The Match Game
The match game is deceptively simple. The rules of blackjack play are few and easily learned, but it is much more than just a game of chance. It contains mathematical and psychological factors which introduce a skill element and make it one of the most fascinating of all guessing games in the world of gambling.
A set of three paper or wooden matches for each player. Two, three, four, five, six, or more people can play at one time. The game is best suited to six-handed competition.
Object of the Game
Each player tries to guess the sum total of the matches held by all the players. The one who guesses the correct total is declared the winner of the game or hand or leg (one game of a series) and is eliminated. Ties are no-games. The remaining players continue playing until only one player is left; and he is the loser of the game.
Selecting the First Player or Caller
Before beginning the game, each player hides his three matches from his opponent or opponents (behind his back or under a table). He puts one, two, three, or no matches into his right hand, closes his fist tightly, and brings it into view.
Any player, by mutual consent, calls out his guess as to the sum total of the matches held by all the players, including himself. Then the player on his immediate left makes the second call, followed by calls from the others in turn, proceeding clockwise. No player is permitted to call a total which has already been called.
After the last player has called his guess, the first caller opens his hand, showing his matches then the other players, in turn, do the same. The exposed matches are counted. Since the person who makes the last guess has the best chance to win because he can base his guess on information derived from the other player’s calls, the player whose guess is closest to the total gets the advantage of becoming the last online poker player in the game or hand about to be played.
The player who makes the next closest call becomes the next to last player, and so on. The player whose guess is furthest from the correct total starts the game by making the first call. With the start of each new hand or game the first call passes to the left so that each player has an opportunity to be last caller and has an equal number of chances to win.
The Two-Handed Match Game
The first player tries to guess how many matches his opponent is holding, adds this to the number he himself holds, and calls the total, which may be any number from zero to six. His opponent follows suit, but may not call for a total that has previously been called.
If neither player guesses the correct total, it is a no-game or a standoff. Neither player wins or loses, and the play continues until one player makes a correct call. Players alternate in making the first call, even after a no-game. The player who first makes two correct calls out of three wins the game.
Many people, at first, think that the match Game is purely one of chance; but any beginner who sits down to play against an expert soon discovers that he is losing far too often and that something more than chance is involved. There are two additional factors: a knowledge of the game’s mathematics, and skill in judging the psychology of the other players. The best two-handed playing strategy is based on the following mathematical analysis of the game.
Each of the two players may hold zero, one, two, or three matches. In order to win, the first player must add to the number of matches he himself holds a correct guess as to the number his opponent holds. Since his opponent may hold zero, one, two, or three matches, the first player has one chance in four of making a correct guess-a 25 percent chance to win the hand. In a two-handed game the first player’s chance of winning the hand is always the same: out of 4, or 25 percent. But the second player’s chances vary, depending on the first call, from 25 percent to as much as 75 percent.
The second player has a better chance of winning poker most of the time because six of the seven possible calls (zero, one, two, three, four, five, six) that the first player can make reveal information which enables the second caller to infer, rather than to guess blindly, the number his opponent holds. The first call of “None” tells the second player that his opponent probably holds no matches and is guessing that the second player also holds none.
If the first player calls “Six,” his opponent can infer that he holds three matches and is guessing that the second player holds three. In the two cases above, the first caller has one chance in four, or a 25 percent chance of winning. But since he will miss three times out of four, or 75 percent of the time. his opponent will win three out of every four times, a favorable chance of 75 percent.
A first call of either “One” or “Five” is slightly less informative. A call of “One” indicates that the first player is probably holding none or one, and a call of “Five” indicates that he is probably holding two or three. This gives the second player an even chance of guessing correctly the number of matches the first player is holding and his chance of winning, therefore, is 37 1/2 percent. The chance that neither player will make a correct guess and the game will be a standoff is also 37 1/2 percent.
The first call of“Two” or “Four” reveals still less. A call of“Two” indicates that the first player may be holding zero, one, or two. A call of“Four” indicates that the first player may be holding one, two, or three. The second player has four chances in seven of winning. The odds favor him at four to three and his chances of winning are 33 1/3 percent. His chance that it will be no game are 41 2/3 percent. A call of“Three” indicates that the first player may be holding zero, one, two, or three matches.
From a mathematical standpoint, this call is, therefore, the first player’s best strategy. But, because of psychological factors, the expert seldom sticks to the first call of “Three.” He studies his opponent’s playing characteristics for faults. If he sees that his opponent prefers a hold of three more often than zero, or if he often repeats previous holds on the next play, etc., the expert may change his strategy accordingly.
The Second Call
Having heard the first player’s call, the second player uses whatever information has been given to him as the basis for his own call. If the first player calls “None,” he probably holds no matches and the correct total is the number the second player holds. If the first call is “Six,” the first caller probably has three matches, and the second player simply adds three to what he himself holds. In both cases, the second player has a 3 to 1 chance against the first player of winning the hand.
