Knowledge for you:
The odds of drawing AA on any one hand is 1/221. It is a single event. The odds of drawing AA on the next hand are also 1/221, I agree. It is also a single event.
However, when you look at the odds of drawing AA 2 times in a row, then you are looking at a single event, that event being AA coming up 2 times in a row, and the odds of that is 1/221 times 1/221, or 1/48841. If you want to look at the single event of AA coming up 3 times in a row, the it is 1/10,793,861,
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