4 Aces 5 times in one hour

[olds442jetaway]

This happened 5 or 6 years ago at Mohegan Sun and I don't expect it will be repeated in my lifetime. I was playing 8/5 Bonus Poker before they yanked out these nice 99.1 % quarter machines that also earned points.  I had just sat down to play and within seconds the first ace quad hit. The last one hit almost exactly an hour after the first one. I would have to approximate the number of hands played at 600. I haven't dusted off my old stat 1000 book yet from 1967 and can't remember how to compute the probability of this happening. If anyone out there feels like doing it for me, I would be interested to know. Since it hasn't been repeated since, and I have drawn at least 50 Royals since then, I am sure the probability is much higher than hitting a single Royal in Draw Poker. I think since then, I have only hit 4 aces twice a couple of times in the same 1 hour time period. ( I know the 50 Royals in 5 years sounds like a huge number, but that represents about 2.8 million hands so it isn't even an average number.)

[Vman96]

For any given set of 600 hands, it's about 1 in 6 million.

Over a lifetime, I might work on that tomorrow, but Excel or other calculators may hate me for it...lol

[olds442jetaway]

Wow!   I knew it had to be high, but had no idea the probability would have been higher than say getting dealt a Royal. On the other hand, after getting 50 or so Royals since then and not getting 4 of a kind in any suit 5 times in that 1 hour time period, I should have realized the probability would have been in the millions. I guess we should not be too surprised at any of these oddball events since the probability of every dealt hand we get lining up exactly that way as to suit and order is in the millions to 1 too. You can get dealt a sequential Royal Flush in 4 suits, but the probability of getting dealt say 4 of hearts, 6  of clubs, 5 of  diamonds, 8 of spades, and 9 of hearts exactly in that order ( a hand nobody would want),  is even less than getting dealt one of the sequentail Royals in any suit. We just don't seem to think about probabilities too much unless it involves something great that we hit or something great we would like to hit!