probabilities teaches us that events will equalise themselves in time,
all that is necessary is to devise some system that will keep a person
from guessing, so that he may catch the pendulum as it swings; and to
add to it some system of betting, so that he will have the best of
it in the long run. Some content themselves with playing a “system”
against banking games, which is merely a guide to the placing of the
bets, the simplest example of which would be to bet always on heads if
a coin was tossed a thousand times, or to bet on nothing but red at
Roulette. Others depend more on martingales, which are guides to the
amount of the bets themselves, irrespective of what they are placed on.
The most common form of martingale is called _=doubling up=_, which
proceeds upon the theory that if you lose the first time and bet double
the amount the next time, and continue to double until you win, you
must eventually win the original amount staked. If there was no end to
your capital, and no betting limit to the game, this would be an easy
way to make money; but all banking games have studied these systems,
and have so arranged matters that they can extend their heartiest
welcome to those who play them.
In the first place, by simply doubling up you are giving the bank
the best of it, because you are not getting the proper odds. If you
double up five times you are betting 16 to 1; but the odds against five
successive events are 31 to 1, as we have already seen, and the bank
should pay you 31 instead of 16. You should not only double, but add
the original amount of the stake each time, betting 1, 3, 7, 15, 31,
63, and so on. If you do this, you will win the amount of your original
stake for every bet you make, instead of only for every time you win.
This looks well, but as a matter of fact doubling up is only another
way of borrowing small sums which will have to be paid back in one
large sum when you can probably least afford it.
Suppose the game is Faro, the chips five dollars a stack, and the
limit on cases twenty-five dollars. The limit on cases will then be
400 chips. If eight successive events go against your “system,” which
they will do about once in 255 times, your next bet will be beyond the
limit, and the banker will not accept it. At Monte Carlo the smallest
bet is a dollar, and the limit is $2,400. They roll about 4,000 coups
a week, and if you were to bet on every one of them, doubling up, you
would win about $1,865, one dollar at a time, and would lose $4,092
simply through being unable to follow your system beyond the limit
of the game during the two or three occasions, in the 4,000 coups,
that your system would go against you for eleven or more coups in
succession. It is useless to say it would not go against you so often,
for probabilities teach us that it would be more wonderful if it did
not than if it did.
It must never be forgotten that the most wonderful things that happen
are not more wonderful than those that don’t happen. If you tossed
a coin a thousand times, and did not once toss heads eight times in
succession, it would be four times more surprising than if you tossed
heads ten times in succession.
Bets
Won. Lost.
10 -
9 -
8 -
- 7
- 8
9 -
- 8
- 9
10 -
- 9
----------
46 41
_=Progression.=_ This is a favourite martingale with those who have
not the courage or the money to double up. It consists in starting
with a certain amount for the first bet, say ten dollars, and adding a
dollar every time the bet is lost, or taking off a dollar every time
a bet is won. If the player wins as many bets as he loses, and there
is no percentage against him, he gets a dollar for every bet he wins,
no matter how many bets he makes, or in what order the bets are won
and lost, so that the number won equals the number lost. That this is
so may be easily demonstrated by setting down on a sheet of paper any
imaginary order of bets, such as the ten shown in the margin, five of
which are won, and five lost; the net profit on the five bets won being
five dollars. No matter how correctly the player may be guessing, and
how much the luck runs his way, he wins smaller and smaller amounts,
until at last he is “pinched off.” But if a long series of events goes
against him his bets become larger and larger, but he must keep up the
progression until he gets even. If ten bets go his way he wins $55; if
ten go against him he loses $145.
It is said that Pettibone made a fortune playing progression at Faro,
which is very likely, for among the thousands of men who play it
the probabilities are that one will win all the time, just as the
probabilities are that if a thousand men play ten games of Seven
Up, some man will win all ten games. At the same time it is equally
probable that some man will lose all ten.
Some players progress, but never pinch, keeping account on a piece of
paper how many bets they are behind, and playing the maximum until they
have won as many bets as they have lost. Against a perfectly fair game,
with no percentage and no limit, and with capital enough to follow the
system to the end, playing progression would pay a man about as much as
he could make in any good business with the same capital and with half
the worry; but as things really are in gambling houses and casinos, all
martingales are a delusion and a snare. It is much better, if one must
gamble, to trust to luck alone, and it is an old saying that the player
without a system is seldom without a dollar. It is the men with systems
who have to borrow a stake before they can begin to play.
