Question 86634
Let L represent the largest number
Let M represent the middle number and
Let S represent the smallest number
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If you were to roll over the numbers one at a time until all three numbers show, there are
six possible outcomes:
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L then S then M
L then M then S
M then S then L
M then L then S
S then M then L
S then L then M
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Since all of these are equally likely, they each have a probability of {{{1/6}}}.
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Notice that two of the outcomes have L as the first draw.  That means that the possibility
of L being the first number you turn up is {{{1/6 + 1/6 = 2/6 = 1/3}}}
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However, your system says that you ignore the first number and proceed. This means that
at this point you have a {{{1/3}}} chance of being wrong and losing.
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Next look at the possibility that you draw M then S then L. By the rules of your "system" you
discard the M, then draw the S, which being smaller than M, you also discard, and you end 
up drawing L on your last turnover. You win. There is a {{{1/6}}} chance of this happening.
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Next possibility. You draw M then L and then S.  By your system you draw M, discard it,
then draw L, and you quit without turning over the third number. You win!. There is a {{{1/6}}}
chance of this outcome.
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Next possibility. You draw S then M then L. By your system you draw S, discard it, then
draw the M. This being larger than S, you quit ... and you lose because L has not been
drawn.
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Final possibility. You draw S then L then M. Again by your system, you draw S, discard it,
then draw L. The L being larger than S tells you to quit. You do, and you win! There is
a {{{1/6}}} chance of this happening.
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Adding it up, you see that you have 3 winning chances [MSL, MLS, SLM] each with a probability
of {{{1/6}}} for a total winning probability of {{{1/6 + 1/6 + 1/6 = 3/6 = 1/2}}}.
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Your losing chances consist of the two chances that L is the first draw and the chance that
the draw sequence would be SML and you stop at M.  This means that the total losing
possibility is {{{1/6 + 1/6 + 1/6 = 3/6 = 1/2}}}
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So your winning chance using the system is fifty-fifty, a significant improvement 
over drawing the first number and quitting.
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Hope this helps you to understand the problem a little better.