Because the second player has a mathematical advantage, the first player sometimes purposely makes a miscall by guessing a total that can’t possibly win for him. His object is to make the first call revert to his opponent. For instance, when the first caller holds one match, he calls “None.” He cannot win the hand he will either lose or the hand will be a no-game. If the second player does hold no matches and supposes that his opponent’s call of “None” means that his opponent is holding none, he cannot call “None” because the rules prevent this, so he calls “One” and is surprised to find this call wins.
Here are all the possible miscalls the first player can make in a two-handed game:
1st Player His Possible
0 matches 4, 5, or 6
1 match 0, 5, or 6
2 matches 0, 1, or 6
3 matches 0,1, or 2
The miscall, when used wisely, is it valuable asset to Match Game blackjack strategy, and can be compared to the bluff in Poker.
Three or More Players
When there are three or more players in the game, the rules of play are the same as for two players, with one exception: The game is now an elimination contest. As each player wins a hand by guessing the correct total, he drops out of the game, he is safe and cannot become the final loser. For example, There are six players: A, B, C, D, E, and F. B guesses the first hand correctly, and is eliminated. A, C, D, E, and F play the next hand, D wins and is eliminated.
This elimination process continues until only two players remain. They continue the play, and the winner of two out of three hands is eliminated. The sole remaining player is declared the loser of the game, and he must pay the amount of the stake originally agreed upon (5 cents, 25 cents, $1. etc.) to each of the other players.
The last caller again has a mathematical advantage, although it is not quite as strong as in the two-handed game. The first caller knows that the total number of matches his opponents may hold ranges from none to six.
The number of ways each of these totals can be made as follows:
Zero or 6 Each can be made 1 way
1 or 5 Each can be made 2 ways
2 or 4 Each can be made 3 ways
3 can be made 4 ways
A combined total of 16 ways
The first player’s call, of course, is the sum of what he guesses his opponents hold plus the number of matches he himself holds. The first caller’s best chance to win, therefore, is to add three to the number of matches he himself holds and call the total. This gives him one chance in four of winning, or 25 percent. The second player reverses the strategy euchre of the first player by subtracting three from the first player’s call.
Example: The first player calls “Six.” The second player subtracts three and infers that the first player holds three matches. The second player now has a 25 percent chance of guessing the number held by the third player. He makes a guess as to the third player’s hold, adds the number he calculated the first player may be holding, adds the number he himself holds, and announces the total. On the occasions when this total has already been called by the first player, the second player’s next best bet is to add or subtract one to the number already called, and announce this total.
If the second player calls three more or three less than the first call, he gives the third player too much valuable information. Example: The first player calls “Six.” If the second player calls “Nine,” he is telling the third player that he holds three; if he calls “Three,” the third player can assume he holds none. Whenever the second player makes a lower call than the first player, the third player can assume the second is holding either zero or one. If the second player calls two or three more than the first player, the third player can assume that the second holds three.
To summarize: When three experts are playing” the first caller has a 25 percent chance of winning the hand, the second has a 25 percent chance, and the third and last has a 331/3 percent chance. The remaining 16 2/3 percent chance is the percentage and chances in favor of a no-game result.
Four, Five, Six, or More Players
When there are four or more players, the last caller’s advantage is diminished somewhat because the more players there are, the greater are the chances that the number the last player wants to call has already been called. Often the next nearest number above or below has also been called. All the last player can do in this case is to call the closest number that has not yet been called.
The best strategy in a game with four or more players is to play the averages. Assume that the average number held by each player is one and one-half matches. Example: In a five-handed game in which you call first, you guess that each of the other four players holds one and one-half matches, a total of six. Add the number you hold to this six-count, and call the total. If you hold none, you call “Six,” Holding one, you call “Seven.” Holding two, you call “Eight.” Holding three, you call “Nine.”
If you have an odd number or opponents and assume that each holds an average of one and one-half matches, your total will contain a fraction of one-half matches, and your total will contain the fraction of one-half. Example: When there are five opponents, you arrive at a total of seven and one-half. Add or subtract one-half for a total of either seven or eights. Then add the number of matches you hold.
In a five-or-more-handed game, if the calls made by the preceding players add to a total considerably above or below the total obtained by allowing them each an average of one and one-half matches, the remaining players or player should increase or decrease the one-and-one-half match average to conform to the information he has gathered from the preceding calls.
The Numbers Game
Although playing the Numbers is more of a lottery than a guessing game, I can’t resist the temptation to get it in print since it’s the most popular illegal form of lottery betting in the United States. My own sample findings of what makes the Numbers so attractive to players show that:
1) players are natural suckers for big odds, the-500-for-1 Numbers odds are tempting to most players;
2) players can select their own numbers and bet their money on their favorite lucky numbers (and what person doesn’t have at least one lucky number?
3) you can make small bets: 25 cents, 50 cents, and sometimes even pennies. In addition, the action is daily, and the players get the Numbers result the same night from the racing section of most metropolitan newspapers.
All of these factors combined make them feel that the Numbers game is honest. Playing the Numbers was once referred to as a poor person’s way of expressing his or her gambling instinct since its participants used to bet pennies on the illusive three digits. Things are different today of the millions who play the Numbers, it is doubtful if one out of a hundred wagers is less than 25 cents on a number.
