Few words on probability theory
January 7th, 2015 at 4:23:51 AM
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Probability Theory
Simply speaking, probability relates to ascertaining what the chances are (in other words, what the odds are) of some event happening, such as winning a jackpot or drawing a certain card or hand. It is the figure obtained when you divide the number of ways an event can occur by the total possible number of outcomes in a given scenario. For example, if we wanted to establish the probability of drawing a red card from a deck of cards, we would divide 26 (total number of ways to draw a red card, since there are 26 red cards in a deck) by 52 (total number of cards in the deck, disregarding jokers), giving us ½ i.e. a probability of 0.5.
The logic behind probability theory has of course been around forever, though the actual mathematical study of it is a relatively new development. The extensive inherent probability scenarios that exist in the ancient pastime of gambling in particular were a major factor in prompting the study of probability in mathematical terms – people wanted to know in more precise detail what their chances of winning were!
The mathematics of probability
The mathematics that describe the laws of probability involve events – represented by algebraic variables, usually “A” – and decimal numbers between 0 and 1. So, the probability (P) of event A (say, drawing a King from a deck of cards) happening is represented as “P(A) or p(A) or Pr(A). An event that has no chance of occurring (drawing five aces from a deck of cards) has a probability of zero, while an event that is certain to occur (drawing a card that is either red or black from a deck of cards without jokers) has a probability of 1.
To calculate the probability of two events occurring at the same time is simply a matter of multiplying together the probability of each of these events. For example, if we spun two dice at the same time, the probability of rolling a 4 on the one dice is one in six (P = 0.1667), while the probability of rolling a 2 on the other is also 0.1667, but the probability of rolling a 2 AND a 4 is 0.1667 x 0.1667 = 0.027. Various formulas for probability exist, and of particular importance in determining which formula to use is to ascertain whether events are independent or dependent.
Have a read through our other pages on the mathematics of gambling to learn about more applications of mathematics in gambling, or view our gambling mathematics glossary for a quick overview of the most important concepts in addition to probability theory.
Simply speaking, probability relates to ascertaining what the chances are (in other words, what the odds are) of some event happening, such as winning a jackpot or drawing a certain card or hand. It is the figure obtained when you divide the number of ways an event can occur by the total possible number of outcomes in a given scenario. For example, if we wanted to establish the probability of drawing a red card from a deck of cards, we would divide 26 (total number of ways to draw a red card, since there are 26 red cards in a deck) by 52 (total number of cards in the deck, disregarding jokers), giving us ½ i.e. a probability of 0.5.
The logic behind probability theory has of course been around forever, though the actual mathematical study of it is a relatively new development. The extensive inherent probability scenarios that exist in the ancient pastime of gambling in particular were a major factor in prompting the study of probability in mathematical terms – people wanted to know in more precise detail what their chances of winning were!
The mathematics of probability
The mathematics that describe the laws of probability involve events – represented by algebraic variables, usually “A” – and decimal numbers between 0 and 1. So, the probability (P) of event A (say, drawing a King from a deck of cards) happening is represented as “P(A) or p(A) or Pr(A). An event that has no chance of occurring (drawing five aces from a deck of cards) has a probability of zero, while an event that is certain to occur (drawing a card that is either red or black from a deck of cards without jokers) has a probability of 1.
To calculate the probability of two events occurring at the same time is simply a matter of multiplying together the probability of each of these events. For example, if we spun two dice at the same time, the probability of rolling a 4 on the one dice is one in six (P = 0.1667), while the probability of rolling a 2 on the other is also 0.1667, but the probability of rolling a 2 AND a 4 is 0.1667 x 0.1667 = 0.027. Various formulas for probability exist, and of particular importance in determining which formula to use is to ascertain whether events are independent or dependent.
Have a read through our other pages on the mathematics of gambling to learn about more applications of mathematics in gambling, or view our gambling mathematics glossary for a quick overview of the most important concepts in addition to probability theory.
January 7th, 2015 at 4:38:34 AM
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very edifying, Sir.
for a project, you could start a gambling wiki
for a project, you could start a gambling wiki
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
January 7th, 2015 at 4:46:44 AM
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Your post and the first link are identical. Is that your web site? The fourth link has Saliu's book for sale. Have you read it? Is is worth $22.95 for the paperback or $32.95 for the hardback, as it's called in the ad?
Many people, especially ignorant people, want to punish you for speaking the truth. - Mahatma Ghandi
January 7th, 2015 at 8:30:32 AM
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Ahh, takes me back to upper level stats classes in college. The truth of the matter is probabilities are actually quite easy to calculate, so long as you break them down to each individual event that effects the outcome. Most people think it's just "crazy math" to come up with the probability between 0 and 1.
Playing it correctly means you've already won.
January 7th, 2015 at 12:20:57 PM
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Fewer words...
Constants aren't and variables don't, sometimes.
Constants aren't and variables don't, sometimes.
Some people need to reimagine their thinking.
January 7th, 2015 at 12:21:33 PM
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One mistake that I noticed:
This is true only if the events are independent. In fact, I had one college professor tell me that this is the definition of "independent events" - events A and B are independent if P(A and B) = P(A) x P(B).
However, if you are rolling a single die, the probability that the next roll is a 1 is 1/6, and the probability that the next roll is a 6 is 1/6, but the probability that the next roll is both a 1 and a 6 is not 1/36.
Quote: JabberwockyTo calculate the probability of two events occurring at the same time is simply a matter of multiplying together the probability of each of these events.
This is true only if the events are independent. In fact, I had one college professor tell me that this is the definition of "independent events" - events A and B are independent if P(A and B) = P(A) x P(B).
However, if you are rolling a single die, the probability that the next roll is a 1 is 1/6, and the probability that the next roll is a 6 is 1/6, but the probability that the next roll is both a 1 and a 6 is not 1/36.
