If Monty has freedom of choice, that is if Monty were to expose a goat BEFORE you made your first choice, then you would be left with a 50-50 pick between the remaining goat and the cash.
But the game is conducted such that Monty can only expose a goat AFTER you have made your initial choice.
Because Monty can only expose a goat AFTER you make your choice then there is a chance that Monty's freedom of choice is removed because Monty cannot choose the door you have already chosen and if you have chosen a goat Monty has no freedom of choice.
Monty's knowledge of where the goats are, coupled with your initial choice sometimes constraining Monty's choice is what changes the odds.
Legend: D1 = Door 1 D2 = Door 2 D3 = Door 3 G1 = Possible game configuration 1 G2 = Possible game configuration 2 G3 = Possible game configuration 3 G = Goat $ = 1 million dollars
List all game/choice possibilities and count the odds. D1 D2 D3 G1: G G $ G2: G $ G G3: $ G G
You choose D1 G1: G X X Monty MUST open D2 to expose a goat - if you change you WIN G2: G X X Monty MUST open D3 to expose a goat - if you change you WIN G3: $ X X Monty can open D2 or D3 to expose a goat - if you change you LOSE
You choose D2 G1: X G X Monty MUST open D1 to expose a goat - if you change you WIN G2: X $ X Monty can open D1 or D3 to expose a goat - if you change you LOSE G3: X G X Monty MUST open D3 to expose a goat - if you change you WIN
You choose D3 G1: X X $ Monty can open D1 or D2 to expose a goat - if you change you LOSE G2: X X G Monty MUST open D1 to expose a goat - if you change you WIN G3: X X G Monty MUST open D2 to expose a goat - if you change you WIN
So it's fairly easy to see that changing will cause you to win more often than not. Actually you will win 66% of the time if you change.
Only for GM cars at the moment but due to support Ford and Chrysler in the future. Eval version here: http://www.starrperformance.com.au/efilivev 5 Of course you'll need to buy an interface to connect to your vehicle.
In case anyone is interested... Here's an example of the OBD-II SAE-J1850 VPW protocol as used by GM, wrapped by another protocol of the hardware interface being used.
This is from a PC based software scan tool called EFILive V5.
The VIN is fake but can anyone tell me where the vehicle was made and by who?
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The Mail is correct.
If Monty has freedom of choice, that is if Monty were to expose a goat BEFORE you made your first choice, then you would be left with a 50-50 pick between the remaining goat and the cash.
But the game is conducted such that Monty can only expose a goat AFTER you have made your initial choice.
Because Monty can only expose a goat AFTER you make your choice then there is a chance that Monty's freedom of choice is removed because Monty cannot choose the door you have already chosen and if you have chosen a goat Monty has no freedom of choice.
Monty's knowledge of where the goats are, coupled with your initial choice sometimes constraining Monty's choice is what changes the odds.
Legend:
D1 = Door 1
D2 = Door 2
D3 = Door 3
G1 = Possible game configuration 1
G2 = Possible game configuration 2
G3 = Possible game configuration 3
G = Goat
$ = 1 million dollars
List all game/choice possibilities and count the odds.
D1 D2 D3
G1: G G $
G2: G $ G
G3: $ G G
You choose D1
G1: G X X Monty MUST open D2 to expose a goat - if you change you WIN
G2: G X X Monty MUST open D3 to expose a goat - if you change you WIN
G3: $ X X Monty can open D2 or D3 to expose a goat - if you change you LOSE
You choose D2
G1: X G X Monty MUST open D1 to expose a goat - if you change you WIN
G2: X $ X Monty can open D1 or D3 to expose a goat - if you change you LOSE
G3: X G X Monty MUST open D3 to expose a goat - if you change you WIN
You choose D3
G1: X X $ Monty can open D1 or D2 to expose a goat - if you change you LOSE
G2: X X G Monty MUST open D1 to expose a goat - if you change you WIN
G3: X X G Monty MUST open D2 to expose a goat - if you change you WIN
So it's fairly easy to see that changing will cause you to win more often than not.
