2-7 triple draw

    • badgerer
      badgerer
      Silver
      Joined: 29.03.2010 Posts: 555
      If a villain is drawing to any 8 or better on the last draw in a HU pot and will pat behind any jack or better if hero draws, what is their average pat hand?

      EDIT: clarity
  • 7 replies
    • badgerer
      badgerer
      Silver
      Joined: 29.03.2010 Posts: 555
      bump
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,915
      If I understand the question correctly,
      Villain already had an 8-lo drawing 1.

      In your question, you say this is the last draw, but then say the villain will "pat behind" if they draw to J or better.

      If this is the last draw, then there is no more opportunity to pat behind.
      There are 158104 combinations of J8765 or better (the v worst J8 lo).
      There are 33664 combinations of 98432 or better. (the v best 98 lo)

      Since the hand must be between those two, I'll make a Wild-Ass-Guess and say that the "average pat hand" would be half-way between.
      The numerical average of those two numbers is 95884
      The hand that beats that many combos is T9652

      I am sure about the combinations, however I am NOT SURE that I am approaching this problem correctly -- but it seems perfectly reasonable to me.

      I don't play 2-7 triple draw, but I've been dabbling in NL 2-7 Single Draw.
      Playing that, I would not break a dealt pat J, unless it was v smooth and no str8 possibilities something like J 7432
    • badgerer
      badgerer
      Silver
      Joined: 29.03.2010 Posts: 555
      hi vorpal,

      thanks for the response, i appreciate the effort you went to. this is actually not the answer i was looking for unfortunately.

      i realise now i havnt done a great job of expressing my question so i will try again with a clearer example.

      Predraw: hero is SB with 2347. BU raises hero 3bets, BU calls.
      1st draw: hero bricks BU draws 2, hero bets BU calls.
      2nd draw: hero bricks BU draws 1, hero bets BU calls.
      3rd draw: hero draws 1 BU pats.

      for the sake of simplicity lets say BU drew to 2348. they automatically pat any J low or better on the 3rd draw and they will freeze-play a strong 8 so they call with 100% of their range of pat hands. what is the average hand they will pat behind with?

      so it will be somewhere between 23458 and 2348J.
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,915
      Will he pat in this position if he pairs his hand?

      For each of the cards, that do not pair his hand:
      5,6,7,9,T,J,Q,K,A
      There are 4 of each except 3 for the 7
      You also block one for each of the cards you threw

      But those don't make a huge difference, so since I'm lazy I'll ignore 'em.

      That means that it's pretty much the average hand is
      2348T

      I don't properly know how to adjust this for all of the combos that pair his hand and yours.

      If you pair the 2 or 3 it might even be worth bluff-catching with -- but I would not know much about that.

      Hopefully, you'll have figured out that I'm talking through my hat when it comes to this game.

      Now badugi, THERE'S a game!
      --VS
    • badgerer
      badgerer
      Silver
      Joined: 29.03.2010 Posts: 555
      your opening up a whole new can of worms if you add snowing into the equation :f_mad:

      the thing that troubles me about 2-7TD is there isn't really a specific range of possible (genuine) pat hands like there is in 5CD. so constructing ranges can be problematic. still, it would be nice to have some kind of reference point to work from.

      I keep reading people in 5CD strategy discussions mentioning the average pat hand is AKQJT or something and talking about the 'average' pat flush amongst other things. how can i work out what the average hand is between a given range? are there any tools available for this? im not brilliant with maths but im prepared to work it out myself if i only knew how.

      its a shame that there are no triple draw experts here willing to chip in.
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,915
      For 5-Card Draw I used Excel's combin(n,m) function, and constructed a table of every possible 5-Card Draw hand, and how many combinations of each there could be.

      So for any given hand, I can tell you how many hands beat it, and what hand is halfway to the top.

      2-7 TD is the same table, only upside down.
      If you have Excel, I can tell you how to construct it, and give your some references for how to calculate the combos

      in your 2,3,4,7 example, I would freeze w/ any 5,6 or 9 and take my chances

      Dealt pat 7s, 8s and 9s are easy. Do you break Ts? Js?

      I have only played 2-7 SD myself, and I don't know how much crosses over between the two games.

      Cheers,
      --VS
    • badgerer
      badgerer
      Silver
      Joined: 29.03.2010 Posts: 555
      i'll almost never keep a J predraw. rough jacks just muck them, smooth jacks much better off drawing. J is just not a strong card to keep with three draws to come. T's are basicly in the same category as J's predraw.

      9's i'll usually break them. I won't break rough 9 or 9 with a straight draw underneath, normally just fold them on later streets if i think i'm beat.

      the only time i'll pat pre with a 9, T or occasional J that i was planning to draw is if im way ahead in the draw and my opponent doesn't draw loose against pat. but that's definitely a semi-snow.

      none of the above aplies to SD, that is a whole different animal. in TD you need to aim to make much better hands on average, the worst 3 card draw i'd regularly play in TD is 268. to give you a rough idea, while 97 is a strong hand in SD, in TD imo its roughly analogous to 86.

      about the spreadsheet, i think that will be a very useful thing to have. i'll have to do a bit of research, im not so good with excel. i think my gf works with it and can probably help me out, but if you could share some of your knowledge with regards to setting it up i'd be grateful. thanks for offering.