Such matters as calculating the probability of a certain horse getting
a place, the odds against all the horses at the post being given, would
be out of place in a work of this kind; but those interested in such
chances may find rules for ascertaining their probability in some of
the following text books.
TEXT BOOKS.
Calcul de Probabilité, by Bertrand.
Philosophy of Whist, by Dr. Pole.
Winning Whist, by Emory Boardman.
Chance and Luck, by R.A. Proctor.
Complete Poker Player, by John Blackbridge.
Bohn’s Handbook of Games.
Betting and Gambling, by Major Churchill.
TEN PINS.
The standard American game of Ten Pins is played upon an _=alley=_ 41
or 42 inches wide, and 60 feet long from the head pin to the foul or
scratch line, from behind which the player must deliver his ball. There
should be at least 15 feet run back of the foul line, and the gutters
on each side of the alley must be deep enough to allow a ball to pass
without touching any of the pins standing on the alley.
[Illustration:
7 8 9 10
4 5 6
2 3
1
]
_=The Pins=_ are spotted as shown in the margin, the centres 12 inches
apart, and those of the back row 3 inches from the edge of the pit. The
regulation pins are 15 inches high, 2¼ diam. at the base, 15 inches
circumference 4½ from the bottom, and 5¼ at the neck. _=The Balls=_
must not exceed 27 inches in circumference in any direction, but
smaller balls may be used.
_=Frames.=_ Each player rolls ten frames or innings, in each of which
he is supposed to have three balls, although as a matter of fact he
rolls two only. In match games, two alleys are used, and the players
roll one inning on each alternately.
_=A Strike=_ is made when all ten pins are knocked down with the first
ball of the innings, and it is scored on the blackboard with a cross,
the number of pins made with the three balls being filled in afterward.
_=A Spare=_ is made when all ten pins are knocked down with the two
balls of one inning, and it is marked with a diagonal stroke. If the
player fails to get either a strike or a spare, it is a _=Break=_,
marked with a horizontal line, under which is written the actual number
of pins down. After each ball is rolled any pins that have fallen on
the alley are called _=deadwood=_, and must be removed before the
second ball is rolled.
_=Counting.=_ If a player makes a strike in one inning, all that he
makes on the next two balls rolled, whether in one inning or not,
counts also on the strike, so as to give him the total score on three
balls for the frame. Three successive strikes would give him 30 points
on the first frame, with a ball still to roll to complete the second
frame, and two balls to roll to complete the third. If he got two
strikes in succession, and 5 pins on the first ball of the third frame,
4 on the second ball, the first frame would be worth 25, the second
frame 19, and the break on the third frame 9; making his total score 53
for the three frames.
If the player makes a spare in one inning, all the pins knocked down by
the first ball of the next inning count also on the spare. Suppose a
spare to be followed by a strike, the frame in which the spare was made
would be worth 20. If he made 5 pins only, the spare would be worth 15.
Although the player is supposed to have three balls in each inning, and
is allowed to count all he makes on three balls if he gets a strike
or a spare, he is not allowed to roll three balls on a break. It was
formerly the custom to let him roll the third ball on the chance of
getting a break of 10. This was afterward changed to giving him 10
pins, without rolling for them, if he got 9 on two balls; but the
present rule is to call it a break if he does not get a strike or a
spare in two balls, and not to waste time in rolling the third ball.
_=Scoring.=_ Instead of putting down the amount made in each inning,
the total of the frame is added to the total of the previous score, so
that the last figure put down shows the total score up to and including
that frame. The following illustration shows the total score of a
player for ten innings. The top line of figures gives the number of the
frame. The second shows the number of pins knocked down by each ball
rolled, and the third line shows how the scores would be actually put
down on the blackboard, the strike, spare, and break marks being placed
above the figures. With the exception of the second line of figures,
which is put in for purposes of illustration only, this might be a copy
of an actual score.
Frames | 1 | 2 | 3| 4 | 5 | 6 | 7 | 8 | 9 | 10
--------+---+---+--+---+---+---+---+---+---+-----
Pins |8-2|5-5|10|9-0|7-2|8-2|10 |8-2|8-1|7-3-9
--------+---+---+--+---+---+---+---+---+---+-----
| \ | \ | X| - | - | \ | X | \ | - | \
Score |15 |35 |54|63 |72 |92 |112|140|149|168
As the player made a spare on the last frame, he had another ball to
roll, on what was practically a new frame, with which he made 9 pins.