The daily average bet on the Numbers for players living in metropolitan areas of the United States ranges from $1 to $2. Many players, however, bet $10 to $20 or more on a single three-digit number; and a few high-rollers think nothing of betting $100 or more on a “hot number,” especially one they dreamed of the night before.
Most people today wouldn’t bet money on a fortune teller’s prediction based on a layout of cards, on tea leaves, or on the juggling of some astrological figures; but most Numbers players believe that the sight or mention of any three-digit number is a psychic sign and that some supernatural force has brought it to their attention, Millions of dollars are bet by Numbers players every day on what they consider to be their lucky number for the day: their street address, the last three digits of their birth year, the sales total of a purchase, or the license number of a passing car.
The favorite reading matters to millions of players is:
1) the newspapers that report the winning numbers,
2) dream books and numerology pamphlets that give interpretations of dreams, daily happenings, birthdays, and so on, in terms of three-digit numbers, Know Your Dream, Lucky Star, King Tut, and Gypsy Queen are among the best sellers in New York City.
The system is simple: If you dreamed last night that you took a trip on a bus, look under Travel. You are told that “traveling means you will change jobs (use number 213).” If you dreamed of visiting a lawyer, this means “you will suffer from a cold (use number 165),” Dreaming of money: “Your luck will change (use number 381).” Dancing girls denote “happiness, and you will come into money (use number 814).” A doctor denotes pregnancy (use number 119) for a woman and illness for a man (use number 415). Oddly enough, although many of these books are published by the same company, they all give different interpretations and numbers.
Let’s take a good look at the Numbers game. Although it’s illegal in every state, city, or hamlet-if you know your way around, it won’t be difficult to find a Numbers runner who’ll accept your bet. The winning numbers are usually based upon the last digits-three in all of the daily mutual betting handle at a major metropolitan racetrack. Let’s say that Monday’s mutual betting and gaming handle for nine races at New York’s Aqueduct Racetrack was $2,586,123. Monday’s winning number is 123.
If you have been lucky enough to bet $1 on that number, you are a winner; and since such a bet pays off at odds of 500 for 1, you receive $500 in return. Some banks, however, payoff at 450-to-l odds; others payoff at 900-for-l odds.
Another bet permitted at the Numbers game is known as “boxing.” When you write your number on the betting slip, you may box it by drawing a square around it. This indicates that you are betting on all possible combinations of the chosen number, and it is known as a six-way combination bet. If you select number 125 and box it, you are betting on 125, 152, 215, 251, 512, and 521. Of course, this reduces the payoff to one-sixth. If the bank pays 500 for 1 on a straight bet, a six-way payoff should be 831/3 for 1; but the operators round the number to 80, and the payoff is 80 for 1.
Any straight or head number that contains two identical digits (such as 121, 323, 556) is known as a three-way combination because only three different combinations can be made with it. If your box number is 121, for instance, you are betting on 121, 112, and 211. Since most banks only pay 80 for 1, the same as on a six-way combination, it is sheer lunacy to box numbers of this sort. Incidentally, most banks insist that the player also bet on a straight number with each combination or box-number bet.
What chance does that lucky number of yours have of hitting and paying off? No complicated mathematics is needed to figure out this answer. There are 1,000 numbers from 000 to 999, and one of them ‘wins. You have 1 chance in 1,000, which means that the odds are 999 to 1 against you. Every player has an equal chance, and the odds remain the same for any number selection, even if it is a repeat of yesterday’s winning number or one that hasn’t appeared in years.
Most banks pay off at less than the usual odds on “cut and disaster numbers.” These are numbers that get too much play because too many players believe they are lucky numbers. Some banks issue a cut-number sheet listing nearly 200 cut numbers. In some sections of New Jersey any three-digit number whose middle digit is a 1, such as 010, 015, 116, 217, and so on, is a cut number and is paid off at 400-for-l odds.
Should a newspaper carry an illustration on its front page showing a cracked-up automobile whose license number reads XY 151, the number 151 is a catastrophe number as far as the Numbers operators are concerned, and winners get paid off at odds of 400 for 1.
The Numbers operators give various reasons as to why they cut as many as 200 numbers, but true or false, cutting numbers reduce the player’s winnings considerably. If the correct odds of hitting three numbers are 999 to 1 and the bank pays only 500 for 1, and in the case of cutting numbers 400 to 1, it should be obvious by now that the only people who consistently make a profit at the Numbers are the operators, their employees, and the politicians and cops that sell protection.
There’s not much point in advising a Numbers player to forget about his favorite stop poker games, and gamble, if he must, at some game whose unfavorable percentage isn’t so high. Many players I know just don’t listen to such advice. If you want to play because it’s fun, and are willing to pay the price, that’s your business. But if you play because you figure to come out ahead, you can forget it. If you have read this far, in this book, you know that bucking a house edge from 50 to 60 percent is a sure way to a pauper’s grave.