[pzhon]

From an exact recursive calculation, you should quit at

26:20,
25:19,
24:18,
23:18, *5*
...
17,12,
16:12, *4*
...
11:7,
10:7, *3*
...
6:3,
5:3, *2*
...
3:1,
2:1, *1*
1:0,
0:0 *0*

Very roughly, it looks like you should quit when you are ahead about sqrt(cards remaining/2).

The value of this game is 41984711742427/15997372030584 = 2.624475...

The probability that you are never ahead is precisely 1/27: Imagine adding a red card to the top of the deck, then cutting to a red card and removing it. You can get from 27 orderings to each other, and precisely one ordering in each group of 27 is never ahead. However, you don't always quit when you are ahead. The probability you end up with nothing when you follow the proper strategy is 27340098667643/123979633237026 = 0.220521...