Constitutional Whig. [volume] (Richmond, Va.) 1824-1832, 1827-01-02


from the lottery Loses of its common and az
ProPria,e characteristics still if there be an equav
chances between the several purchasers the tick
as well as bcoesn the purchasers and the ,n,nrers hi
variation from the general idea of lottery ought no
10 be considered material For instance: suppose
lottery to be arranged according TO the old system thus
QUO tickets at $40 each, and one prize o 600
w'chs equal To the price OF all the tickets: aud TO b,
drawn in the old way by putting all the ticke.s into on,
wheel the prize aud blanks Into another, &C.; now The
tickets held nv the different purchasers have an cana
chance of drawing the prize; and If the manace,
thinks proper to retain any OF the tickets Tor himself
he also is upon equal terms with TIE purchasers for the
tickets which he retains are TO be estimated at $40 =
piece, since he will lose that amoun, fer each ticket
he fails draw the prize. But ii the mapager by an,
means whatever, can con'ive TO pu, himself The
holder of tickets, upon better ground than that which
the purchasers OCCUPY, the latter must cncc sec
must be playing losing, game, with much certainty
as If they playing with antagonist who was
provided with mar ked cards false dice. As i'm the
scheme just supposed, IT, instead of prize of 600
the manager should allot but prize of $4,000 sell
hn( the tickets, (which would give him the amount si
the prZe and retain tho other half for himself il is OBJ
vious that he would have the chance of drawing
the prize all the purchasers of tickets together toi
ont paying hasardin cent for IL: for il the prlZe
shont be drawn by another, the rnanag has receiv
the amount IN the price of the tickets sold. put this
case by way of illustration, well knowing no mana
ger w"nid attempt an imposition easy discover
when there are many modes OF riiefing the same
thing hct cannot be expused without considerable
attention and labor The managers of the con- binaton
lottery, have very successfully adopted one al least of
these modes, which shall now cndeayonr TO OK plain
IL VIII be recollecied from what has been said in
relation TO the formation of the tic kets that Of crey
three numbers in the thirty SIX formed SIR tickets
differing from each other only the 0,dcr in which
The Numbers placed upon them: hence IL follows
htnt MI the tickets The scheme (42 SIO) ua be ,1ru
easily Drunged in classes earh class confgjnnr
eran'y combinntion IF The nto!e Sc NUMBERS h,ru-
ne *n"e numbers as nc others, and differing from them
only IN the order Of arrangement. Each class We ud
then contain 7,l40 TICKETS Suppose one only of these
tcasses o! ticket: should be Sold the managers retain
ing Tie 1--we other classes, and that AT the drawing OF
The lottery, any particular numbers should como out
VIZ 9, now if II should appear that anv purchaser
had ticket, containing these three numbers i'm any
'Huer, u would DC certain that the managers had re
tanned the fre 0for tickets containing the same npm.
hers differently arranged So ALSO il "A ticket sold
shon appear to have tro las ~ i,e numbers
drawn, II would be certain that the managers had
retained i've others containing the two figures
ana 81 any number OF tickets sold should contain the
same two the manage have retained fre times
as man, nf the same character Suppose by the scheme
the highest prize To be assigned to the lst, cd and Sd
drawn numbers the order drawn; and the nutnlo,
drawn, 9, as before. If it should appear tina,
ticket, containing these three gnrcs but in s,is order
. q, was held BY purchaser, II would be certain
that the managers alcEe entitled TO the prize
Again. suppose SIC of the highest prizes the lottery
TO be assigned 10 the three numbers first drawn In
with specification of the order uf the nr,ho :: now
IT purchaser of ticket draw these h rrizes
the managers must have tie other IRE. itf.o,it pur
suing this mode of illustration anv further Al prcsenr
aud To show more distinctly, the use which may be
made of This eilssifc1ion of tickets, shall exhibit
small scheme of combination and pcrInu.atnn lottery
IN lis principal details; from whcl any one although
entirely ignorant Of the mathematical PRINCIPLES IN
Volved IN It, may its character and results b,
inspection. will assume the series OF numbers fro,
10 inclusive, BY ti.a ternary combination and pcr
mutation OF which all the tickets will be med l.,
the teinary roanbinafio Of III - six numbers tprcuiv
t'tis may be formed and kets themselves &c iii
be as follows | 3D. ] Cd 125, 1876 1914 I35
/ ) ., D, | 4 G.. 4 . G.. Z.
. 6, 9 6, j 3, ID 6, 6, Sc. or Tins class
will tee observed fco tickets contain il same the
numbers. Now, is obvious that by merely changing
the order oil the numbers cac of these tickets fire
oihe's may De made differing from il, not in lire run
bers, hut IN their arrangements hence the whole num-
Der OF tickets in the scheme will be hundred ard
twenty, (6X5X1=l20.) and the remaining five classes
OF go tickets in each, follows FIRST ciass:-l
i De, SO, GO, ll3, 53, 163 l51 1Gt
o. 3, 953, . 3, 2 81, s +, 6 ), :; , 4,
| 5 4, 6 5, -Second:-2 g. 214 2I5
2 s, 3 4, 3 5, 6, d / ;, 4 | s, S 6 3 . L.
80 ., go, 425 90, 6, 4 3 ,, 436, S g.,
D 4 G-Ibird:-23 /, 2 j /, i, 2GI, 1851
SO l. !. a !, ST /, 40, IS Sc g 452
6 .. . 2, ) 3, Il 3, 3, 5 64.-Fou,,ir-
3 ,, 4, ,, 9, Q, 4I3 5I36I 3sI d.
6 I i, e 5, 2 3, 5 3, G23, ; Cd, ga 6 D
. 3 !, 3 4, 50 5, 5.-Fiftir-3 ~ 42l52
% j. l. So l, 3 1, 5 4 !, 6 j /, G ) l. l32
6 5 1.
Such being The TICKETS, l! announce The scheme
in winch we shall observe very nearly the same pro
portion between the highest prize and the price of the
whole number of tickets that the MANAGERS nf tI,e
combination lotteries have hher!y USUALLY done, rs
follows:
no. Lottery by combination and Formulation.
Three numbers % he drawn
Piize OF $500 is 5000
80 50