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Old 12-20-2005, 04:36 PM
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Default What is the expectation of this game?

I've been playing a game on all day called "Lucky Dice." In the game you throw three dice, and I bet 10 points on one, 10 points on two and 10 points on three.

So if none of the die come up one/two/three I lose the 30 points I bet.

if any one die comes up one/two/three I get 20 points back (so I lose 10 overall)
if any two die are the same and come up with one/two/three I get 30 points (so I lose nothing overall)
if all three are the same and come up with one/two/three I get 100 points (so I get 80 points overall)

so for example if the die roll as ...
one, one, five. I get thirty points but I bet thirty points so overall I get nothing.
if they rolled as four, five six I get nothing (so my net gain is -30)
if they rolled as one, two, three I get 20 back for each (net gain is 30)
if they rolled as one, one, three I get 50 back, (so my net gain is 20)

ANyway, enough examples. The reason I'm going on about it is it seems to have really good return, like a really high positive expectation. And given that I've been playing all day I really am quite surprised to be still winning.

Does soembody familiar with basic probability want to calculate expectation for my strategy?
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