Shove or wait - a probability question

[CDAC]

I am trying to quantify the ‘push now or wait for a better spot’ decision. It’s been a long (!) time since I studied basic probability so can someone check my math / methodology. Thanks in advance.

The question is, given a range of hands that I want to push all in with, how long will I have to wait for one of those hands to be dealt to me. To keep it simple, lets say my range is only AA, KK, and AKs.

Probability I am dealt AA is 4/52 * 3/51 or .0045, KK is same, and AKs is 8/52 * 1/51 or .003
Therefore the total probability that I am dealt one of those hands is .0045+.0045+.003 = .012

Given that probability, on average I would have to wait 1 / .012 = 83 hands before I saw AA, KK or AKs. Is that all correct or have I completely donked this up?

The follow up question: ‘On average’ I will get dealt 1 of those 3 every 83 hands over a statistically significant sample. How would I define a standard deviation from ‘average’ so that I would know that the range was between say once every 65 to 95 hands?

Thanks again.