m the player will receive if he wins--are as follows: For day numbers,
5 for 1; for station or first numbers, 60 for l; for saddles, 32 for 1;
for gigs, 200 for 1; for capital saddles, 500 for 1; for horses, 680 for
1; and for station saddles 800 for 1. Cross plays--the numbers to come
in either lottery--may be made at the same rate, subject to a deduction
of 20 per cent. You see that some of these offer a remarkable margin for
profit. The station saddle, with its 800 for 1, seems to offer unequaled
facilities for making a fortune. But since the game was started, no one
has ever been known to hit one. To get a station saddle you must not
only guess two of the thirteen numbers drawn, but you must also guess
the position they will occupy in the slip. The chances of this is so
very remote that the policy-player, sanguine as he generally is, very
seldom attempts it. The next in order is the capital saddle, with its
500 for 1. A capital is two of the first three numbers drawn. Of course
there must be a first, second, and third number, and either two of these
three constitute a capital saddle."

The chances of playing a "capital saddle," "gig" or "horse" in policy
are easily determined by the following formulae, well known to all
students of the advanced branches of Algebra:

The number of combinations that can be formed of _n_ things, taken two
and two together, is

_n_ * [(_n_ - 1)/2]

For _n_ things, taken three and three together, the number is

_n_ * [(_n_ - 1)/2] * [(_n_ - 2)/3]

For _n_ things, taken four and four together, the number is

_n_ * [(_n_ - 1)/2] * [(_n_ - 2)/3] * [(_n_ - 3)/4]

Applying these formulae to policy, it will be seen that to ascertain the
number of "saddles" in any combination you multiply by the next number
under and divide by 2; for "gigs," multiply by the next two numbers
under and divide by 6; while for "horses" you multiply the next three
numbers under and divide by 24. Thus,

78 X [(78 - 1)/2] = 3,003 "saddles."

78 X [(78 - 1)/2] X [(78 - 2)/3] = 76,076 "gigs."

78 X [(78 - 1)/2] X [(78 - 2)/3] X [(78 - 3)/4] = 1,426,425 "horses."

In other words, there are 3,003 "saddles" in 78 numbers, and it follows
that any person playing a capital has two chances in his favor and 3,001
against him.

There is a joke among policy-players that the game is the best in the
world, because so many can play it at once. Different players have
various ways of picking out the numbers th