Chance, as its name suggests, cannot be predicted and the randomness of events is completely, well, random. However, many mathematicians have devised and come up with theorems that try to explain crazy behavior. For example, the improbability principle states that relatively rare events have high chances of happening again and again, as paradoxical as it may seem. However, another law called Borel's law states that events with negligible probabilities can be disregarded completely i.e they never happen. Other such principles are as follows:
The law of large numbers: This states that if events are repeated a considerable number of times, the average of the event occurring meanders towards the actual mean
Bell curves: Curves which are shaped like bells and in which the curved part represents the mean of the distribution.
Gaussian distribution: The normal way a set of observations would behave i.e with the correct mean.
The law of really large numbers: This law contrasts with the previously mentioned one as it states that when the set of observations is really really large(measurable on the cosmic scale), then we should expect to see rare occurrences quite frequently. A paradox.
Regression to the mean: This principle states that systems always deviate towards their actual means and follow normal distribution patterns.
Sod's law: This states that the worst possible outcome in any scenario will always occur. It explains why you will encounter a red signal when en route to an important meeting you're late for.
The gambler's fallacy: This is a common misconception, especially in casinos, where people think if they haven't encountered a particular card or color for a while, their chances increase with every turn. The probability of encountering a certain event remains the same on every occasion, unless some other circumstances dictate otherwise.
The average payout law: People should bet an amount of money based on the average payout they will get by adding all the individual probabilities. Eg: if, in a game, you have 50% chance of winning $4 and a 50% chance if winning nothing, then the average payout is 1/2*0 + 1/2*4= $2. So if the player bets $1, then he can expect to profit even though $2 can never be won.
Gaussian distribution: The normal way a set of observations would behave i.e with the correct mean.
The law of really large numbers: This law contrasts with the previously mentioned one as it states that when the set of observations is really really large(measurable on the cosmic scale), then we should expect to see rare occurrences quite frequently. A paradox.
Regression to the mean: This principle states that systems always deviate towards their actual means and follow normal distribution patterns.
Sod's law: This states that the worst possible outcome in any scenario will always occur. It explains why you will encounter a red signal when en route to an important meeting you're late for.
The gambler's fallacy: This is a common misconception, especially in casinos, where people think if they haven't encountered a particular card or color for a while, their chances increase with every turn. The probability of encountering a certain event remains the same on every occasion, unless some other circumstances dictate otherwise.
The average payout law: People should bet an amount of money based on the average payout they will get by adding all the individual probabilities. Eg: if, in a game, you have 50% chance of winning $4 and a 50% chance if winning nothing, then the average payout is 1/2*0 + 1/2*4= $2. So if the player bets $1, then he can expect to profit even though $2 can never be won.
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