BB Facing Steal

bb facing steal situation: button opens to 3bb, bb calls, bb checks flop, button bets 5bb, bb raises to 16bb laying ~2.5:1. button calls w/ one of three ranges. if button calls bb is assumed to check/fold the turn.   

question: for different button ranges, which flops are best for check-raising? 

cliff notes: surprisingly enough, some flops hit more
starting hands than others. if you are playing against players who
don't fully appreciate this shocking discovery, the following analysis
should prove useful. if not, it may still be worthwhile to skim the 'results' and then move to the 'more discussion' section, as i thought this analysis (and the accompanying spreadsheet) were somewhat helpful for framing questions about good/bad double barrel spots. 

method: simulations were run using stoxev, where button was given a specific opening range (top x%) and flop texture was defined. the button's c/r calling range was then set and fold % was determined. 

results (opening %, fold % range 1; fold % range 2; fold % range 3) (disclaimer: i'm not so great w/ details sometimes, so take this fwiw and please let me know if something looks wrong):         

1. flop: Ah9c3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (41.1); [56.7]; {70.9}
• 30, (38.0); [48.9]; {71.9}
• 40, (47.9); [59.4]; {79.9}
• 50, (47.1); [58.2]; {74.6}

2. flop: Kh9c3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (25.4); [61.3]; {72.6}
• 30, (31.5); [56.7]; {77.4}
• 40, (45.9); [64.7]; {83.6}
• 50, (51.9); [69.5]; {84.5}

3. flop: Qh9c3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (25.6); [54.4]; {63.1}
• 30, (32.4); [53.6]; {73.2}
• 40, (42.4); [62.4]; {79.8}
  
• 50, (49.9); [69.5]; {83.5}

4. flop: Jh9c3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (25.3); [54.2]; {61.6}
• 30, (31.2); [52.7]; {69.9}
• 40, (39.2); [58.9]; {75.3}
• 50, (46.6); [65.0]; {78.3}

5. flop: 8c9c3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (43.9); [67.9]; {69.1}
• 30, (34.6); [53.5]; {59.9}
• 40, (32.1); [52.1]; {63.8}
• 50, (37.7); [56.1]; {69.2}

6. flop: 5d5c3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (65.6); [67.7]; {70.2}
• 30, (69.8); [73.9]; {76.0}
• 40, (66.4); [71.8]; {74.1}
• 50, (63.7); [71.6]; {75.7}

7. flop: AhQc3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (3.70); [50.0]; {70.1}
• 30, (26.0); [56.3]; {72.1}
• 40, (42.7); [68.2]; {80.1}
• 50, (42.2); [64.7]; {75.1}

8. flop: 8h8c7d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (62.7); [80.8]; {81.8}
• 30, (57.6); [74.8]; {79.1}
• 40, (46.3); [66.2]; {75.4}
• 50, (50.9); [67.3]; {77.8}

9. flop: ThTc3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (53.6); [56.3]; {72.2}
• 30, (67.1); [68.9]; {79.9}
• 40, (74.2); [75.3]; {84.4}
• 50, (76.8); [77.8]; {87.0}

10. flop: JhTh9d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (1.35); [27.5]; {38.8}
• 30, (5.50); [31.1]; {38.0}
• 40, (13.9); [38.9]; {44.4}
• 50, (22.4); [45.4]; {50.1}

some observations:

1. the effectiveness of check-raise bluffs on some flop textures is WEAKLY dependent on button OPENING range, see flops 1, 5, 6, 8 and 9.
2. the effectiveness of check-raise bluffs on some flop textures is WEAKLY dependent on button CALLING range, see flop 6, and to a lesser extent 8 and 9 (note that these flops are all paired and all included in observation 1).
3. the effectiveness of check-raise bluffs on some flop textures is STRONGLY dependent on button OPENING range, see flops 2, 3, 4, 7 and 10.
4. the effectiveness of check-raise bluffs on some flop textures is STRONGLY dependent on button CALLING range, see flops 1-5, 7 and 10.

