5-Card Draw Break a Pair or not?

    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,915
      Feral Cow Poker
      PokerStars Limit 5 Card Draw $0.10/$0.20 - 4 players

      Button: $3.69 (Hero)
      SB: $2.21
      BB: $1.61
      UTG: $1.44

      Dealing Hands: ($0.15) :9h: :Qh: :Jc: :Jh: :8h: (4 players)
      UTG folds, Hero raises to $0.20, SB folds, BB calls $0.10

      First Draw: ($0.45) (2 players)
      BB discards 3, Hero discards 1,
      :9h: :Qh: :Jh: :8h: || :Ah:
      BB bets $0.20, Hero raises to $0.40, BB calls $0.20

      Hero showed :9h: :Qh: :Ah: :Jh: :8h: , a flush, Ace high
      BB mucked :4c: :4s: :Ac: :4d: :Qs:
      Hero won $1.19
      (Rake: $0.06)

      This worked out, but I think this was the wrong play in the long run.
      This BB was quite tight, so I was thinking that he did not defend much.
      I was wrong, but ...
  • 1 reply
    • bigpooch
      bigpooch
      Basic
      Joined: 16.01.2012 Posts: 44
      Shouldn't break the pair there if BB is defending properly: if he always reraises AA+ and calls with 88-KK, you can estimate your equity when drawing three cards by using twodimes.net:

      http://twodimes.net/h/?z=9267805
      pokenum -mc 500000 -l27 jh jc - 8s 8d / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 93439 18.69 406561 81.31 0 0.00 0.187
      8s 8d 406561 81.31 93439 18.69 0 0.00 0.813

      http://twodimes.net/h/?z=9267808
      pokenum -mc 500000 -l27 jh jc - 8s 8c / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 94165 18.83 405835 81.17 0 0.00 0.188
      8s 8c 405835 81.17 94165 18.83 0 0.00 0.812

      equity versus 88: 0.812396

      http://twodimes.net/h/?z=9267813
      pokenum -mc 500000 -l27 jh jc - 9s 9c / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 94203 18.84 405797 81.16 0 0.00 0.188
      9s 9c 405797 81.16 94203 18.84 0 0.00 0.812

      http://twodimes.net/h/?z=9267814
      pokenum -mc 500000 -l27 jh jc - 9s 9d / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 93931 18.79 406069 81.21 0 0.00 0.188
      9s 9d 406069 81.21 93931 18.79 0 0.00 0.812

      equity versus 99:0.811866

      http://twodimes.net/h/?z=9267815
      pokenum -mc 500000 -l27 jh jc - ts td / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 118036 23.61 381964 76.39 0 0.00 0.236
      Ts Td 381964 76.39 118036 23.61 0 0.00 0.764

      http://twodimes.net/h/?z=9267816
      pokenum -mc 500000 -l27 jh jc - ts tc / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 118065 23.61 381934 76.39 1 0.00 0.236
      Ts Tc 381934 76.39 118065 23.61 1 0.00 0.764

      equity versus TT: 0.763898

      equity versus JJ: 0.5



      http://twodimes.net/h/?z=9267824
      pokenum -mc 500000 -l27 jh jc - qs qd / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 372420 74.48 127580 25.52 0 0.00 0.745
      Qs Qd 127580 25.52 372420 74.48 0 0.00 0.255

      http://twodimes.net/h/?z=9267825
      pokenum -mc 500000 -l27 jh jc - qs qc / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 372637 74.53 127363 25.47 0 0.00 0.745
      Qs Qc 127363 25.47 372637 74.53 0 0.00 0.255

      equity vesus QQ: 0.254943

      http://twodimes.net/h/?z=9267826
      pokenum -mc 500000 -l27 jh jc - ks kd / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 383994 76.80 116006 23.20 0 0.00 0.768
      Ks Kd 116006 23.20 383994 76.80 0 0.00 0.232

      http://twodimes.net/h/?z=9267829
      pokenum -mc 500000 -l27 jh jc - ks kc / qh 9h 8h
      5-card Draw 2-7 Lowball: 500000 sampled outcomes
      cards win %win lose %lose tie %tie EV
      Jc Jh 383617 76.72 116382 23.28 1 0.00 0.767
      Ks Kc 116382 23.28 383617 76.72 1 0.00 0.233

      equity versus KK: 0.232388

      total combinations of hands 228777 ( 11559 for JJ; 32274 for 88,99,QQ and 60198 for TT,KK )

      overall equity: ~ 0.552517896 when drawing three to JJ.

      If you draw one to the 12-out straight flush, you only make a pair+ 24/47 ~ 0.510638298 and some of those times, you don't win. You can also bluff if you miss and extract more value when you hit when the BB makes trips+. I'd guess that if you held the same draw with 99 or 88, you should break against a player that doesn't defend extremely wide.