| WHAT IS GAMBLING? | | | | had been losing money on this proposition, |
| | | | and he wanted to know why. |
| Gambling consists in risking something one | | | | |
| possesses in the hope of obtaining something | | | | Pascal worked on the problem and found that |
| better. No one can avoid gambling, because | | | | the Chevalier had the best of it by 3.549% |
| life itself forces us to make bets on Dame | | | | with his one-die proposition. Throwing a |
| Fortune. In business, education, marriage, | | | | double six with two dice, however, would |
| investment, insurance, travel, in all the | | | | theoretically require 24.6+ rolls to make it |
| affairs of life we must make decisions which | | | | an even-money proposition. In practice it |
| are gambles because risk is involved. | | | | can''t ever be an even money bet, because you |
| | | | can''t roll a pair of dice a fractional |
| Many people, for pleasure or gain, also risk | | | | number of times: it has to be either 24 or 25 |
| money on online games of chance, games of | | | | rolls. Here is a calculation I have never |
| skill and games which combine both chance and | | | | seen in print before: The exact chances of |
| skill. | | | | rolling two sixes in 24 rolls are: |
| | | | 11,033,126,465,283,976,852,912,127,963,392,28 |
| Games of chance are those in which there is | | | | 4,191 successes in |
| no element of skill. | | | | 22,452,257,707,354,557,240,087,211,123,792,67 |
| | | | 4,816 rolls. |
| Gamblers call these "mechanical games." There | | | | |
| are hundreds of such free kid games , and | | | | This means that dice hustler De Mere had been |
| they are the most popular form of gambling. | | | | taking a beating of |
| They include lotteries, raffles, policy | | | | |
| numbers, Bingo, wheels of fortune, slot | | | | 27 +% on the bet. If he had bet that two |
| machines, most dice games (Craps, | | | | sixes would come up at least once in 25 rolls |
| Chuck-a-Luck, Hazard, Under and Over Seven, | | | | he would have enjoyed a favorable edge of |
| Beat the Shaker, etc.), and some card games | | | | .85%. |
| (Faro, Bac¬carat Las Vegas style, etc.). | | | | |
| | | | Pascal corresponded with mathematician Pierre |
| Games of skill are those in which the element | | | | Fermat about this and similar gambling |
| of chance is com¬pletely or nearly | | | | problems and these two men formulated much of |
| nonexistent, such as Scarney, Teeko, | | | | the basic mathematics on the theory of |
| Checkers, Chess, bowling, horseshoe pitching, | | | | probability. |
| tennis and golf.online games of chance and | | | | |
| skill combine both elements and include most | | | | History doesn''t state how many francs |
| games played with cards: Poker, Gin Rummy, | | | | Chevalier de Mere lost on his double-six |
| Bridge, Black Jack, Pinochle and many others. | | | | betting proposition before Pascal explained |
| Sports contests such as horse racing, | | | | why he was getting the worst of it, but I do |
| baseball, football, basketball and | | | | know that nearly 300 years later, in 1952, a |
| prizefights are usually thought of as | | | | New York City gambler known as "Fat the |
| contests of skill. But we must include them | | | | Butch" lost $49,000 by betting that he could |
| in this category because, from a gambling | | | | throw a double-six in 21 rolls. |
| viewpoint, they all involve a certain amount | | | | |
| of chance which sports fans know as "the | | | | Fat the Butch, although a smart |
| breaks of the game." In baseball, forexample, | | | | gambling-house operator who has made millions |
| a bad hop of the ball may lose the game for | | | | booking dice games, went wrong on the bet |
| either team. Also, present-day bookies'' | | | | because he figured it this way: There are 36 |
| methods of handicapping or laying the odds on | | | | possible combinations with two dice, and a |
| national sports contests are such that the | | | | double-six can be made only one way-so there |
| element of skill plays little part in helping | | | | should be an even chance to throw a |
| a bettor pick a winner. | | | | double-six in 18 rolls. Consequently, when |
| | | | "The Brain," a well-known big time gambler, |
| GAMBLERS AND SCIENTISTS | | | | offered to bet $1,000 that a double-six would |
| | | | not turn up in 21 rolls, Fat the Butch |
| Dice are the oldest of all gambling devices. | | | | thought he had the best of it and jumped at |
| Man''s earliest written records not only | | | | the opportunity. |
| mention dice and dice games but crooked dice | | | | |
| as well. Dice of one sort or another have | | | | After twelve hours of dice rolling, Fat the |
| been found in the tombs of ancient Egypt and | | | | Butch found himself a $49,000 loser, and he |
| the Orient, and in the prehistoric graves of | | | | quit because he finally realized something |
| both North and South America. | | | | must be wrong with his logic. He was, later, |
| | | | part owner of the Casino de Capri in Havana, |
| The earliest gamblers thought that the fall | | | | and when I told him it would need 24.6 rolls |
| of the dice was controlled by the gods, and | | | | to make the double-six bet an even-up |
| although a few of them tried to outwit | | | | proposition, and that he had taken 20.45% the |
| divinity by loading the cubes, most of them | | | | worst of it on every one of those bets, he |
| probably considered that any prying into the | | | | shrugged his mas¬sive shoulders and said, |
| matter was sacrilegious. | | | | "Scarne, in gambling you got to pay to learn, |
| | | | but $49,000 was a lot of dough to pay just to |
| In the sixteenth century at least one gambler | | | | learn that." "That is for sure," I agreed. |
| began to wonder if the scientists who were | | | | |
| beginning to make valid predictions about | | | | Although most of the odds and percentage |
| other matters might not also be able to | | | | problems you will en¬counter in this book |
| foretell how the dice would fall. An Italian | | | | can be calculated simply, a few, like the |
| nobleman asked Galileo why the combination 10 | | | | double six problem above, are more complex. |
| showed up more often than 9 when three dice | | | | Here is the formula for figuring problems of |
| were thrown. The great astronomer became | | | | this type. To find out when the chances are |
| interested in dice problems and wrote a short | | | | approximately equal in any single event, |
| treatise which set forth some of the first | | | | multiply the "odds to one" by .693, the |
| probability theorems. His reply to the | | | | co-log of the hyperbolic log of 2. This will |
| gambler was that 6 X 6 X 6 for a total of 216 | | | | give the approximate number of chances, |
| combinations can be made with three dice, of | | | | trials, rolls, guesses, etc., needed to make |
| which twenty-seven form the number 10 and | | | | any event an even or fifty-fifty proposition. |
| twenty-five the number 9. | | | | |
| | | | For example: the odds are 35 to 1 against |
| In France, in 1654, the philosopher, | | | | throwing double sixes with two dice in one |
| mathematician and physicist Blaise Pascal was | | | | roll. Multiply 35 X .693 and you find that a |
| asked a similar dice question by one of the | | | | double-six can be expected to appear in the |
| first gambler-hustlers on record. The | | | | long run once in approximately 24.255 rolls. |
| Chevalier de Mere had been winning | | | | (The figure of 24.6+ given earlier is more |
| consistently by betting even money that a six | | | | exact.) To calcu¬late the approximate |
| would come up at least once in four rolls | | | | number required for a double event such as |
| with a single die. He reasoned from this that | | | | throwing double-sixes twice, multiply the |
| he would also have an advantage when he bet | | | | "odds to one" by 1.678. For a triple event |
| even money that a double six would come up at | | | | multiply by 2.675; a quad event, by 3.672; |
| least once in 24 rolls with two dice. But he | | | | and a quint event, by 4.670. |