1000000030

G A

propedy, God il ao excellenl remedy 'in dropfies, ca·

chexies, jaundice, aílhnllS, catarrhs,

in Ihe worfl

cutaneolls eroptions.

GAME, in general, fignifies any diverfion, or fport, Iha!

is per(ormcd with regularity, and rellrained to eemin

rules. See GAMINe.

GAMES, in anliquity, were public diverfions, exhibited

00 falerno occafions. Such, among the Greeks, were

!heblympic, Pythian, Inhmiao, Nemeao,

&c.

games;

and, among the Romans, Ihe Apollinarian, Cire<!ofian,

Capitolioe,

Ce.

games. SeeOLYMPIC, PvrHIAN,

&c.

GAMB, in law, fignifies birds or prey, laken or killed by

(owling, or huoting. There are feveral natutes (ot

puoi!hing olfenees commined by per(ons 001 qU1\li6ed

by la\Y 10 take Or denroy Ihe

g.me

GAME·COCK, a 6glning cock, or one kepl for fport ;

a barharou! praétiee, which is a difgrace tO any civili·

Ied nation .

GAMEllA, in Greciaa antiquity, a nuptial fean, or

rather faclÍfice, held in the ancient

Gmk

families on

Ihe day befare a marriage; thus called, (rom a eunom

Ihey had of !haviog themfelves on Ihis occafion, and

pre(enting their hair 10 fome deilY ·10 whom they had

particular obligations.

GHIELION , ia the aocienl chronology, was the eighth

month of the Alhenian year, eontaining Iwenly-nine

days, and an(\Yering to the laner pan of our January

and beginning of February.

was Ihus called, as

being, iD the opioion o( Ihe Atheoiaos, Ihe mofl pro·

per (ea(oo of Ihe year for marriage.

GAMING , the

art

of playing or p"étifiog any game,

particularly Ihofe of hazard, as cards, dice, lables,

&c.

Mr de Maine, ia a \rcati(e de Men(ura Sortis, has

computed the variety of chances in (emal cafes that

occur iD gaming, !he laws of which may be uadernood

by what (ollows.

Soppofe

Ihe number of cafes io which an eveot

may happeo, aod

the numberof cafes whmin il may

not happeo, both fide! have thé degree of probabililY,

which is lo each other as

10 9,

If two gamenm,

and

engage on Ihis fooling,

Ihal, if Ihe cafes

happen, A !hall win

bUI ir 9hap·

pen,

!hall wio, aod !he nake be

the chaoce of

will

be~'

and Ihal of

eonfequently, if

;+1

;+9

Ibey (ell Ihe expeétancies, tbey !hould have Ihal for

!hem relpeétively.

Aand

play with afingle die, on Ibis condilion, thar,

ifAthrow IWO or more aces

elght Ihrows, he !hall win:

~Iherwife

!hall win

",hal is the mioof their chances!

Since there isbut oos cafe \Yherein an ace may

turo

up, and

/ive wherein il may not, let _=1 , and

b=S '

And,again,

flnce Ihere are eighlthrowsof Ihe die, le!

n=8

¡nd,you

'«Iill have

~" -b"-nab"-I,

b"+nab"-I:

Ihat is, the ehance of A will be to Ihat of

66399 1 lO

JOI)6P5'

or n",ly

2 ro

A and

are cng.ged

fingle quoits

and,

~(Irr

playingfome time, A

vr¿nl!

4 o( boing up, alld

G A M

bUI

is fo much Ihe bwer gameOer, thal his cllanee

againn A upon afingle Ihrow would be as 3to 2

what

is the ratio of Iheir chanw! Since A \l/aOla

and

H6,

the game will be ended al nine throws

there.

fore, raife

a+b

10 Ihe ninth power, and il will be

+908 b+36 a' lb+84

.6b

1 + 126

arb'

+126

a'b r ,

84nlb6+36aQb'+6abl+bP:

eall a3,aod

and

you will have the ralio of ehanees iD numbm, o;z,

17 S9077

1940~.

Rnd

play at .Gngle quait!, aod

is Ihe

be~

gameller, fo that he can give

2 in 3, whal is the

mio of Iheir chancea at a Gngle throw? Suppofe

th.e

chances as %10 l• .and raife Z+ I tO il! cube, which

will be %)+ 3z '+3'+1. Now Gnce A cauld give

OUlof 3, AJllight undcnake

win tbree IhroWl

runoing; and, eon(equently, the ehances in !his cafe

will be as %) 10 3%'+ 3z+l. Hence

z)=3z'+H+¡ ;

.or,

2%1=%1+3,'-3z+I, And, therefore,

'V1=

%+1

and, confequently,

:-v

2":¡'

TheehaaccI.

Ihmfore,are

v:~'

and

refpeétively.

Again, fuppofe

have

111'0

wagers depending, in ¡he

Srn of whieh I have ; 10 2 Ihe befl 01 Ihe lay,

and

in the feeond

what is the probabílity,

win

bOlh w.gers

The probabililY of winning Ihe firn is

.¡.,

tbU

is the oumber of chances

hare 10 win, divided by

Ihe number of all the chanC(!: the probabilily of wjn–

ning the feeond is

,..¡.:

Ihercfore, muhiplying tbefe

twO

fraaions loge!her, Ihe produét will be

.¡..¡..

whicb

Ihe probability of winning both wagers.. No",! IhlS

fraétion being fubtraded from 1, Ihe retnalnder

whieh is the probability I do not win both wagerl:

Ihercfore the odds againn me are

1021.

2.lf

I would koow what the probability is of wia–

ning the firn, and lofing the (eeond, largue thu.s.: Ihe

probability of winning Ihe firn is

Ihe probablluy

10fing the feeond is

y{. :

thm(ore

~.ultiplying

~y ~.

Ihe produll

will be Ihe

probabll~ty

of.;ay wlOOIng

Ine lirO, and loflog the feeond; whlch belng Iubtraét·

ed from I Ihere will remain

whieh il the proba–

bility

d;not win the firn, and al the fame .time lofe

Ihe fecand.

If I would know what Ihe

pr~babilily

win–

ning Ihe (econd, aod al the fame time lofing Ihe firO,

I fay thus : Ihe probabililY of \l/inniog Ihe feeond i,

the probabílity of

lofi~g

Ihe firn is

:¡.:

thercfore,

muhiplying thefo lWO fraétlons togelher, Ihe produll

is the probability

win Ihe feeood, aod alfo

Ihe filn.

I would KnOW wh.t the{'r.obabililY is or lo–

fing both wagers, I fay, .

t.he

probability of lofing

t~e

firl! is

and the

pro~¡blluy

.of lofing the (eeon?

"1:

thercfore, the probablllty of lofing.them bOl? IS

TI ;

which being rubtraétcd from t, there remalOs

Iherefore, Ihe odds of lofing halh wagm is 47 10 8,

This way of reafoning is 3pplieable to the.hoppen–

ing or

faili~g

of any eveots tha! may

f.lI

.unoer

c~~fi

derallOll.