Actually it's 2 back to back hands that happened at a table Iv'e played in recently. Every time I try to calculate the prob. I get absurd numbers.S anyways, this guy, in back-to-back hands, was dealt pocket jacks and both time flopped QUADS!! Doubt I'll ever see anything like that again in another 10 lifetimes even. Can anyone do the math on that?

Assuming that you are guaranteed to see a flop on your next 2 hands, the probability that your next 2 hands will both be pocket jacks and that you will flop quads on both hands is 1 in 7,814,560,000.

However, the fact that this happened is not incredibly amazing, as the probability of anything happening is extremely unlikely, yet happen they do. For example, someone always eventually wins the lottery, even though the probability of your winning the lottery is extremely low.

I figured the probability of being dealt JJ as 1 in 221, and the probability of being dealt JJ on your next 2 hands as 1 in 221^2, which is 1 in 48,841. A flop can come quads one of six ways (let us assume you have two black jacks for this example):

Jh Jd Xx (1/50*1/49)
Jh Xx Jd (1/50*1/48)
Xx Jh Jd (1/49*1/48)
Jd Jh Xx (1/50*1/49)
Jd Xx Jh (1/50*1/48)
Xx Jd Jh (1/49*1/48)

The sum of the probabilities of each of the six possible quad flop combinations is 1 in 400.

Therefore, the probability of your next one hand meeting this scenario is 1 in 400*221, which is 1 in 88,400. The probability of your next two hands meeting this scenario is 1 in (400*221)^2, which is what I stated above. If you want to extend it to three in a row, the probability rises from 1 in 7.8 billion to 1 in 690,807,104,000,000 (690.8 trillion).

If you do not specify that the hand must be pocket jacks but must merely be back to back pocket pairs flopping quads, or if you just say the next 2 hands (pocket pair or not) flop quads, the probability becomes extremely less unlikely.

These probabilities are for one person. The probability that you will see this back to back jacks flopping quads scenario is multiplied by how many players are at your table and further multiplied by the number of hands you play or observe.

Once in a tourney,had a guy catch quads five out of six hands.
We joked about him only having trips in the the fifth hand,telling him he was slipping.
This type of occurance changed how I look at -/+ EV.
Sometimes it just don't apply.

All 6 of those have the same probability 1/50*1/49. The ones that start with Xx would need to start with 48/50, and the ones with Xx in the middle need to have a 48/49 for that term.

1/50 * 1/49 * 6 =~ 1 in 408.33

or just note that there are 48 possible flops ignoring order.

48/C(50,3) = 48/19600 =~ 1 in 408.33

Thank you for the correction, Bruce.

Probability of the next hand is 1 in 90,241.6.
Probability of the next two hands is 1 in 8,143,558,402.7 (8.1 billion).
Probability of the next three hands is 1 in 734,888,282,864,004.629 (734.9 trillion).
Probability of randomly shuffling a deck and having it become reordered identically to how it came from the factory is 1 in 80,658,175,170,943,878,571,660,636,856,403,766,975 ,289,505,440,883,277,824,000,000,000,000 (1 in 80,658.2 vigintillion).

Another way of thinking about how unlikely the probability of the next two hands: Think of a string extended from the surface of the sun to the surface of the earth. There is a stretch of string 60'2.5" (that's a little over 60 feet long) that is painted red, while the rest of the string is white. The probability that you randomly grab a portion of that string and it is red is the same as the probability that your next 2 hands are JJ and you flop quads.