casino royale. fair dice game shooter wins … fixed dice game modesty wins …
TRANSCRIPT
Casino RoyaleCasino Royale
Fair Dice GameFair Dice GameShooter wins …Shooter wins …
FAIRShooter 1 2 3 4 5 6
1 0.000 0.000 0.333 0.400 0.455 1.0002 0.000 0.333 0.400 0.455 1.000 0.4553 0.333 0.400 0.455 1.000 0.455 0.4004 0.400 0.455 1.000 0.455 0.400 0.3335 0.455 1.000 0.455 0.400 0.333 1.0006 1.000 0.455 0.400 0.333 1.000 0.000
Shooter Win = 49.3%
Bank
Fixed Dice GameFixed Dice GameModesty wins …Modesty wins …
FIX ModestyModesty 1 2 3 4 5 6 Win
1 0 0 0.5 0.5 0.5 1 0.4172 0 0.5 0.5 0.5 1 0.5 0.5003 0.5 0.5 0.5 1 0.5 0.5 0.5834 0.5 0.5 1 0.5 0.5 0.5 0.5835 0.5 1 0.5 0.5 0.5 1 0.6676 1 0.5 0.5 0.5 1 0 0.583
Modesty Max Win = 66.7%
Lisa
Lisa strikes backLisa strikes back
ppn
pnppW
n
p
)1(1
)1(1
)1(
facesother ofnumber
die sLisa'on 2 ofy probabilit
Lisa’s worst caseLisa’s worst case
10
110
Wp
Wpn
ppn
pnppW
)1(1
)1(1
)1(
Lisa’s 2Lisa’s 2ndnd worst case worst case
75.00
12)1(21
)1(1
5.0
2
Wdp
dW
ppdp
dW
ppWn
p
ppn
pnppW
)1(1
)1(1
)1(
Lisa’s best caseLisa’s best case
950
31
)1(4
31
2
Wdp
dW
p
ppWn
p
ppn
pnppW
)1(1
)1(1
)1(
Lisa’s edgeLisa’s edge
Hence, if Lisa’s die shows 2 one third of the time and shows 1, 3, 4 and 5 each one sixth of the time, then
Modesty wins 5/9 (55.6%) of the time
But Lisa is paid 1.5 times for each win
Therefore, Lisa’s margin per game is+1/9 (11.1%) of the stake
Lisa’s Casino adviceLisa’s Casino advice
Don’t go into a casino thinking it’s a way of making money
Treat it as entertainment which you have to pay for
Pick games with low house odds
Set yourself limits on how much you are prepared to lose and win!