I am a participant in a football betting pool where every
participant picks 10 football games (NCAA or NFL) each week. This Saturday I
picked 8 of 10 college football games correctly (I hardly ever pick NFL games)
which made me wonder about my chances were to win this weeks’ betting pool. We
also have a tie breaker in place (the total points scored in the Monday night
game), but since only the over/under and not the standard deviation of points
scored is known, I was not able to solve tie breaker scenarios. Also I assumed
that each team has a 50% chance of covering the spread (all spreads are set to
x ½ points so there are no pushes)
The table below shows the standing Saturday night when all
NCAA games were over. 14 of my fellow pool participants (names Alf to Nick)
still had a chance to catch up or overtake me (10-max wins is the number of
games they had wrong already) and there were 13 NFL games to be played this
weekend.
What is the chance that I win outright (meaning no one else
got 8 correct picks)?
What is the chance that I ended up in a tie for first place
(meaning at least one other player has 8 correct picks and no one has more than
8 correct picks)?
What is the chance I was guaranteed a top three finish?
What is the lowest place I could have finished after the tie
breaker is decided (assuming I could finish last in the tie breaker)
Hint: The chance that Alf wins outright is 15.94% - If you
cannot match this number you likely have it all wrong!
Name
|
max
|
wins
|
AZ
|
CLE
|
PHI
|
GB
|
TB
|
JAC
|
CIN
|
NYJ
|
IND
|
SD
|
CHI
|
NOR
|
BAL
|
wins
|
so
|
AT
|
AT
|
AT
|
AT
|
AT
|
AT
|
AT
|
AT
|
AT
|
AT
|
AT
|
AT
|
AT
|
|
far
|
ATL
|
DAL
|
WAS
|
DET
|
CAR
|
HOU
|
KC
|
STL
|
NE
|
DEN
|
SF
|
OAK
|
PIT
|
||
Volker
|
8
|
8
|
|||||||||||||
Alf
|
10
|
5
|
GB
|
CIN
|
IND
|
DEN
|
NOR
|
||||||||
Bert
|
9
|
3
|
ATL
|
WAS
|
GB
|
TB
|
IND
|
BAL
|
|||||||
Chris
|
10
|
1
|
WAS
|
GB
|
TB
|
CIN
|
NYJ
|
NE
|
SF
|
NOR
|
BAL
|
||||
Doe
|
10
|
1
|
DAL
|
WAS
|
GB
|
TB
|
HOU
|
CIN
|
STL
|
IND
|
DEN
|
||||
Eric
|
10
|
0
|
AZ
|
CLE
|
PHI
|
DET
|
JAC
|
KC
|
NYJ
|
NE
|
SD
|
BAL
|
|||
Fred
|
10
|
0
|
ATL
|
WAS
|
GB
|
TB
|
CIN
|
NYJ
|
DEN
|
SF
|
NOR
|
BAL
|
|||
Gino
|
10
|
0
|
AZ
|
CLE
|
PHI
|
GB
|
TB
|
CIN
|
IND
|
SD
|
CHI
|
NOR
|
|||
Herb
|
8
|
4
|
AZ
|
CAR
|
HOU
|
SF
|
|||||||||
Ina
|
8
|
2
|
WAS
|
GB
|
TB
|
CIN
|
STL
|
NOR
|
|||||||
Jeff
|
8
|
6
|
ATL
|
HOU
|
|||||||||||
Kyle
|
8
|
5
|
WAS
|
IND
|
BAL
|
||||||||||
Liam
|
8
|
4
|
DAL
|
IND
|
DEN
|
NOR
|
|||||||||
Matt
|
8
|
4
|
WAS
|
STL
|
DEN
|
BAL
|
|||||||||
Nick
|
8
|
2
|
WAS
|
GB
|
CIN
|
DEN
|
NOR
|
BAL
|
The link to the pdf is here
