The theory of probabilities in poker
The theory of probabilities is one of the most difficult mathematical disciplines, gentlemen. Paradox, but thus acquire its essence the child may also, so this essence is simple. It is not so necessary for you to learn difficult mathematical formulas to represent, about what there is a speech. It is enough to familiarize with elements.
So, gentlemen, the basic and main in theory of probability, that we should study, are parity of quantity of required cases to their general quantity. What such case? Anything you like, gentlemen, anything you like. A throw of a coin or playing slots. One delivery of cards. And even giving to cats of a rat poison. What is the total of cases? The total is that possible variants by which experiment may be finished. For example, if you throw playing craps it may drop out any of six sides upwards. Hence, total of cases equally to six. And if you throw a coin it may drop out upwards either one or another side, and total of cases equally to two.
Wow! - You will tell. The cat, after absorption of a poison may wash a muzzle and go to walk further, and can, as it is sad to play in box; variants two, truly? (But it is not necessary to carry out this experiment on a cat of the wife; after that there is no guarantee, that it will be not lead on you, gentlemen). Not absolutely so. Unless it is a mathematical cat. Actually, in a reality two will not take place, and huge quantity of different variants, starting from instant death without uniform miaow and down to heart-rending cat's shout together with dirty flat.
Therefore in the subsequent let's agree for convenience to operate with the conditional objects always working in our interests. Playing craps do not fall from a table, coins kindly do not hang in air, and cats….. cats or live, or die at once.
What is the quantity of required cases?
About, it is absolutely simple, gentlemen. This quantity of those, cases, which we, shall tell, so, try to achieve from experimental object. With a devil smile measuring a doze of poison, we wish the unfortunate striped creature of death. And if the cat fairly follows our arrangement a required case will be one death of a cat.
If we want to throw out one side on a coin the quantity of required cases will be equal to one. And if we want to throw out on playing craps the five or the six the quantity of required cases will be equal to two.
Now, having defined with concepts, we approach to the main thing gentlemen, as the probability is determined. And it is very simple as it was already mentioned, the attitude of required cases to total. Considering death of our distressful mathematical cat, we come to the following. The quantity of required variants - death is equal to one.
The total of variants… either will die, or will not die - equally to two. Hence, the probability of purchase of the cat's coffin (with brocade) is equal 1/2. Fifty percents. Only it is necessary to remember, gentlemen, that a cat at us mathematical and conditional, and that is easy to run into error of one known student, which on a question of the professor: What is probability of what today you will meet a dinosaur? - with readiness responded: 1/2 or meet, or not.
If the quantity of possible variants coincides with quantity required the parity, accordingly, is equaled to unit. It means, that event will come absolutely precisely (mathematical). It is more than unit this attitude, naturally, may not be. Required cases can be chosen only from total of cases.
This formula of calculation of probability can be applied practically to any event. If we still should throw out on playing craps the five or the six the probability is events it will be equal two to divide into six (total of sides), that is 1/3. What this number means? This number, gentlemen, means, that on three carried out experiments (throw craps) will have about one at which will drop out five or six.
In practice, you may throw craps ten times and required figures and will not turn to you pitted holes… You see, each subsequent throw does not depend at all from previous. At playing craps there is no memory, gentlemen.
But if to take big enough series of throws and to look, as the five or the six then we and shall see that frequently dropped out, that they dropped out approximately each third time. Proceeding from this general rule, it is possible as approximately to make forecasts and for the future throws. The main thing to remember, that for each subsequent throw the probability always remains identical and does not depend in any way on the previous series though there ten times would drop out one.
Translating conversation is closer to games, from this forecast it is possible to take practical advantage. For example, it is possible to calculate fair (unfair) rates at a bet. We admit your comrade puts, that at a throw playing craps the number from one up to four inclusive will drop out. You insist, that now the long-awaited five or the six all the same will appear. Your chances of success are equal 1/3. Chances of your comrade are four to divide into six - 2/3.
Thus, of you it is fair to demand the appropriate rates concerning to each other in the same proportion, as well as probability - 1/3 to 2/3 or one to two. That is, you put ten dollars, he - twenty. At such rates and long game hardly someone will win much. About two throws you will to give on ten dollars, and on the third to receive them back.
And if hardly to change a parity - to make his five dollars to fifteen your comrade - gawk seriously may be lost at long game. Why? Very simply, gentlemen. The parity of rates becomes one to three while the parity of probabilities remains former - one to two. A difference is in your advantage, gentlemen. Conditionally speaking, on the first throw you give five dollars. On second five more. And on third you receive back the lost ten, and earn moreover five more dollars. But it is not necessary to do so. It is bad.
Poker submits to the same laws. The theory of probabilities in poker shows that at calculation of probability of occurrence of a combination, it is necessary to divide total of required combinations or all possible variants of this combination into total of all in general possible combinations. But this subject is worthy separate clause.
Also remember - too much frequently good luck breaks all mathematical laws. We wish you good luck, gentlemen!www.pokerbest.net
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