So I was playing a medium stakes game and the first three cards on the flop were all 2s and I thought wow that’s pretty unlikely, with a nothing card coming out on the turn but then on the river a 4th 2 came out putting a 4 of a kind on the board for every player, does anybody know what the odds of this happening is?
Very low I should imagine, probably 1 or 2% maybe. At least you know on the river that nobody else has a 2.
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The number of different 5 of 52 card combinations is
52 x 51 x 50 x 49 x 48 / (1 x 2 x 3 x 4 x 5) = 2,598,960
There are 13 Quads, 2222 - AAAA, and the 5. community card is one of 48.
13 x 48 = 624 Quads in this 2,598,960 different community cards.
Chance:
2,598,960 / 624 = 4,165
1 Quad in 4,165 community cards.
624 / 2,598,960 = 0.024 %
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Poki65 to the rescue with perfect Vulcan wisdom as always. We are good.
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Great work Poki, makes you wonder what the odds would be that 4 players had the Ace kicker to win the hand? Probably 10 or more decibels lol 
@Litenin
The question:
On table are the cards 2 2 2 2, the 5. card on table is, I say, 3d. 4 players on table. How high is the chance everyone has an A on hole?
The answer:
47 cards are in deck.
The number of all different holecards what the 4 players can have:
47 x 46 / 2 x 45 x 44 / 2 x 43 x 42 / 2 x 41 x 40 / 2 / (2 x 3 x 4)
= 33,018,036,975
The 4 x AX holes:
4 x A at the players, 43 cards in deck
Player 1‘s second card can be one of this 43, Player 2 can have to all of them 42 for second card, player 3 41, player 4 40.
43 x 42 x 41 x 40 = 2,961,840
Chance:
33,018,036,975 / 2,961,840 = 11,147.8
1 in 11,147.8
2,961,840 / 33,018,036,975 = 0.00897 %
I have an app for looking to such things too. I made the app because missions, to know the needed hands for a mission. It can look to all hole cards what can be, and i had there the same numbers/result.
The numbers are in German format.
Brilliant work Poki and Thank you very much!