Expected Value in Human Life - Essay Example

Expected Value Science and mathematics have lot of importance in human life. Mathematics helps people to make better calculations intheir present life to achieve a better future. All the people like to have a happy future life and without proper planning, it is difficult to achieve better life at present and in future. Many wealthy people failed to live happily in their future life because of their poor planning in present and past life. In short, better planning is essential for a better future life and mathematics helps people in making better plans for future. Even if we take extreme precautions, it is difficult to formulate a 100% perfect plan for the future. This is because of the unpredictability of certain parameters which are associated with our planning. For example, in a cricket match, winning the toss has major role in deciding the victory. Most of the cricket pitches are underprepared which may favor either batting or bowling initially and then changes its characteristics later during the second innings. The toss winning captain can take decisions about whether to bat/ bowl first or to include pace bowlers or spinners in the team, based on the evaluation of the pitch. Many of the cricket teams underprepare their cricket pitches based on their strengths in batting and bowling. However, if they fail to win tosses, their planning cannot be implemented successfully. This is because of the fact that the chances of winning a toss are 50-50 since the coin has only two sides. In other words, the probability of getting a head or tail is 50-50. In such uncertain situations, the mathematical term “expected value” can help people in taking decisions. Expected value in mathematics is the weighted average of all the possible values. In other words, all the possibilities of a particular event will be evaluated properly while calculating the expected value. In industries and casinos, expected value has significant role to play. This paper analyses the history and importance of expected value. History of expected value The exact date of origination of the idea about expected value is still unknown to us. However, it is widely accepted that the expected value concepts were used during the latter half of the seventeenth century. Blaise Pascal, a French scientist and mathematician, is believed to be the founding father of the expected value theory. During the middle part of seventeenth century, the question of how to solve the problems of points or the problems of division of stakes raised major challenges to the mathematicians. Blaise Pascal and his associates started to solve these problems and the idea of expected value originated from their efforts. Even though, Pascal and his associates used different methods to solve this problem, they got same results since they used the same fundamental principle of mathematics in all their calculations. Apart from Pascal and his associates, a Dutch mathematician called Christian Huygens also contributed heavily to the development of expected value theory. Significance of expected value theory in casinos Expected value theory has greater significance in gambling. The chances of winning and losing in gambling depend on various parameters associated with the particular game selected for gambling. For example, poker is a game, which works on mathematical principles. Even though the nature and characteristics of the players play a vital role in deciding the winners of the poker game, many calculations including permutations and combinations are necessary to make sound decisions. For example, the right frequency to bluff in a situation is determined based on the likelihood your opponent will fold in that particular situation. In limit, for example, when all the cards are out, how do you determine whether you should bluff on the river? If you can figure out that the pot is offering a caller 5:1 odds to call, but you know that they will fold the best hand 1 in six times, then bluffing now becomes mathematically correct (Importance of Math: expected value, bluffing frequency, and randomization) The amount of bet is also determined in poker game by mathematical calculations. The bet amount should be decided based on the assessment of the holdings of opponent and the calculations based on the expected value. It is impossible to know what cards the opponent is holding in the poker game. Because of the uncertainty of that, the expected value calculations should be done before placing the bet. Expected value is the amount of money a person may win or loss while playing games like poker. Expected value can never guarantee something to the player. It only shows the probability of winning or losing. The +EV or positive expected value is computed by multiplying the money you’re going to win with the probability of winning. The –EV or negative expected value, on the other hand, is the money you’re going to lose with a poor bet. You can get your –EV by multiplying the money you’re going to lose on a bad bet with the probability of losing. Let’s apply the basic example of a flush draw. Let’s say that our hand is A 2 and the flop side is Q K 3 7, the pot contains $100 and our opponent goes all in with $50, this means that we have a chance to win $150. The probability of hitting a flush is 0.2, though, and the probability of losing our flush is 0.8. The formula would look like this: ($150 x 0.2) + ($50 x 0.80) ($30) + – ($40) $30 – $40 EV = -$10 (The Importance of Expected Value in Poker) The expected value calculations can be explained with the help of another simple example of tossing a coin. Suppose a person place a bet for head. The chances of getting a head are only 50%, ?, or 0.5. He can calculate his expected value as follows. + EV = $1.00 x 0.5 -EV = -$1.5 x 0.5 Total EV = +EV+-EV= 0.5 + - (0.5) = 0 The coin tossing game or similar games are not much popular in casinos because of the least chances of making profits. As evident from the earlier calculations, the chances of winning and losing are equal in coin tossing and hence the casino owners may not get much profit in the long run. They always favor games, which have a negative expected value. For players, games with positive expected value are more attractive. However, the intention of the casino owners is to maximize their profits rather than giving money to the players, which is the secret of selecting games with negative expected value in casinos. Take roulette as an example, the wheel is equally divided into 38 pockets, 18 reds, 18 blacks and 2 greens. The probability that the ball drop on any of those pockets is 1 / 38 = 2.6315%. As you know, it does not matter whether you bet on red or black if the number comes out to be green you will lose. So dealer has 2 x 2.6315% = 5.2630% more chance to win. Your chance (or probability) of wining by betting on red or black is 18 x 2.6315% = 47.3670%. Your chance of losing by betting on red or black is (18 + 2) x 2.6315% = 52.6300% .The Expected Value of betting on red or black is Bet x (47.3670%) + Bet x (-52.6300%) = (-5.2630%) (Chen) From the above statistics, it is clear that the dealers or the casino owners has more chances of making money than the players. In other words, the players will be the loser ultimately when we consider long term playing effects of casisno games. Winning of a casino game once or twice, will motiovate the palyers further to play the game again and again. No player will stay inactive if he wins a game. The greedy players will play more times and without knowing the fact that they may lose their money in the long run. Slot machine in the casio games has the highest negative expected value compared to other games. This