Calculating Cat hop odds

    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,910
      On this site:
      http://www.nichepoker.net/draw-poker/five-card-odds/
      They state that when holding trips, drawing two, the odds of getting a Full house are 15.4 to one.

      How to they figure this?
      Can someone point me to a reference on how to calculate this?
      I used this page:
      http://en.wikipedia.org/wiki/Draw_%28poker%29, and using the formulas there, I can reach most of the same numbers as on the first link, however this one eludes me.

      When I try, I get this:
      For the first card, you want to draw any card that is NOT one to match your set, so you have 46 outs, and 47 unknowns.
      For the 2nd card, you have 3 outs (to match the first card), and 46 unknowns.
      So the calculation is 46/47 * 3/46
      This equals: 0.064
      To make this x : 1, this is .936 : 0.064 or 14.7 : 1
      So what am I doing wrong?

      While were on the subject of odds calculations, we used to call it "cat hopping" when drawing 2 to a flush or straight.
      Using the same technique above, I make it 29 : 1 to make a flush drawing two. Anyone have a reference I can check this against?

      And finally,
      Which is better:
      Drawing 5
      Drawing 4, keeping an A
      Drawing 3, keeping AK
      Drawing 2 to a flush

      Like I said elsewhere, I often get a freeplay in the BB, but have crap, and don't know which draw is the best odds.

      Thanks,
      --VS
  • 4 replies
    • madorjan
      madorjan
      Bronze
      Joined: 13.11.2009 Posts: 5,561
      Hey Vorpal,

      I guess you're mistaken at the point of Card Removal here, since 2 of the cards don't have 3 outs on the 5th card to improve just 2 (since you already saw one of those). I'm not sure, so let's do the calculations:

      Let's assume you have AAAKQ for the example's sake and you discard the KQ. Now there are 2 possibilities:

      - 6/47 of the times you'll hit a K or a Q on the first card, and then you have only 2 outs to improve, so it will be 6/47*2/46

      - 40/47 of the times you'll hit a different card (and not A either), and will have 3 outs to improve, so it will be 40/47*3/46

      - 1/47 of the times you'll hit an A and will be drawing dead for the full.:D

      So the real formula is: 6/47*2/46 + 40/47*3/46 + 1/47*0 = 0.0056 + 0.0556 + 0 = 0.0612

      So in odds formula this is .9388 : .0612 = 15.34 : 1 - how did they make that 15.4:1 I don't really know, but I guess it's the proper calculation. (Maybe I rounded the numbers a bit to liberally.)

      In the dr5/dr4, keeping A, etc. discussion I can't help you, since I'm not sure either, but usually it looks like we should build our hand so that if it hits a hand, it would have a good equity against the field. So if like 5 guys limp before you, I'd much prefer drawing to a 2 card flush than to the A, since with keeping the A we're basically not c/f-ing with trip As (sometimes As up, but it's not that strong I guess), however heads up hitting a pair of As still might be the winning hand at showdown. So more guys in the pot, I'm more inclined to draw to the rare nuts than drawing to a single pair kind of hand. So HU I definitely draw to the AK, since I feel As and Ks (or sometimes AK hi) is a winner more often, and don't need a flush to put bets in postdraw. However, I can't say I'm a 100% sure in it, just my thoughts on the question.
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,910
      Thanks!
      That is absolutely something I overlooked.

      I'm guessing they rounded up, to make the estimate more conservative.

      As it turns out, I used this today, and chose a gutshot (11:1) over a 3-flush (29:1) and hit the straight. I can't remember the last time I deliberately drew to a gutshot.

      What a difference a day makes.
      Today, it seemed to be my turn to pick off opponents big hands.

      Whoever said 5CD was low variance hasn't seen my graph.

      --VS
    • jbpatzer
      jbpatzer
      Bronze
      Joined: 22.11.2009 Posts: 6,944
      Originally posted by VorpalF2F
      Whoever said 5CD was low variance hasn't seen my graph.
      This. What stakes are you playing? I'm trying to get established on $1/$2 atm.
    • Huricano
      Huricano
      Bronze
      Joined: 29.08.2010 Posts: 2,228
      Originally posted by VorpalF2F
      On this site:
      http://www.nichepoker.net/draw-poker/five-card-odds/
      They state that when holding trips, drawing two, the odds of getting a Full house are 15.4 to one.

      How to they figure this?
      Can someone point me to a reference on how to calculate this?
      I used this page:
      http://en.wikipedia.org/wiki/Draw_%28poker%29, and using the formulas there, I can reach most of the same numbers as on the first link, however this one eludes me.

      When I try, I get this:
      For the first card, you want to draw any card that is NOT one to match your set, so you have 46 outs, and 47 unknowns.
      For the 2nd card, you have 3 outs (to match the first card), and 46 unknowns.
      So the calculation is 46/47 * 3/46
      This equals: 0.064
      To make this x : 1, this is .936 : 0.064 or 14.7 : 1
      So what am I doing wrong?

      While were on the subject of odds calculations, we used to call it "cat hopping" when drawing 2 to a flush or straight.
      Using the same technique above, I make it 29 : 1 to make a flush drawing two. Anyone have a reference I can check this against?

      And finally,
      Which is better:
      Drawing 5
      Drawing 4, keeping an A
      Drawing 3, keeping AK
      Drawing 2 to a flush

      Like I said elsewhere, I often get a freeplay in the BB, but have crap, and don't know which draw is the best odds.

      Thanks,
      --VS
      Drawing 2 to a flush is nothing else than runner-runner flush in Holdem. 4%
      If you have (AKJ :heart: ) 72 it's like A :heart: K :heart: on flop J :heart: 7 2
      than it's 10/47*9/46 = ~4,2%

      Drawing from a freeplay is tought because you never now what will give you a win. Against limping SB keep 2 high cards, discard 3 and try to hit a pair.
      But if you have 3 high cards in one color eg. (AKJ :spade: ) 32 than discard 2. You can also raise this as a bluff and follow with continuation bet.

      If you have shit like K8432 against limping sb keep K8 but multiway keep K and discard 4.

      Hand like KJ (876 :heart: ) HU keep KJ, multiway go for cat hope.

      /sorry for English