Holding only the deuce for variant deuces wild

[DAAnMAAn]

Had a question, largely theoretical, but I thought more brilliant minds can answer...or at least access to computer software.Mostly concerning the more variant versions of deuces wild...loose deuce and triple deuces.
Basically the question is, if I only hold the wild deuces, any deuce, on the first flop, regardless of what flops, what is the statistical expectation of hitting a quad deuce in how many hands?I do know that playing optimum play, I can expect to hit a quad deuce in loose deuce about 1 in 4,664 hands... and triple deuces hit quad deuce 1 in 4465 hands.Is this question even answerable? Does it go down to say, 1 in 3,000 hands? 1 in 2,500 hands? Hym. Enquiring mind wants to know. Was thinking of doing a test with single line nickle loose deuce, but it would tell us nothing since the sample size needs to be tens of thousands of hands. So...Any thoughts?...