History ofProbability

By James FoscoMath Department Chair

Tampa Bay Technical High School

1600's In the 1600's a man, by the name of Chevalierde Méré, made a bet that he could roll a 6 in 4 tries. After time of not winning very often, he changed his bet to get better results. He made a new bet that he could get double 6's in 24 tries. He soon realized that this was getting him less wins. He asked his friend, Blaise Pascal, why this was happening. Pascal thought and thought and finally found out why. He found out that the probability of winning using the new approach wasonly 49.1 percent compared to 51.8 percent using the old approach.

Why?The probability of not rolling a six is 5/6. If you are going to roll 4 times, then the probability of not getting a 6 is (5/6)^4. To get the probability of rolling a 6 in 4 rolls is (1-(5/6)^4). Which is .51774. Now if you want to get double 6's in 24 rolls, you have 36 possibilities. Only one of those possibilities will give you the double 6's. So the probablity of not getting double 6's is 35/36. You will do 24 rolls so the probability of not getting double 6's is (35/36)^24. To get the probability of rolling double 6's in 24 rolls is (1-(35/36)^24). Which is .4914. Obviously, 0.51774 is greater than .4914. Not by much, but when it comes to probability (especially gambling) every thousandths counts.

Card ExperimentLet's say you have four cards. They are all 8's but of every suit. I want to get an 8 of hearts. There is only one out of the four cards. So the probability of getting this card is .25. 1. I shuffle the cards2. I pick a card (hoping that it is an 8 of hearts)3. The card is the 8 of clovers ): I try again (replacing the card) ... Once again, I got the 8 of clovers )':

Card Experiment

Numero DosI now have eight cards. I have 8's and 2's. Both with their four suits. I want to get an 8 and a 2 with replacement. P(getting an 8 card) = .5P(getting a 2 card) = .5 P(both events) = 0.25 1. Shuffle and pick a card2. It's an 83. Put card back, shuffle, pick a card4. It's an 8 ):5. I lose.

$$$GET MONEY$$$$ !!

Have you heard of Blackjack? It is a casino game where you play against the dealer. You are trying to get 21 or as close as you can to it without going over. You must be closer than the dealer to win. I believe it is the only beatable casino game. This is done by 'counting cards'. Now, this is NOT illegal.. but it IS frowned upon. (pssh, i don't care i want money) anyways ..

How Counting Cards WorksEvery card in the deck has a value and you must keep count of what it's worth is. 2,3,4,5,6 have a value of +17,8,9 have a value of 010,J,Q,K have a value of -1 So lets say the 15 cards where dealt:7,4,9,3,J,2,6,5,Q,3,7,J,5,8,3 What's the count?Well there are 8 cards with a value of +1There are 4 cards with no valueThere are 3 cards with a value of -1 The count is 5!

What does a count of 5 mean?When the count is more than or equal to 4, you should bet more money. This mean the deck's "Hot". Your chance of winning is greater, because there are more high cards left in the deck. When the count is less than 4, there are more low cards, which favors the dealer. In this case, BET $$$$$ .

TitleCounting cards gives you .02 more chance of winning than the dealer. You might think "Wow, big deal?" IT IS. Like I mentioned before, every thousandths place counts when you're gambling using probability.

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NOW GO PLAY BLACKJACK!!

LOL JK , YOU'RE NOT

21 (;