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What's the % of this happening

    • Kruvi45
      Kruvi45
      Bronze
      Joined: 13.10.2008 Posts: 4
      Hey all,

      Not sure if that's the correct place to ask this, but I'm having a bit of a difficulty calculating the probability of the below set of events.
      We thought it was a pretty unique occurrence which shouldn’t really happen too often, so just wondering what’s the % chance of all of this coming together.
      Basically I think there were 3 players in the hand (if not an issue please also say how big is the chance with 6 players)

      Everyone got pocket pairs (22, 33 and JJ)
      All went all in and everyone hit a set on the flop straight away (so trips for everyone)
      Turn & River cards didn’t add or change anything.
      I know the general odds of getting a pocket pair or hitting a set, however for 3 people to get pockets and also hitting on flop in the same hand shouldn’t really happen too often I suppose ?

      Anyways we had a great laugh over it and just wondering how many hands we need to play for it to happen again (and that time hopefully I’ll have JJ+ rather than 33)

      Also is there a probability calculator which lets you input hands like this and find out the %.
      Maybe I didn't know where to look but all I saw concentrated on finding out your winning percentage/equity and stuff like that.
      This way I won’t have to trouble again with a trivial curiosity issue.

      Thanks in advance.
  • 1 reply
    • belayd
      belayd
      Global
      Joined: 17.03.2011 Posts: 1,021
      Well, there are 52 cards in the deck, and three sets of hole cards have been dealt, leaving 46. Of those 46, there are two that would make a set for one of you, so the chance of one of you getting a set is 2/46 or 1/23. For all three of you to make a set, the chances are 1/23 * 1/23 * 1/23, or 1/23 cubed. Calculate that number in decimal form and then multiply by 100 to get the percentage.

      I hope I got that right, but I got 54% as a final mark in 12th grade math, so very likely I'm wrong.