New calculation --
Spragg: you are right that the number of spoiled hands is greater than 10%. It's actually 41% (rounded), as follows:

The odds of being dealt a non-spoiled hand is: 47/52 x 46/51 x 45/50 x 44/49 x 43/48 = 184,072,680 / 311,875,200 = 0.5902 or 59% of the time. Therefore, spoiled hands account for 41% of hands dealt (1 - 59%).

So total time is 105 years + (.41 x 105 years) = 148 years.

Or something close to that.
Now I'm going to bed. Hope I don't dream about all this!