means that the chances of losing money for the player is more in slot games. Blackjacks seems to be the only casino game which has a posiitve expected value. This is because of the pecualiar nature of the design of this game. The destiny cahnges from card to card and hand to hand in blackjack game. It is quite possibel that in this game the palyers may face situations in which the expected value of winning may become positive. The ability of the palyer to identify such circumstances is the necessary skill needed for a blackjack player. Cricket is another game in which betting is taking place across the world. Recently some of the Pakistani players were arrested for giving information to the betters while playing cricket. In fact many of the cricket matches played recently were in the shadows of suspicion. This is because of the fact that in many of the matches held in recent times, the stronger team played poorly and the weaker team won the matches. Nobody will place their bet on poor teams while engage in cricket betting. It is difficult to expect that world champions India or Australia could be beaten by weaker times like Ireland or Holland. Most of the betters will place their bets on stronger teams like India or Australia when they play with weaker teams. However, the lobbies which control the cricket matches may have illegal connections with the players and they will offer big money to the players for underperforming. The lack of knowledge about such malpractices behind the cricket matches may force a better to place their bets on stronger teams and ultimately they may lose their money. In other words, unpredictability of cricket matches made the expected value calculations difficult. Sports betting are also theoretically beatable, though very few people are actually successful at doing so. Expected value (or “EV” for short) helps identify the difference between smart bets and stupid bets. Bets with a significant negative expected value are obviously stupid. For example, if you lived on a quiet street and bet your friend that 10,000 cars would drive by in the next 30 minutes, that bet would have a very low expected value. Since it’s almost impossible for that many cars to drive by, the value of your bet is effectively $0 (Gambling tips) Expected value in industries Expected value has significant roles in industries also. Most of the entreprenuers forecast the probability of winning and losing in their business based on the expected value calcualtions. No entreprenuer may invest in an industry, if the expected value yields a negative quotient. On the other hand, all the entreprenuers would like to invest in industries in which the expected value yields positive results. For example, real estat sector was an industry which yielded positive expected value before the recent recession. However, recent recession has decreeased the demand in real estate industry considerably and the business people started to stay away from this industry because of the negative quotient of the expectedr value. The importance of expected value in business can be explained with the help of the following example from share market; An investor should buy a stock when its market price is significantly lower than its expected value; the greater this difference, higher the returns. Similarly, a firm should buy back its stock when it is trading below the expected value and so transfer wealth from the short-term stockholders to the long-term stockholders. Expected value is the best prediction of a variable's value, and is computed by multiplying each outcome by the probability of its occurrence and then averaging them. Mathematically it is described as the probability-weighted average values of all possible outcomes, and is a measure of central tendency of a random variable or mathematical expectation (Expected Value) From the above statistics, it is clear that expected value calculations are equally important for both the buyers and sellers in share market. Markets are controlled by various expected and unexpected factors. The recent recession was an unexpected one even for the economic pundits. In other words, expected value calculations can be wrong at times in the business world because of the uncertainty of the events happening in business world. For example, the killing of Bin Laden occurred recently quite unexpectedly. This killing resulted in heavy fluctuations in oil prices. Since oil prices are one of the prominent factors which determine the prospects in share market, many of the organizations faced severe fluctuation in its share prices recently. In short, the chances of making wrong expected value calculations is more in the business world at present because of the unpredictability of future events. Expected value in Reality shows At present, lots of television reality shows are taking place which offer huge prize money to the performers. Deal or no Deal is one of the popular reality shows taking place across the world. In this show the participant has the option of opening some boxes which are marked with some amount of money inside. The participant will be shown a money tree in one side is marked with gold (Bigger amounts) and the other side marked with silver (Smaller amounts). The biggest possible winnable amount is marked at the top of the gold part and the lowest winnable amount market at the top of the silver part. The participant can take one box as his own and he can keep that box till the end of the show. The chances of winning more money depend on the amount he lost by opening boxes at different rounds. In the first round the participant needs to open five or six boxes. If he opens boxes which contain lesser amounts, he will get big offers from the banker to exchange his box against the money offered. Here the banker’s calculations are always based on the probability of the amount contained the participants box. If the participant consistently opening boxes containing smaller amounts, the probability of having bigger amount in the participant’s box will be increased. The banker delivers his offers after careful calculations with respect to the expected value of the participant’s box. The expected value of the participant’s box increases when he opens boxes of smaller boxes and decreases when he opens boxes of bigger amounts. Based on the amount remaining in the money tree and the amount lost by the participant, the banker and the participant make lot of calculations about the expected value of the particular box in the hands of the participant. The participant decides to continue his competition or not, based on the offer of the banker, and the amounts remaining in the money tree and the expected value of his box. For example, suppose the amount left in the money tree at the last round was $ 1000000 and $ 500000. In this case, the banker may offer an amount in between $ 1000000 and $ 500000 since the chances of having $ 1000000 in the participant’s box is 50-50. The participant can decide whether to accept or reject the banker’s offer based on his perceptions and expected value calculations. To conclude, the influence of expected value in our daily life is tremendous. Knowingly or unknowingly, we are making lot of expected value calculations before taking certain decisions. In sports, casinos and in industries, expected value calculations play an important role. Works Cited 1. Chen, Andrew. “Casino Gambling, Expected Value and Blackjack Strategy”. 2008. Web. 11 May 2011. 2. “Expected Value”. Web. 11 May 2011. 3. “Gambling Tips”. Web. 11 May 2011. 4. “Importance of Math: expected value, bluffing frequency, and randomization”. Web. 11 May 2011. 5. “The Importance of Expected Value in Poker”. Web. 11 May 2011. Read More