Evaluating Conceptual Plays
129
P
P
P
P
P
1
1
P
, i f
0
1
P
, i f
1
[
]
[ ]
(
)
(
) [ ]
(
)
[ ]
T
T
m
g
g
r
m
n
mn
g
r
r
m
N n
N n G
G
N n G
G
m
n
m
m
n
n
−


 
= =  =
×
+
=
×


 


 −
+
−
=
 
= 
 

−
≥
 

 

∑
∑
u
u
u
u
u
u
(5.18)
Also,
P play has at least one pool P
1
1 P
0
1
1
P
[
] [
]
[
]
(
) [ ]
m
g
r
m
N
N
m
=
≥
= −
=


=
−
−




∑
u
u
(5.19)
For example, case II gives u g = 0.57 and u r = 0.68. If M = 6, then
6
P
1
0.57 1 1 0.68
0.57, and
P
0
1 0.57 0.43, or 43%
[
]
(
)
[
]
N
N


≥
=
− −
=


=
= −
=
The expected value of N is given as
1
E
E
1
E
1
P
1
1
P
1
[ ]
(
)
(
)
[ ]
(
)
[ ]
T
g
g
n
mn
g
r
r
n
n
m n
g
r
r
r
m
n
N
N G
N G
m
n
m
n
m
m
m
n
−
−
−


=

+ −




 
=
−
 
 
−


=
−


−


∑ ∑
∑ ∑
u
u
u
u
u
u
u
u
u
(5.20)
Therefore,
E
E
E
P
expected number of prospects
[ ]
[ ]
[ ]
[ ]
g
r
m
N
M
M
m m
= × ×
=
=
∑
u
u
(5.21)