_=Averages.=_ If a team is playing a match, and one of the players
is unavoidably absent, it is the custom to give him credit for his
average, according to the records of his previous games during the
tournament or the season. This is considered better than appointing a
substitute to play for him.
There are a great many varieties of Ten Pins, the most interesting
of which will be found described in the following Laws of the
game, which are reprinted here by the kind permission of the
Brunswick-Balke-Collender Co., from their 1908 edition of the “Bowler’s
Guide.”
BOWLING ALLEY LAWS. RULES AND REGULATIONS GOVERNING THE GAME OF
AMERICAN TEN PINS.
_Revised at Louisville, Ky., March 19-21, 1906. In effect Sept. 1,
1906._
The alleys upon which the game shall be played shall not be less than
41 nor more than 42 inches in width. The length from the centre of No.
1 pin spot to the foul line shall be 60 feet. Back of the foul line
there shall be a clear run of not less than 15 feet. The pin spots
shall be clearly and distinctly described on or imbedded in the alleys
and shall be so placed 12 inches apart from centre to centre. They
shall be 2¼ inches in diameter. The pin spots numbered 7, 8, 9 and 10
shall be placed 3 inches from the pit edge of the alleys, measuring
from the edge to the centre of such pin spots.
The pins shall be spotted on the pin spots placed upon the alleys
according to the following diagram, and the pins and spots shall be
known by the numbers as follows:
[Illustration:
7 8 9 10
4 5 6
2 3
1
]
The pins shall be of the following design and measurements: 15
inches in height, 2¼ inches in diameter at their base, 15 inches in
circumference at a point 4½ inches from their base, 11⅝ inches in
circumference at a point 7¼ inches from their base, 5¼ inches in
circumference at the neck, a point 10 inches from the base; 8 inches in
circumference at the head, a point 13½ inches from the base. The taper
from point to point shall be gradual, so that all lines shall have a
graceful curve.
The balls shall not in any case exceed 27 inches in circumference nor
exceed 16 pounds in weight. Any sized ball of less circumference or
weight may be used.
Two alleys immediately adjoining each other shall be used in all games.
The contesting teams shall successively and in regular order roll one
frame on one alley, and for the next frame alternate and use the other
alley, so alternating each frame until the game is completed.
In delivering the ball the player must not permit any part of his foot,
while any portion thereof is in contact with the alleys, to rest or
extend on, over or beyond the foul line, nor shall any part of his
person be permitted to come in contact with any part of the alleys
beyond the foul line, at any time before the delivered ball shall have
reached the pins. A ball delivered contrary to the provisions of this
rule shall be a foul ball, and shall be so declared by the umpire
immediately such ball so becomes foul.
No count shall be made on a foul ball, and any pins which are knocked
down or displaced thereby shall be at once respotted. A foul ball shall
count as a ball rolled against the player.
Pins which are knocked down or displaced by a ball which leaves the
alley before reaching the pins, or from a ball rebounding from the rear
cushions, do not count, and they shall be immediately respotted.
Every ball delivered, unless it be declared a dead ball by the umpire,
shall be counted against the player.
Pins which are knocked down by another pin rebounding in the play from
the side partition or rear cushion are counted as pins down.
Pins which are knocked down or displaced from any cause except by a
fairly delivered ball shall in all cases be respotted.
Should a player by mistake roll on the wrong alley, or out of his turn,
or be interfered with in his play by another bowler or spectator, or
should any of the pins at which he is playing be displaced or knocked
down in any manner before his delivered ball reaches the pins, or
should his ball come in contact with any foreign obstacle on the
alleys, then the ball so delivered by him shall be immediately declared
a dead ball by the umpire, and such ball shall not count, and shall be
immediately re-rolled by the player after the cause for declaring such
ball dead has been removed.
Pins which are knocked down by a fair ball, and which remain lying on
the alley or in the gutters, are termed dead wood, and shall be removed
before the next ball is rolled.
Should a standing pin fall by removing dead wood, such pin or pins
shall be at once respotted.
Should a pin be broken or otherwise badly damaged during the game, it
shall be at once replaced by another as nearly uniform with the set in
use as possible. The umpire shall in all such cases be the sole judge
in the matter of replacing such pin or pins.
