The Full Table of Probabilities for the Monty Hall Problem

Key: Yellow is Stay-Win, Red is Stay-Lose, Green is Switch-Win, Blue is Switch-Lose.

PRIZE
LOCATION
FIRST
CHOICE
DOOR
REVEALED
ACTION RESULT PROBABILITY
Door 1
(1/3)
Choose 1
(1/3)
Shows 2
(1/2)
Stay
(1/2)
WIN 1/36
Switch
(1/2)
lose 1/36
Shows 3
(1/2)
Stay
(1/2)
WIN 1/36
Switch
(1/2)
lose 1/36
Choose 2
(1/3)
Shows 3
(1)
Stay
(1/2)
lose 1/18
Switch
(1/2)
WIN 1/18
Choose 3
(1/3)
Shows 2
(1)
Stay
(1/2)
lose 1/18
Switch
(1/2)
WIN 1/18
Door 2
(1/3)
Choose 1
(1/3)
Shows 3
(1)
Stay
(1/2)
lose 1/18
Switch
(1/2)
WIN 1/18
Choose 2
(1/3)
Shows 1
(1/2)
Stay
(1/2)
WIN 1/36
Switch
(1/2)
lose 1/36
Shows 3
(1/2)
Stay
(1/2)
WIN 1/36
Switch
(1/2)
lose 1/36
Choose 3
(1/3)
Shows 1
(1)
Stay
(1/2)
lose 1/18
Switch
(1/2)
WIN 1/18
Door 3
(1/3)
Choose 1
(1/3)
Shows 2
(1)
Stay
(1/2)
lose 1/18
Switch
(1/2)
WIN 1/18
Choose 2
(1/3)
Shows 1
(1)
Stay
(1/2)
lose 1/18
Switch
(1/2)
WIN 1/18
Choose 3
(1/3)
Shows 1
(1/2)
Stay
(1/2)
WIN 1/36
Switch
(1/2)
lose 1/36
Shows 2
(1/2)
Stay
(1/2)
WIN 1/36
Switch
(1/2)
lose 1/36

Last updated 3 June 2000
http://www.rdrop.com/~half/Creations/Puzzles/LetsMakeADeal/FullTable.html
All contents ©1998-2002 Mark L. Irons

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