Mathematical_Recreations-Kraitchik-2e

128 Mathematical Recreations
a n" a n" a n"
0 20 8 492 16 84
1 60 9 484 17 60
2 120 10 456 18 40
3 200 11 408 19 24
4 288 12 340 20 12
5 420 13 252 21 4
6 448 14 144
7 492 15 112
Disregarding the valueless hands, the total number of possible
games is
21
29· Ln .. = 29· 4,940 = 143,260 .
.. -1
The total number of games which the player can win is
21
Lan .. = 42,540.
a-I
Hence the probability that a punter will win a game is
42,540: 143,260 = 0.297, or about 3: 10.
9. RUSSIAN BANK. Two like packs of 32 cards each are
used. The banker sells to each punter as many cards from
one pack as the punter desires, at a fixed price per card.
When the punters have bought their cards, the banker turns
up 9 cards from the other pack. He pays the cards which
match his as follows:
1 times the stake on his first 2 cards,
2 times the stake on his next 2 cards,
3 times the stake on his next 2 cards,
4 times the stake on his next 2 cards,
9 times the stake on his last card.
If the punter's card happens to be matched by one of the
first two cards, it is customary for him to leave his stake and
exchange his card for another. Also, the bottom card of the