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dealt decues probabilities

Richard Boston asked:

Can someone remind me the supposed frequency of the quad deuces in DW. Every
how many hands?

Dean Zamzow gave me this info-

Here are the numbers requested (rounded)

Dealt cards:
1) Dealt 4 deuces - 1:54,145
2) Dealt 3 deuces - 1:576
3) Dealt 2 deuces - 1:25
4) Dealt 1 deuce - 1:3.3

Redeal only:
5) Held 0 cards, redraw 5 and get 4 deuces - 1:35,673
6) Held 1 deuce, redraw 4 and get remaining 3 deuces - 1:4054
7) Held 2 deuces, redraw 3 and get remaining 2 deuces - 1:360
8) Held 3 deuces, redraw 2 and get remaining 1 deuce - 1:23.5

Does the dealt deuce probability account for hands with 1,2 or 3 deuces where you don't hold just the deuces? For example, does 10dJd2c2s count as being dealt 2 deuces? Even though you have 2 deuces, you have no chance for 4 deuces because you are holding 2 additional cards. I think Dean's are just for being dealt 2 deuces, even if you keep more than just the deuces.