Probabilities in online casinos games
Probabilities in online casinos
Gambler's introduction to the probability theory and the law of large numbers
The probability theory and everything that is related to it is a vast topic that cant be possibly covered by one simple introduction on an online casino related website. Moreover, special topics of it deal with maths and more or less advanced things, which would probably of no interest to gamblers. We will present a short overview of the probabilities and odds in this article.
The probability is a likelihood of an event happening. For the curious, professional expression that is used for describing a set of events is called an experiment, and each event is called an outcome.
The simplest and most classic example of a probability is the flipping coin experiment. We will use it to cover our basic examples on the probability.
A coin has two sides: heads and tails. Whenever you flip a coin, it will essentially land on one of the sides. There's no other possible outcome for this experiment. As we know that the probability of either of the events happening in an experiment is 100% (because, as we said, the coin WILL land on either of the sides), we can say that the probability of the coin playing out heads is 50% and tails is also 50%:
We have 2 equally likely outcomes, and a probability that one of them will play out is 100%.
Therefore the probability for each of them would be 100% / 2 = 50%, or in more traditional form, 1/2.
When we say that the probability of something is X/Y it is the same as saying that out of Y attempts to produce a wanted result, X times we will succeed. It is also the same as saying that the event we're trying to achieve has odds of X to Y. However, remember that these numbers do not mean that out of 4 times you flip the coin you will get tails exactly 2 times and heads another 2 times; probabilities work more or less precise on a large scale: for 10,000 coin experiments the coin will produce something very close to 5,000 tails and 5,000 heads, but you will almost never get an exact number. Probability is a mathematical guesswork!
Notice this very important distinction mentioned above: we're implying that both heads and tails are equally likely outcomes. This is true for a coin because its sides are equal. If, however, we were to take an experiment in which there's no equality, we would have to know how are the likelihoods of outcomes related.
Imagine for instance the following experiment. You have a deck of 10 cards. The experiment is about drawing either black or red card. If the deck has 5 red and 5 black cards then, after thorough shuffling, the likelihood of either color card being drawn would still be 1/2 just like in the flipping coin experiment. However, if before the shuffling we were to put 7 black cards and 3 red cards into the deck instead, we'd know that after the shuffling, the likelihood of black coming out would be 7/10 and red 3/10.
Another necessary implication that we're making here is that the event is random: that is, the coin is flipped and the deck is shuffled. If we were to just take a coin and put it on the table, it'd most likely lay down as it was when we took it. If we were to open a new deck of cards, we would most certainly draw the first card and find it to be two, an ace or a joker, depending on how the deck was printed and packed on the factory. This is exactly the reason why deck shuffling destroys card counting in games like Blackjack: a randomly shuffled deck is said to be in an unpredictable (unknown) state, while the sole purpose of card counting is to predict (know) the state of the deck.
Let's take a more real life example: American Roulette. The American Roulette table has 38 pockets in the wheel. The ball is spun and the wheel is rotated: this provides an adequately random environment to say that the likelihood of a ball landing in any of the pockets is equal. Therefore we say that at any given moment of time the probability of the ball landing in a particular slot is 1/38. However, what would be the probability of the same number playing out twice in a row (two spins one after another?).
If you want to find out a probability of otherwise unrelated events A and B happening one after another, simply multiply the probability of event A by probability of event B:
If we want to find out what is the chance of american roulette wheel catching double zero in the first round and 12 in the second round will be:
1/38 * 1/38 = 1/1444
As you can see, 1 chance out of 1444 is a very weak likelihood indeed.
This concludes our basic probability tutorials. For more detailed and advanced information such as mutually exclusive events, aggregate probabilities, standard deviation and sample space rules, look on the web.