
Expectation of mathematicsExpectation of mathematics is the amount that will give an average of winning or losing a bet. It is an important concept because it shows a gambler how to assess most of the gambling problems. To examine a poker play, mathematical expectation is useful in the best way. Let's say if you have bet with a friend for $1 on the flick of a coin. If it comes head, you win and if it comes tails, you lose. The odd of heads are 1to1 but you have bet $1 to $1. Since you cannot expect mathematically, either to be ahead or behind after 200 flick or after 2 flick, your mathematical expectation is exactly zero. Your rate of hour is also zero. The amount of money you require to win per hour is known as hourly rate. In an hour you can flick a coin 500 times, you will neither earn nor lose money if you are not getting good or bad odds. The betting intention is not bad for a serious gambler. But it is just a time waste. Let's say if an imbecile is interested to bet $2 to your $1 on the flick of coin. Immediately you will have a positive expectation of 50 cents per bet. Why 50 cents? On an average you win one bet for every bet that you lose. You bet your $1 and lose $1; you bet $2 and won $2. You bet $1 twice and you are in lead with $1. 50 cents have been earned for every $1 bet. If you deal with 500 flick of coin per hour $250 will be your hourly rate because on an average you will win two dollars 250 times and will lose one dollar 250 times. This means $500 minus $250 will give you a net gain of $250. Note your mathematical expectation is 50 cents which is the amount averaged to win per bet. That happens to be 50 cents per bet. Results mean nothing in mathematical expectation. Even if the imbecile wins the first ten coin flick in a row and getting 2 to 1 odds on money proposal, you still can earn 50 cents per bet. As long as bankroll is with you to cover your losses easily, it will make no difference whether you win or lose a single bet or series of bet. You will win till you continue to make these bets and in the long run this will move towards the sum of your expectation. You can make a bet with the best of it whether you win or lose the bet or has earned something on that bet where the odd is in your favor. On the other hand, you can make a bet with the worst of it whether you win or lose the bet or have lost something on that bet where the odds are not in your favor. You can have positive expectation if you have the best of it and where the odds are in your favor. You can even have negative expectation if you have the worst of it and where the odds are against your favor. When the serious gamblers have the best of it, they bet and they pass when they have the worst of it. What do you understand by having odds in your favor? It means to win more on a result than real odds warrant. The real odds of a coin's head that comes are 1to1 but you get 2to1 for your money. In this case, the odds are in your favor. With a positive expectation of 50 cents per bet you can have the best of it. There is slight complex example of mathematical expectation. A number from one to five is written by a person and wants you to guess the number for which he bets $5 against your $1. Will you accept the bet? What would be your mathematical expectation? On an average one will be right and other four guesses will be wrong. Therefore guessing correctly against the odds is 4to1. There are chances that in a single try you lose the dollar. On the other hand, on 4to1 proposition you are getting $5to$1. You have the best of it where the odds are in your favor and you should take the bet. If you take the bet five times and lose $1 four times but win $5 only once, you have gained $1 on five bets for positive expectation of 20 cents per bet. The best is to take the odds as he wins more than he bet as in the above example. He may lay the odds as he wins less than he bets. Whether a person takes the odds or lays the odds, he can have a positive or negative expectation. If you place $50 to win $10 on a 4to1 favorite you have a negative expectation of $2 per bet where you lose $50 once but win only $10 four times which means after five bets you have a net loss of $10. On the other hand, if you place $30 to win $10 on a 4to1 favorite, you have a positive expectation of $2 per bet where you lose $30 once but win $10 four times for a net profit of $10. The first bet is a bad one and the second bet is a good one has been shown from the mathematical expectation. The heart of every gambling situation depends on the mathematical expectation. When a football bettors is required by the bookmaker to lay $11 to win $10, he has a positive expectation of 50 cents per $10 bet. It has a positive expectation of about $1.40per $100 bet, the casino gives the money on the pass line at the table as the game is arranged so that the pass line bettor loses 50.7 percent of its time and win 49.3 percent of its time, on an average. Perhaps, it is miniature positive expectation which imparts the casinos to earn huge profits around the world. The owner of Vegas World casino, Bob Stupak has exclaimed that the worst to have onethousandth of one percent when he plays continuously and that onethousandth of one percent will make the richest man in the world go out of the action. The odds are constant on any given bet in most of the gambling situations like roulette and casino craps. How to assess a particular situation can been shown by mathematical expectation in case if other changes. For example in blackjack, to make the right play resolve, your expectation to play a hand in one way or in another way has been estimated by the mathematicians. The play that gives highest positive expectation or the lowest negative expectation is the best one. For example, if you have 16 against dealer's 10, you are sure to lose. However, if 16 is 8, 8 spilt the 8s doubling your bet to make the play poker best. Against the dealer's 10, split the 8s which will make you to lose more money than you win but you can strike 8,8 against a 10 if you have a lower negative expectation. 

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