Probability of the dealer hitting to 21

Curious as to what the probability is of the dealer hitting, once or repeatedly, and attaining a total of 21. I would try to solve it myself, but I don't have any specialized software and so it is quite daunting.

I'm assuming the dealer stands on any 17.

Appreciate any answer (or, any relatively simple way to calculate by hand, though I doubt I have overlooked one)

Wizard's Blackjack Appendix 2 indicates that the probability is about 7.7%

Thank you very much, did not see that!

Realistically, the algorithm must account for your hand total, your current bet, and how much you have invested in winning. Because the better your total, the more you have out there, and how much it's going to mean to you if you lose MUST play a large part in how frequently a dealer drawing to 21. I know this is true because players tell me about it at length every night.