Streaks

This problem is about Freecell streaks (in this site in particular). A run of wins is called a streak. The standard Freecell game has 8 columns of cards and 4 free cells. This version is commonly referred to as 8x4. There is a wide range of other variants too. The number of columns of cards may range from 4-13, and the number of free cells may range from zero to 10. Thus, a game with 13 columns of cards and no free cells is referred to as a 13x0. The game is currently scaled so that when your streak is small, you are automatically given somewhat easier games. As your streak increases, the difficulty level will go up until at a streak of 50 you will be playing complete random deals (difficulty level 10). Here's the progression:

Streak	Difficulty
0-9	5
10-19	6
20-29	7
30-39	8
40-49	9
≥50	10 (random)

There is a unique degree of "winnability" for each variant. 12-sum games such as the standard 8x4 are usually pretty winnable. But when you trend down into the <10 sum games and such, winnability gets pretty dicey. 5x4 games, a 9-sum variant, are only rarely winnable. At any level there are 2¹⁵ different games for any variant (numbered 0 to 32767). What is average streak length for 10x2 variant assuming you can win any "winnable" game dealed randomly? The number of unwinnable games by level for 10x2 given as below:

Level	Count
5	1
6	2
7	5
8	6
9	12
10	18

Input format: streak length rounded to 15 digits after the decimal point. See also: streaks info