- May 8, 2020
Professors Name Subject
Gameof Chance involving Probability
BothBlaise Pascal and Daniel Bernoulli were great mathematicians thatcontributed a great margin to what is today referred to asstatistics. They both used games of chances in trying to prove someof their theories. For example, Daniel Bernoulli used the St.Petersburg paradox to explain a game of chance that is related toprobability. The game of chance that Daniel used trying to prove aprobability situation was a lottery game that has a random variablewhose expected values are somehow infinite. The funny aspect of thisgame is that the probability has a very minimal impact on the playersparticipating in the game.
Thetechnical aspect of the game involves tossing of a fair coin at eachand every stage. The fair coin is tossed for a single player, and ina situation where the outcome is a head, then the player enters thenext stage where the fair coin is tossed again. The process is redonean infinite number of times if the outcomes remain to be the head. Ina situation where the outcome is tail, then the game of chance isconsidered to be over, and the participant is given the amount thathe or she might have accumulated in the tossing sequence.
Thereis a fixed amount placed that the player can get after the firsttoss. The amount doubles every time a toss outcome turns out to behead.
Anexample of the paradox.
Assumingthat the amount placed at the first toss is m and the number oftosses that the outcome is head is K, then the knowledge ofprobability can be used to calculate the amount of money that asingle player won (About.com Education).
Forthe amount that the player won to be calculated, there are limits putin place to make sure that a theoretical value is obtained, and thislimits are
mMust be greater than zero
kMust be a whole number and at the same time greater than zero
Fromthese assumptions the payout that a player can expect can becalculated using the formula shown below
Ina situation where the player is lucky enough to a situation where thenumber of outcomes is headed, and the host of the game who in mostcases is the casino has a large reserve of money, then the game canbe played to an infinite number of times.
Althoughthe probability theory of Daniel paradox is something that can becalculated, there are those things that are unrealistic with thisgame of chance. Firstly, the game assumes that the casino has aninfinite amount of wealth to make the result infinite, but it is amatter of fact that at a casino will always have a finite amount ofstakes at their disposal.
Thereare other factors that should be considered to make the formula usedby Daniel in the game of chance to make it realistic. For example,there is need to include the total amount that the casino can coverin case a player gets lucky. To achieve this, the casino can quote amaximum amount of money that a player can win (The St. PetersburgParadox: A Discussion of Some Recent.).
Theparadox proposed by Daniel in his game of chance helps only in asituation where the player does not get over lucky with the tosses.More research should be dedicated to perfecting this paradox to makeit more realistic and concrete.
Https://www.facebook.com/people/Courtney-Taylor/100009813047380."What Is the St. Petersburg Paradox?" About.comEducation.N.p., 2015. Web. 19 Nov. 2016.
"TheSt. Petersburg Paradox: A Discussion of Some Recent." N.p., n.d.Web. 19 Nov. 2016.