Odds of this happening in poker

AAAintheBeltway · Nov 7, 2007

Quote from EricP:

I think you are misunderstanding the question.

You are correct, for a different question: Once you draw pocket aces twice in a row, the odds of getting pocket aces on the next hand is 1/221.

However, the question I answered was what are the odds of drawing pocket aces on three consecutive hands. In other words, what are the odds of drawing pocket aces on the next three consecutive hands? The correct answer for that question is 1/221 per hand, or (1/221)^3, or 1/10,793,861
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Sorry, you are obviously correct.

hapaboy · Nov 8, 2007

Quote from EricP:

The odds of being dealt pocket aces are 1/221.

Note that this is calculated as follows:
Odds of getting an ace on first card = 4/52
Odds of then getting ace on second card = 3/51
Overall odds = 4/52 * 3/51 = 1/221

The odds of being dealt pockets aces twice in a row = 1/48841 (i.e. 1/221 * 1/221)

The odds of being dealt pocket aces three times in a row = 1/10,793,861 (i.e. 1/221 * 1/221 * 1/221)

The odds of being getting a royal flush on the flop is 1/649,740

Calculated as follows:
20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 1/649,740

Note that the first card is 20/52, since any A, K, Q, J or 10 will start the royal flush. After the first card, the suit must match on subsequent cards.

So, to put things in perspective, it is much more rare to have pockets aces three in a row, than even flopping a royal flush. Put another way, if you are a poker addict, and play one hand of poker every minute, 24 hours per day, 365 days per year, you could expect to wait <b>20.5 YEARS of continuous poker play</b> before the first time you receive pocket aces on three consecutive hands.
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A big mahalo, Eric!

Renegen · Nov 8, 2007

The probability to draw pocket aces is 1 over 221, that's pretty well known. That holds of course for any pocket pairs, 13 in total.

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Odds of this happening in poker

AAAintheBeltway

hapaboy

Renegen