Answers to Selected Problems - West Valley College

Problem Sets Physics 4D
The Wave Equation for Poker.
You decide to play your friends poker with five cards being dealt per hand. The following table gives the
probability of being dealt a specific hand before the draw using 53-card deck - including Joker. Construct
a wave function that represents your hand before you take a look. Assume each hand is mutually
exclusive (orthogonal). For example, you can hold either a three-of-a-kind or one-pair, not both. (See
next page)
The probability of being dealt...
(before the draw)
Expressed in
percent (%) is...
The odds against it
are...
Number of
possible
combos
5 ACES 0.00* 2,869,684 to 1 1
STRAIGHT-FLUSH
Royal Flush
Other Straight Flush
0.01
0.00**
0.01
14,066 to 1
119,569 to 1
15,942 to 1
FOUR-OF-A-KIND 0.03 3,465 to 1 828
FULL HOUSE 0.15 656 to 1 4,368
FLUSH 0.27 367 to 1 7,804
STRAIGHT 0.71 139 to 1 20,532
THREE-OF-A-KIND
3 Aces
Three-of-a-kind
(Large: K's - 8's)
Three-of-a-kind
(Small: 7's - 2's)
TWO-PAIR
Aces-up
K-up, Q-up, J-up
Small Two-Pair
(Tens-up and under)
2.21
0.37
0.92
Melvin J. Vaughn Page 50 of 61 West Valley College
0.92
4.83
1.10
1.69
2.03
44.3 to 1
271 to 1
108 to 1
108 to 1
19.7 to 1
89.6 to 1
58.0 to 1
48.2 to 1
204
24
180
63,360
10,560
26,400
26,400
138,600
31,680
48,600
58,320
ONE PAIR 42.34 1.36 to 1 1,215,024
PAIR OF A,K,Q,J (Openers)
Aces
Kings
Queens
Jacks
SHORTS
Shorts
(Large: 10's - 7's)
Shorts
(Small: 6's - 2's)
14.19
4.81
3.13
3.13
3.13
28.15
12.51
15.64
6.05 to 1
19.8 to 1
31.0 to 1
31.0 to 1
31.0 to 1
2.55 to 1
6.99 to 1
5.39 to 1
407,184
137,904
89,760
89,760
89,760
807,840
359,040
448,800