Between the Sheets EV

[Siegmund]

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.

[ QUOTE ]
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.

[/ QUOTE ]

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

[cardsharkk04]

I play without antes, so people can just bet whenever they feel like it. Almost all my friends have the misconception that you should bet a lot on something like K 2, but they think that it is stupid to bet a lot on something like J2 or Q3. Optimal play would be potting everything over a 7 gapper. Which I did last time I played and my friends all laughed at me when when I potted a massive pot with J2 and posted. So they all think I'm an idiot and the game goes on. I'll get em eventually.

The 44 are the number of cards that can come that will win or lose 1 bet.

52 cards in the deck less 2 cards on the board and 6 cards that will lose 2 bets = 44 cards.