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Old 12-23-2005, 12:42 AM
Posts: n/a
Default Re: Between the Sheets EV

Assuming it's a single deck, and the two faced cards are different, you have 6 ways to lose 2 units; 4*G ways to win 1 unit from a gap of size G; and 44-4*G ways to lose 1 unit.

You want EV = 6*(-2)+4G-(44-4G)>0.
-12 + 4G - 44 + 4G > 0
8G - 56 > 0
G > 7.

That is, the game is -EV with a gap of 6 or less, neutral with a gap of 7, +EV with a gap of 8 or more.

Left as exercise to the reader to calculate how often a sufficiently large gap will come up.

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Where did the 44 come from? Everything else is logical, I just can't seem to put my finger on that number.
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