Mathematics, a subject that America fears, is very closely associated with one of the greatest passions of this country — gambling. Most people are aware that the casino or the bookies always win, but what is it that drags them into betting? For instance, take the Pennsylvania Lottery.
To win a ten million dollar jackpot, you have to pick six numbers out of a possible 50. The order of the numbers does not matter. If more than two people pick the same numbers, the prize is divided equally among them. The odds of picking the six winning numbers are so infinitesimal that the probability of being hit by a meteorite is higher. In fact, it is interesting to note that it is best to buy a ticket for the Saturday lottery on Friday, since if you bought it earlier, the chance of winning the lottery is lower than the chance of being run over by a car. This statistic comes from the fact that chance of winning the jackpot is 1 in 14,000,000, while the chance of being run over by a car over a period of two days is 1 in 10,000,000.
There is also a lot of mumbo-jumbo about picking numbers. If a certain number has not appeared for four weeks, most people would suppose that the number is "due" soon. This is utter nonsense. If I were to toss a coin ten times and get heads all the time, the eleventh toss is no more likely to be heads than the first one. Each of these events is independent. In fact, there might be reason to suspect the opposite, that is, one might be inclined to think that the coin is biased towards heads in a certain way. Similarly, if a number were appearing several times, its ball might be slightly heavier than the rest. However, since most people will then start picking that number, it would be in your best interest to avoid it!
Often, the odds of winning are not astronomical, for instance in horse racing. Here the odds offered by the bookies seem reasonable. If the odds of a horse winning are 1 to 2, then if you bet $10, you stand to lose it or gain an equal amount. These seem like fair odds and we might wonder how the bookie makes a profit. Rest assured, he makes one. Take for example, a race in which there are three horses with the following odds —
Nifty NedEven (= 1/2)
Fiery Fred2:1 (= 1/3)
Old Hag3:1 (=1/4)
If three friends Tom, Mike and Sally were to bet a dollar each on different horses, their average profit can be calculated by multiplying the probability of winning and the amount won.
Result Odds(O) How much winner gets (W)O x W
Nifty Ned1/2150 ¢
Fiery Fred1/3267 ¢
Old Hag1/4375 ¢
The profits of Tom, Mike, and Sally add up to $1.92. Considering the winner gets back their invested dollar, two dollars were still lost, and the bookie makes a profit of 8¢. At first, this may seem absurd, but the trick here is that the odds do not add up to one, as they should. In fact, they add up to 1.08, which is exactly why the bookie makes profit a profit of 8¢. If you ever discover a bookie whose odds add up to less than 1, place bets with him immediately!
There is no easy way to make millions of dollars. If it were possible, the industry would have shut down long ago. The fact is that for every dollar won, more than a dollar and a half are lost. This is what keeps Vegas and Atlantic City alive.
http://edop.thetriangle.org/2003/05/16/gambling.html
To win a ten million dollar jackpot, you have to pick six numbers out of a possible 50. The order of the numbers does not matter. If more than two people pick the same numbers, the prize is divided equally among them. The odds of picking the six winning numbers are so infinitesimal that the probability of being hit by a meteorite is higher. In fact, it is interesting to note that it is best to buy a ticket for the Saturday lottery on Friday, since if you bought it earlier, the chance of winning the lottery is lower than the chance of being run over by a car. This statistic comes from the fact that chance of winning the jackpot is 1 in 14,000,000, while the chance of being run over by a car over a period of two days is 1 in 10,000,000.
There is also a lot of mumbo-jumbo about picking numbers. If a certain number has not appeared for four weeks, most people would suppose that the number is "due" soon. This is utter nonsense. If I were to toss a coin ten times and get heads all the time, the eleventh toss is no more likely to be heads than the first one. Each of these events is independent. In fact, there might be reason to suspect the opposite, that is, one might be inclined to think that the coin is biased towards heads in a certain way. Similarly, if a number were appearing several times, its ball might be slightly heavier than the rest. However, since most people will then start picking that number, it would be in your best interest to avoid it!
Often, the odds of winning are not astronomical, for instance in horse racing. Here the odds offered by the bookies seem reasonable. If the odds of a horse winning are 1 to 2, then if you bet $10, you stand to lose it or gain an equal amount. These seem like fair odds and we might wonder how the bookie makes a profit. Rest assured, he makes one. Take for example, a race in which there are three horses with the following odds —
Nifty NedEven (= 1/2)
Fiery Fred2:1 (= 1/3)
Old Hag3:1 (=1/4)
If three friends Tom, Mike and Sally were to bet a dollar each on different horses, their average profit can be calculated by multiplying the probability of winning and the amount won.
Result Odds(O) How much winner gets (W)O x W
Nifty Ned1/2150 ¢
Fiery Fred1/3267 ¢
Old Hag1/4375 ¢
The profits of Tom, Mike, and Sally add up to $1.92. Considering the winner gets back their invested dollar, two dollars were still lost, and the bookie makes a profit of 8¢. At first, this may seem absurd, but the trick here is that the odds do not add up to one, as they should. In fact, they add up to 1.08, which is exactly why the bookie makes profit a profit of 8¢. If you ever discover a bookie whose odds add up to less than 1, place bets with him immediately!
There is no easy way to make millions of dollars. If it were possible, the industry would have shut down long ago. The fact is that for every dollar won, more than a dollar and a half are lost. This is what keeps Vegas and Atlantic City alive.
http://edop.thetriangle.org/2003/05/16/gambling.html
