"You see there are placed in the wheel 78 numbers, from which are drawn 12, 13, 14, or 15, as the case may be. The latter number will not be drawn but once a week. Suppose 13 to be drawn. The rates--that is, the sum 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 formulæ, 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 formulæ 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 they think will come out. Some go by dreams exclusively, some play chance numbers they run across in the streets, or signs or express wagons, while others make a study of the game and play by fixed rules.