some discussion: the obvious general cause of observations 1 & 2 is that these flops are hard to hit (few draws and 2pr+ hands) and that 'any pair' ~ >=mp ~ >=tp. that is, the ranking of starting hand strength is relatively unchanged after the flop. for example, on flop 1 Ah9c3d it should be obvious that once the button opening range includes all Ax and pp(TT+), there is no way to further increase the number of top or 1p>mp hands. similarly, observations 3 & 4 identify flops that interact strongly with the top x% of starting hands. i suspect that the ability to quickly and accurately adjust to these types of flops is a major source of reciprocal gold. 

more discussion: consider flop 2,          

Kh9c3d; (btn calls any pair, fd, gutshot+); [btn calls >=mp, fd, oesd]; {btn calls >=tp, fd, oesd}

• 20, (25.4); [61.3]; {72.6}
• 30, (31.5); [56.7]; {77.4}
• 40, (45.9); [64.7]; {83.6}
• 50, (51.9); [69.5]; {84.5}

two obvious points stand out: first, the button is very susceptible to being c/r bluffed if he is not calling w/ mid pairs. second, c/r bluffing against a btn capable of calling light or floating greatly reduces the profitability of an isolated flop c/r. considering turn play, if we take the open-raising range of 40% and use the second c/r calling range of [>=mp, fd], we find that btn is left holding <=mp on the turn 51% of the time. thus, if btn continues past the turn only w/ a range of {>=tp, fd, 1p+>=gs}, they will be folding 43.8% of the time, and provide the bb an opportunity to fire a profitable 2nd barrel. considering a complete decision tree, where bb fires all turns, btn calls w/ {>=tp, fd, 1p+>=gs}...bb bets river with >=tpmk (checks otherwise), btn calls w/ >=tp, or bets when checked to w/ >=2p (bb always folds river after checking). we find that the flop c/r ev = 4.8bb, and the turn 2nd barrel ev = 9.4bb. interestingly, there is not a -ev decision for either bb or btn in this particular tree if the bb calls preflop w/ atc. if we apply this identical analysis to other flops, we find:     

     1. Ah9c3d

• btn cbet ev = 1.6bb
• bb c/r ev = 3.9
• bb 2nd barrel ev = 9.6bb

    3. Qh9c3d

• btn cbet ev = 1.0bb
  
• bb c/r ev =  4.5bb
  
• bb 2nd barrel ev = 8.3

    4. Jh9c3d

• btn cbet ev =  1.4
  
• bb c/r ev =  4.2
  
• bb 2nd barrel ev = 7.3

    5. 8c9c3d

• btn cbet ev =  2.7
  
• bb c/r ev =  2.7
  
• bb 2nd barrel ev = 7.3

    6. 5d5c3d

• btn cbet ev =  1.4
  
• bb c/r ev =  4.3
  
• bb 2nd barrel ev = 0.5

    7. AhQc3d

• btn cbet ev =  2.4
  
• bb c/r ev =  3.2
  
• bb 2nd barrel ev = 2.7

    8. 8h8c7d

• btn cbet ev =  2.4
  
• bb c/r ev =  3.2
  
• bb 2nd barrel ev = (1.9)

    9. ThTc3d

• btn cbet ev =  1.5
  
• bb c/r ev =  4.2
  
• bb 2nd barrel ev = (0.7)

    10. JhTh9d

• btn cbet ev =  6.9
  
• bb c/r ev =  (1.6)
• bb 2nd barrel ev =  (1.7)

unless i'm missing something, the thing that stands out here is that c/r bluffing and 2nd barreling are rarely significant ev mistakes v. most btn open ranges. that's not to say that these plays are anywhere near optimal. [note: btn cbet ev is biased by the bb pf call + flop c/r range of ALL HANDS.] i've expanded this ev analysis to include the ten flops above across the different opening ranges in this spreadsheet: http://spreadsheets.google.com/pub?key=pvjFKb7H91Rrpd-aisSImAQ