The definition of the word chance is commonly defined by society (T1 – Synecdoche) as “the possibility of something happening”. We measure chance by creating a determination of the likelihood that an occurrence will happen, as expressed typically by putting numbers together into a fraction.
Probability and chance is apart in our everyday lives. Every day we are making decisions and judgment based on the outcomes of chance and probability. Chance is derived from chance games played in the classical era. In the sixteenth and seventeenth century, people needed help with their gambling skills, and advanced in chance.
Football teams begin the game by putting their fate into the hands of a chance; a coin is used to represent it (SP1). One team decides to place their bet on one side; the other, the corresponding side (SP2) (for the sake of this essay the two sides will be referred to as heads and tails) (S1 – Parenthesis). Now supposing that there are no other variables acting on the coin besides the toss, such as the coin being weighted on one side, the chances of that coin landing on either side are exactly 50/50, or when expressed in terms of just one side the chances are 1/2. The side of the coin that is facing up after the toss represents the winning party, and both parties have had their fates decided. But, let’s say now that the coin that was flipped lands facing heads up. And when flipped again, lands heads up. And again, and again, and again (S2 – Anaphora). While this is happening the chance of the coin landing heads up each time decreases little by little, starting at 1/2, then going to 1/4, then 1/8, and will continue to halve no matter how many times the coin is flipped. Now suppose the coin is flipped an infinite amount of times. Is it possible the coin will forever continue to land on heads, or will it eventually succumb to infinity and land on tails?
The St. Petersburg Paradox is a paradox that relates to probability theory and decision theory (Math Fun Facts). It is based on a theoretical lottery game which results in an infinite expected value. To put this into a real world scenario, suppose a casino is trying to figure out what amount to charge potential gamblers for entering a new game they have come up with. The game involves flipping a coin numerous times until the tails side appears, resulting in a “game over”, and the player receives the money in the pot. Now for the money side of things, the pot starts at one dollar, and will double every time heads is flipped. Broken down into simple terms, the game starts with a 1/1 chance the player will receive a single dollar, cut in half to 1/2 when the coin is flipped to receive two dollars, 1/4 chance of four dollars, 1/8 chance of eight dollars, etc (S3 – Ellipsis). Assuming the casino has an unlimited amount of money, and there is no other way to end the game besides the dealer flipping tails, the expected win for the player is infinite. If the expected outcome is infinite, the casino...