Death Mark, new hotness, or basic?

For those curious, if a troop gets deathmarked, and the debuff is not cleansed, after 10 turns the troop has a 23.23% chance to die. The troop’s chances to die are as follows:

 Turn | Mortality per turn (if still deathmarked) | Cumulative mortality
 ---- | ----------------------------------------- | --------------------
 1    |  9%                                       |   9.00%
 2    |  8%                                       |  15.48%
 3    |  7%                                       |  19.56%
 4    |  6%                                       |  21.77%
 5    |  5%                                       |  22.76%
 6    |  4%                                       |  23.12%
 7    |  3%                                       |  23.21%
 8    |  2%                                       |  23.23%
 9    |  1%                                       |  23.23%
10    |  0%                                       |  23.23%

The formula to determine total mortality after 10 turns is daunting:
1.0 - ((0.1 * 1.0) + (0.9 * 0.9)((0.2 * 1.0) + (0.8 * 0.9)((0.3 * 1.0) + (0.7 * 0.9)((0.4 * 1.0) + (0.6 * 0.9)((0.5 * 1.0) + (0.5 * 0.9)((0.6 * 1.0) + (0.4 * 0.9)((0.7 * 1.0) + (0.3 * 0.9)((0.8 * 1.0) + (0.2 * 0.9)((0.9 * 1.0) + (0.1 * 0.9)((1.0 * 1.0) + (0.0 * 0.9)))))))))))

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