Blackjack

How Lucky Are You?

Today, you will conduct a statistical experiment. Statistics is all about comparing what we expect to get with what we actually get. What we expect to get is called the Expected Value. What we actually get is called the Observed Data. In our experiments, as scientists, we expect nothing significant to occur. Expecting nothing significant is the same as assumimg events will occur randomly. Random events are chancery, haphazard, and chaotic, without cause or purpose. Statisticians are always hoping their assumptions are wrong—that something unexpected will happen, like someone winning the lottery twice, rolling seven 7's in a row, or finding a new drug that cures everyone of AIDS. When it does, they know their experiment was not an accident, and something other than chance determined the outcome of events. In other words, they have discovered significant results. Significance is measured by finding the difference between the expected and the observed. If the difference between the two is big enough, then we conclude:

For more about statistics, there is always the Wikipedia.

Today you will find out if you are lucky by comparing probable results with actual results. First, you will compute what you would expect by chance. Second, you will collect data by playing a simplified version of the game of Blackjack 104 times. Third, you will measure the difference between the probable outcome and your actual data to see if you scored significantly better than chance expectations. If so, we will call you Lucky.

Below is an EXPECTED PROBABILITY table for you to fill in.
Answer the questions as you have done in previous assignments.
When you answer a question, show your calculations.
When you complete the table, screencopy and email it to your instructor.
Below are some definitions to help you answer the questions.

• A DECK of cards is a set of 52 cards.
• The deck contains 4 subsets called SUITs.
• The 4 suits are called Diamonds, Clubs, Hearts, and Spades.
• Each card in a deck belongs to one and only one of these suits.
• Each card in each suit has a RANK from Ace to King.
• The 13 ranks are: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.
• Thus, there are 4 cards of each rank, one for each suit.
• There are 4 Aces, one for each suit.
• Jacks, Queens, Kings are called FACE cards.
• There are 16 cards that are either a FACE card or a TEN.
• A BLACKJACK is two cards: one an ACE and the other a FACE card or a TEN.
  The order does not matter.
• You win each time you are dealt a hand with a Blackjack.
• To DEAL a card is to take a card off the top of the deck.
• A DEAL in Blackjack is any two cards dealt off the top of the deck. The order matters.
• A HAND of Blackjack is any two cards dealt off the top of the deck. The order does not matter.

DATA COLLECTION — PART 1

BLACKJACK APPLET INSTRUCTIONS
1. Click the [HIT ME!] button to shuffle and deal your deck of cards.
2. The applet deals 2 cards at a time until it deals 26 hands.
3. Blackjacks are indicated by cards with CYAN backgrounds.
4. The applet counts the cumulative number of Blackjacks over 4 shuffles & deals.
5. Do NOT scroll up and down. The applet generates errors if you do.
6. Repeat steps B to E three more times. Wait 1 second between shuffles and deals.
7. When finished, you will have dealt 104 hands.
   
   
8. The applet totals all your Blackjack hands over the 4 shuffles and deals. Write this total down.
9. Then repeat steps B thru H for 10 times in all.
10. Each time, write down your total Blackjacks for that set of 104 deals.
11. Do not scroll up and down between shuffles and deals, or your count will be wrong.
12. Do not cheat by continuing to play till you accumulate beaucoups of Blackjacks.
13. There is a maximum number of Blackjacks possible. (Why?)
14. If you go beyond this maximum, you will need to redo the set of 104 deals.
15. Enter your 10 totals in the OBSERVED DATA table below.

OBSERVED DATA — PART 2

• Below is an OBSERVED DATA table for you to fill in with your 10 totals.
• Average these 10 totals on the AVERAGE row.
• To average them, add all 10 sets and divide by 10.
• Screencopy and email the table to your instructor.

EXPECTED PROBABILITY — PART 3

QUESTIONS:
1. How many ways can you deal a Blackjack from a deck of 52 cards?
2. How many Blackjack hands are there? Read the definitions of deal and hand.
3. How many ways can you deal 2 cards?
4. How many 2 card hands are there?
5. What is the probability of dealing a Blackjack? (round off 3 places)
6. You should expect a Blackjack once in every ______ hands. (round off)
7. How many Blackjacks should you expect in 104 hands?

COMPARE DATA — PART 4

Below is a COMPARE DATA table.
This table compares your observed data to expected probability to see if you are lucky.
The COMPARE DATA table asks these questions:

8. How many Blackjacks on average did you deal in 10 sets of 104 hands?
(Copy the AVERAGE from your OBSERVED DATA table.)

9. What fraction of 104 is your average number of Blackjacks?
(Divide your average numbr by 104.)

10. Compare your answer from question 8 to the answer from question 7.
If these numbers are apporoximately the same, enter OK.
If one number is almost twice the other, rethink question 5, and enter ???.
(You may want to check out other students' observations.)

11. What is the positive difference between line 7 and line 8?

12. Divide line 11 by line 7.

13. Write line 12 as a percentage.
This is the % error between the expected results and your observed data.
The % error determines how lucky you are.
If line 8 is more than line 7, you are lucky by the amount on line 13.
If line 13 is more than 99%, you will soon be banned from every casino.
If line 8 is less than line 7, you are unlucky by the amount on line 13.
If line 8 is 0, you are a cooler. They will love you in Vegas.

14. Are you lucky? If line 13 is more than 99%, enter YES, otherwise enter NO?

After you have compared your data, screencopy the table above, and email it to your instructor.