, pull tabs, racetracks, betting wires and punch cards to make money for thepeople who run them. In the process we'll also learn some basic ideas about statistics and how theyhelp us to see patterns and to use those patterns to assess risk and make decision in much the sameway that Shirley did in figuring out whether or not she should take that risky winter drive to the cities.

Let's put Shirley on plane and send her of on a Vegas vacation, rescuing her from her winter wasteland. She braved the drive, got lucky and dodged the blizzard, got the job and has some extra cash. Shewants to play and she wouldn't mind winning enough to pay all her expenses, and if she got really luckyagain, a new four wheel drive truck to take a bite out of winter.

To purchase Season Passes, Daily Tickets or to learn more about these offerings, simply click the images below and start planning your Holiday World & Splashin’ Safari getaway! (Our tickets are not for re-sale. Please do not risk being scammed: do not purchase tickets from any online sales or auction site.). Mar 25, 2018 It’s real and 50k is still out there. The dudes that robbed RollerWorld got put away, but the money was never recovered. And the rumor’s still rampant!

What is RollerWorld money? At the end of Season 2, the stollen RollerWorld money that Monse (Sierra Capri), Ruby (Jason Genao), Cesar (Diego Tinoco), and Jamal (Brett Gray) paid off: Cesar and his older brother, Santos majordomo Spooky (Julio Macias), use the cash to take down the Prophets, the Santos’ rival and the gang that had been hunting.

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If she wants to maximize her chances of winning, what game should she play when she gets toVegas?

Click on as many of these games as you want and then give an answer.

Poker <http://www.contrib.andrew.cmu.edu/org/gc00/reviews/pokerrules>

Blackjack <http://www.netcore.ca/~billk/vegas_casino.2.html>

Roulette <http://www.gamblingtimes.com/basroult.html>

Craps <http://www.gamblingtimes.com/bascraps.html>

Other <http://www.gambling.com/directory/directory.cfm?ID1=293>

Unsure <http://www.arizonaweb.com/gambling/gamble4.html>

{Ideally there would be a form here that allows students to select an alternative. Al l responses wouldbring students to <http://www.arizonaweb.com/gambling/gamble4.html> The Unsure response wouldsimply bring them to the same site immediately }

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It's Those Tumbling Dice

Hallelujah, great odds!!!

The Tumbling Dice site announces that Craps is the best game for Shirley to play and proceeds to justifythat claim by making a statistical argument that we are going to spend some time understanding. Whatthis discussion demonstrates is a method that is at the heart of all reasoning with statistics and that canbe extended to the most complex explorations of pattern that the human mind is capable of. In fact, thebranch of mathematics that is called statistics really developed from the efforts of a eighteenth centurymathematician, Thomas Bayes <http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Bayes.html>,

who was interested in finding 'a method by which we might judge concerning the probability that anevent has to happen, in given circumstances, upon supposition that we know nothing concerning it butthat, under the same circumstances, it has happened a certain number of times, and failed a certainother number of times.' Today Bayes search for patterns is at the center of scientific study of everythingfrom computers to life and the brain. But let's start with a simple problem, a pair of dice and listing allthe possible outcomes we can get throwing that pair of dice.

Here they are.

Chart of Possible Outcomes - One Throw of a Pair of Dice

2 3 4 5 6 7

3 4 5 6 7 8

4 5 6 7 8 9

5 6 7 8 9 10

6 7 8 9 10 11

7 8 9 10 11 12

If we count the total number of potential outcomes (or multiply the number of faces on each di by eachother) we get 36 potential outcomes, one 2, two 3's, three 4's, four 5's, five 6's, six 7's, five 8's, four 9's,three 10's, two 11's and one 12.

For any single throw of the dice then what are the chances we will get Or 2?

Think about our discussion of the binomial distributions. In order to determine the chances of making aparticular number of trips without encountering a blizzard we counted all the potential outcomes, given acertain number of trips, and found we had one chance in four, eight, sixteen, etc. of avoiding theblizzard. Here we have a similar situation, but the outcome on any particular trial (trip or throw of thedice) is not the simple either/or outcome that the binomial pattern describes. For each one of Shirley'strips, remember, there was a 50/50 chance, or one chance in two, that she would avoid the blizzard. Each time we throw a pair of dice we have 36 possible outcomes.

How may ways can we get Or 2?

That's right, there is only one way to get 2. Our chart of 36 possible outcomes indicates exactly that. So we have one chance in thirty-six of getting a 2 on any particular throw. Statisticians say theprobability of getting a 2 on a throw of the dice is 1/36 expressed as a fraction. In word it is the numberof different ways we can get a particular total divided by the total number of outcomes. Looking at thechart we can see that the probability of each total is revealed by the pattern on the chart.

{The bold face numerals in these charts should be on the screen in colors (e.g. blue 3, red 4, etc.)}

For 3

2 3 4 5 6 7

How Much Is The Rollerworld Money Real