Each player shall roll two balls in each frame except when he shall
make a strike, or when a second strike or spare is made in the tenth
frame, when the player shall complete that frame by rolling a third
ball. In such cases the frame shall be completed on the alley on which
the first strike or spare is made.
A strike is made when the player bowls down the ten pins with his first
ball delivered in any frame and is credited and designated in the score
by an X in the upper right hand corner of the frame, and the count in
such frame is left open until the player shall have rolled his next two
balls, when all pins made, counting ten for a strike, shall be credited
therein.
A spare is made when the player bowls down all the pins with his second
ball in any frame, and is credited and designated with / in the upper
right hand corner of the frame in which it is made. The count in such
frame is left open until such player shall roll his next ball in the
succeeding frame, when the number of pins rolled down thereby shall
be added to the ten represented by his spare, and the total shall be
credited therein.
A break is made in all cases where the player does not secure either a
strike or a spare in a frame, and in such cases only the number of pins
knocked down are credited in the frame where the break is made.
If at the end of the tenth frame the team scores shall be a tie,
another frame shall be immediately bowled, and play is so continued
until at the close of even frames one of the teams shall have a greater
number of pins than their opponents, which shall conclude the game.
COCKED HAT.
The game is played with a head pin and the right and left corner pins
as shown in the following diagram:
[Illustration:
O . . O
. . .
. .
O
]
Balls not exceeding six inches must be bowled, and they must be rolled
down the alley (not cast or thrown). The rules of American Ten Pins
except in St. Louis, where there is a special association with local
rules, generally govern this game also, with the exception of three
balls instead of two to the frame, but strikes and spares count three
instead of ten, and each pin counts one as in Ten Pins. If the bowler
knocks down three pins with the ball which is first bowled, in any
frame in the game of Cocked Hat, it is a strike, and counts three,
and is marked on the blackboard the same as in Ten Pins. What pins the
bowler knocks down in the second frame with his first two balls must
be reckoned as in Ten Pins, i.e., one for each pin bowled down, which
pin or pins must be added to the strike and placed to the credit of
the player in the inning where the strike was scored (the strike being
computed as three); such strike must be added to pins knocked down with
the two succeeding spare balls; thus, should the bowler score a strike,
and should he in the next new frame knock down but one pin with his
two spare balls, the strike and pin scored must be computed as 4--the
strike counting 3 and the pin 1.
Poodles, or balls rolled down the gutter, are fair balls, and any pin
or pins which they may get must be counted and placed to the credit of
the bowler; dead wood is removed from the alley, and any pins knocked
down through dead wood remaining on the alley cannot be placed to the
credit of the bowler. The maximum number which can be bowled is 90.
COCKED HAT AND FEATHER.
[Illustration:
O O
O
O
]
The pins are spotted as above, the centre pin being the feather.
Ten innings constitute a game, and three balls (not exceeding 6 inches
in size) must be used in each inning.
All the pins except the feather have to be bowled down or the inning
goes for naught.
If the feather is left standing alone, the innings count one.
There are no penalties. The dead wood must be removed. Any pins knocked
down through dead wood remaining on the alley cannot be placed to the
credit of the bowler.
The maximum is 10.
THE BATTLE GAME.
THE PINS ARE SET UP THE SAME AS FOR THE GAME OF TEN PINS.
Four or six innings constitute a battle or game, except in the case of
a tie, when another inning is played. In case that inning should result
in a tie also, still another inning is played--in fact, until the
scores are unequal. In any inning where a tie occurs the score stands
over until the next inning, when each point is counted double. If the
two innings result in a tie, the score is tripled. Should the total
score result in a tie, sufficient innings are played to make the grand
score unequal.
The team having the largest score in the previous inning must bowl the
first ball, so that the weaker party will have the last ball.
Three balls of regulation size (27 inches in circumference) or under
are allotted to each player in each inning.
Each pin bowled down counts 1, including the king pin.
If all the pins except the king pin are bowled down, it counts 12.
The pins are set up as soon as the nine pins are knocked down, or the
king pin is the only one left standing.
The alleys are changed alternately.
The dead wood is removed after each ball is rolled.
In case of uneven teams the Dummy or Blind is filled by any substitute
the captain may pick out to bowl. He can select any one of his men he
chooses, without regard to rotation, or he himself can bowl, but no man
can take the place of the blind twice until every member of the team
has acted as the substitute.
