I have been considering this problem for a long time, and I would really appreciate it if anyone can provide me some thoughts.
Provided there is a specific set of playing cards that have values from 1-10 and they have the same possibilities of 1/10. And assume that drawing cards away would not affect this possibility. Now starting to draw card one by one until the sum of the your holding cards exceeds 21. a condition of your holding can be: 2+8+8+5
Now I would like to know what is the possibility distribution function of the sum of the cards JUST BEFORE the sum exceeds 21? In the previous example, the summation would be:
That is to solve P(12) to P(21).
Thanks in advance.