Actually you will win 66% of the time if you change.
Only for GM cars at the moment but due to support Ford and Chrysler in the future.v 5
Eval version here:
http://www.starrperformance.com.au/efilive
Of course you'll need to buy an interface to connect to your vehicle.
In case anyone is interested...
0 0,$00,$550 0,$560 0,$00,$4B0 0,$420 0,$00,$670 0,$D20 0,$00,$340 0,$FB0 0,$00,$315 4,$CC0 0,$00,$324 C,$120 0,$00,$333 5,$AA0 0,$00,$4C0 0,$77
Here's an example of the OBD-II SAE-J1850 VPW protocol as used by GM, wrapped by another protocol of the hardware interface being used.
This is from a PC based software scan tool called EFILive V5.
The VIN is fake but can anyone tell me where the vehicle was made and by who?
22:27:12.226: Scanning for T16 - Multiplex Engineering's #T16 interface on Com1
22:27:12.226: Connected to Com1 using baud=19200 parity=N data=8 stop=1
22:27:12.326: Send: $1F,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$00,$
22:27:12.346: Recv: $40,$80,$42,$02,$7F,$55,$05,$5A,$5F,$00,$00,$00,$
22:27:12.346: Interface: T16 V66.127
22:27:12.346: Auto detecting OBD-II protocol: SAE J1850VPW (GM)...
22:27:12.346: Probing OBDII link...
22:27:12.356: Send: $1F,$82,$05,$68,$6A,$F1,$01,$00,$00,$00,$00,$00,$
22:27:12.397: Recv: $40,$82,$48,$6B,$10,$41,$00,$BF,$BF,$F9,$90,$B5,$
22:27:12.397: OBD-II protocol: SAE J1850VPW (GM) detected.
22:27:12.397: Request OBD compliance.
22:27:12.467: Send: $1F,$82,$05,$68,$6A,$F1,$01,$1C,$00,$00,$00,$00,$
22:27:12.507: Recv: $40,$82,$48,$6B,$10,$41,$1C,$01,$2F,$00,$00,$00,$
22:27:12.507: OBD compliance: OBD-II (California ARB)
22:27:12.507: Request GM PCM#.
22:27:12.567: Send: $1F,$82,$05,$6C,$10,$F1,$3C,$04,$00,$00,$00,$00,$
22:27:12.607: Recv: $40,$82,$6C,$F1,$10,$7C,$04,$00,$F7,$81,$C2,$52,$
22:27:12.607: PCM#: 16220610
22:27:12.607: Request GM VIN.
22:27:12.667: Send: $1F,$82,$05,$6C,$10,$F1,$3C,$01,$00,$00,$00,$00,$
22:27:12.707: Recv: $40,$82,$6C,$F1,$10,$7C,$01,$00,$36,$48,$38,$56,$
22:27:12.767: Send: $1F,$82,$05,$6C,$10,$F1,$3C,$02,$00,$00,$00,$00,$
22:27:12.807: Recv: $40,$82,$6C,$F1,$10,$7C,$02,$4B,$36,$39,$46,$59,$
22:27:12.867: Send: $1F,$82,$05,$6C,$10,$F1,$3C,$03,$00,$00,$00,$00,$
22:27:12.907: Recv: $40,$82,$6C,$F1,$10,$7C,$03,$35,$38,$31,$33,$36,$
22:27:12.907: Vin: 6H8VTK69FYL581365
22:27:13.859: Request Diagnostic Trouble Codes.
22:27:13.869: Send: $1F,$82,$05,$68,$6A,$F1,$01,$01,$00,$00,$00,$00,$
22:27:13.899: Recv: $40,$82,$48,$6B,$10,$41,$01,$00,$07,$60,$00,$89,$
22:27:13.899: No diagnostic trouble codes detected.