casino royale. fair dice game shooter wins … fixed dice game modesty wins …

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

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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!