Poodles count as balls rolled. Any pin or pins knocked down by such
balls are set up again in their former positions.
A rebounding ball does not count, and any pin or pins knocked down by
it are set up, as in the case of a poodle ball.
When a ball has left the hand and touched the alley, it goes as a
rolled ball.
NINE UP AND NINE DOWN.
THE PINS ARE SET UP THE SAME AS FOR THE GAME OF AMERICAN TEN PINS.
Three balls (not exceeding 6 inches in size) are bowled in each inning.
The player must knock down a single pin, which counts 1; then with two
remaining balls he endeavors to leave one pin standing, which counts 1.
Failure to do either, the inning goes for nothing.
No penalties are attached. Dead wood must be removed. Any pins knocked
down through the dead wood remaining on the alley cannot be placed to
the credit of the player.
Ten innings constitute a game.
The maximum is 20.
HEAD PIN AND FOUR BACK.
[Illustration:
O O O O
. . .
. .
O
]
The pins are set up as above.
Three balls (not exceeding 6 inches in size) are allowed in each
inning.
If the four back pins are bowled down and the head pin is left
standing, the score is 2. If all the pins are bowled down, the score is
1.
There are no penalties. The dead wood must be removed. Any pins knocked
down through the dead wood remaining on the alleys cannot be placed to
the credit of the player.
Ten innings constitute a game.
The maximum is 20.
FOUR BACK.
[Illustration:
4 3 2 1
O O O O
]
The pins are spotted as above.
Three balls (not exceeding 6 inches in size) are allotted to each
inning.
Each pin counts as spotted, and only one pin can be made at a time; if
more than one pin is made with one ball, it is termed a break, and the
player loses that inning and scores nothing.
There are no penalties. The dead wood must be removed. Any pins knocked
down through the dead wood remaining on the alley cannot be placed to
the credit of the players.
TEN PINS--HEAD PIN OUT.
ALSO KNOWN AS AMERICAN NINE PINS.
[Illustration:
O O O O
O O O
O O
]
The pins are set as in the diagram.
Ten innings constitute a game.
Three balls (not exceeding 6 inches in size) are bowled.
One pin of the frame must be left standing, or the inning goes for
nothing.
There are no penalties. The dead wood must be removed. Any pins knocked
down through the dead wood remaining on the alley cannot be placed to
the credit of the player.
The maximum is 10.
FIVE BACK.
[Illustration:
O O O O
. . O
. .
.
]
The pins are set as shown in the diagram.
Three balls (not exceeding 6 inches in size) are bowled in each inning.
Should a left-handed bowler be bowling, the second quarter pin can be
set up on the left quarter spot.
Strikes and spares count five each.
No penalties are attached. Dead wood must be removed. Any pins knocked
down through dead wood remaining on the alley cannot be placed to the
credit of the player.
Ten innings constitute a game.
The maximum is 150.
THE NEWPORT GAME.
THE PINS ARE SET UP THE SAME AS FOR THE GAME OF AMERICAN TEN PINS.
Three balls (not exceeding 6 inches in size) are allowed in each inning.
Ten frames constitute a game. The object of the game is to bowl down
an exact number of pins from 1 to 10, but not necessarily in routine
order. The player who, in ten innings, scores the least number of
winning innings is the loser. For instance: A bowls down 2, 5, 7, 8 and
10; B bowls down 1, 6, 8 and 9. Here B loses, as A has one more inning
to his credit than B.
Note.--As the larger number of pins are easy to obtain, the superior
skill lies in picking out the small numbers. For this reason the pony
ball is used, and the small numbers are the points of attack from
the start. When the player has bowled down a certain number of pins
corresponding with any score he has made, and his remaining ball
or balls will be of no avail, an (X) is placed under that number,
indicating that the inning goes for naught, as he has already made that
score.
Only one score is allowed to each inning. Players alternate in the use
of alleys.
Balls bounding from the cushions go for naught.
DUCK PIN GAME.
THE PINS ARE SPOTTED THE SAME AS THE AMERICAN GAME OF TEN PINS.
A regulation Duck Pin shall be 9 inches high, 1½ inches in diameter at
the top, 3½ inches in diameter at the body of the pin, and 1⅜ inches
in diameter at the base; shall taper gradually from the bottom to the
largest part of the body, and shall be as near uniform in weight as
possible.