864t, button v. big blind: following up on thursday's post

quoted text from the previous post is in grey, new stuff follows:

...

raised pot oop w/o initiative, c/r flop: 

• btn-or top 50% [22+, Ax, Kxs, suited 2-gap+, offsuit 1-gap+] v. 
• bb-cc middle 14.3% [55-99, 50% Axs, broadways JTo-AJs, 98s-J9s]
• bb checks flop
• btn bets all hands
• bb raises all hands - EV = -13.6bb
• btn continuing ranges:
• [>=1p, >=bdfd, >=gs] = 79.6%
• [>=tp, fd, oesd, 1pr+gs, 1pr+bdfd] = 46.4%
• [>=tp, fd, oesd] = 35.7%

• if we define a more complete decision tree as follows:

• btn cbets [1pr+, fd, overs+bdfd, gs+, and var2% of all other hands]...
• bb c/r [tp+, fd, pr+gutter, oesd and var1% of all other hands]...
• btn shoves [tp+, fd, pr+gutter or better], folds otherwise...
• bb calls [tp+, fd, oesd], folds otherwise.

• we we can then vary var2 horizontally (btn cbet air %) and var1 vertically (bb c/r air %) to get an idea of how the ev of bb's c/r (in bold) fares v. different btn cbet tendencies shown in the following table:
  
  
  
  

  	0	25	50	75	100
  0	1.13	1.23	1.32	1.39	1.46
  25	0.09	0.41	0.68	0.92	1.13
  50	-0.95	-0.42	0.04	0.44	0.79
  75	-1.99	-1.25	-0.61	-0.04	0.46
  100	-3.03	-2.08	-1.25	-0.52	0.12

  
  
  
  
  

the not-so-surprising conclusion is that the more air btn cbets the more air bb can get away w/ raising. that said, even if btn is cbetting 100%, bb does best by only raising their legit value/semibluff hands. i think this is an interesting result, as i know i often feel compelled to c/r w/ weakish hands on this flop v. those compulsive blind thieves who cbet like it's their job.

these numbers, and my interpretation, might be off somewhat. i've asked some questions of the software developer on 2p2 that will hopefully clear things up...

864t, 3-bet pot cutoff v. button

actually, i changed my mind again. i'll get back to the question of whether we need/want a oop 3b calling range, but i want to keep going on this flop for a bit. so, this situation is basically the same as what i looked at yesterday, but i now want to consider btn's optimal c-betting range...

3b ip w/ initiative, cbet or no?:

• co opens top 25%,
• btn 3bets 10.5% of hands: [TT+, AQ+] + 40% of [Axs, KQs, QJs, KJs, scs, ATo-AJo, KQo] + 25% of [other suited broadways, suited gappers, offsuit connectors],
• co calls 25% of [55-QQ, ATs-AQs, KQs, AQo] + 10% frequency for [AA-KK, 22-44, 54s-JTs],
• co checks,
• btn cbets [tp+, fd, oesd, var3% of all other hands], EV (var3=25%) = +11.3bb
• co shoves [tp+, fd, oesd, 1pr+bdfd, 1pr+gutter], EV(25%) = +7.3bb
• btn calls [tp+, fd], EV = +27.1bb

if we then vary var3 (btn cbet 'air' %), and plot the ev of the btn cbet (blue points) and co c/r w/ a pure value/semibluffing range (red) and value+50% air (orange), we get the following chart:

this is probably largely intuitive, but cbetting air is -ev, and the value of co's c/r increases rapidly as button makes that mistake. obvious conclusions are:

1. btn would benefit from a check-behind range v. aggressive opponents (see blue points), and 
2. co needs btn to be cbetting air to turn a profit on his c/r (see red points),
3. co does not need to c/r w/ air,

basically, this is a flop that both btn and co should play very honestly, but if the button cbets too much, co gets a license to c/r a ton of hands. other thoughts?

next i suppose i should look at those lines that start with the flop checking through...

yesterdays direction leads to slight digression...

so, here's another scenario that might play out on our favorite flop 864t (incidentally, this happens to be my favorite flop - i like to call it the 'heart mattack'):


3b pot, oop, w/o initiative, c/r v. cbet:

• co opens top 25%,
• btn 3bets 10.5% of hands: [TT+, AQ+] + 40% of [Axs, KQs, QJs, KJs, scs, ATo-AJo, KQo] + 25% of [other suited broadways, suited gappers, offsuit connectors],
• co calls [55-QQ, ATs-AQs, KQs, AQo] + 10% frequency for [AA-KK, 22-44, 54s-JTs],
• co checks,
• btn cbets all hands w/ equal frequency, EV = +6.6bb
• co shoves [tp+, fd, oesd, 1pr+bdfd, 1pr+gutter], folding 31%, EV = +15.3bb
• btn calls [tp+, fd], folding 62%, EV = +15.4bb

i guess that's pretty interesting. the basic lessons are:

1. co perspective: c/r a wide range of hands w/ equity if you're going to call oop v. a light 3b from button, and you expect him to cbet a balanced range,
2. btn perspective: you can cbet in this spot profitably w/ your entire range, even if co is shoving hands as weak as T8s, [it's possible that it's more profitable to check behind, but i'll save that for another day...]
3. i ignored a co flop calling range, and didn't address how the hand might play out if btn checks back, but i'd like to move on to a related topic, so w/e...

the related topic is whether we should or need to call 3bets oop like this at all. i'll post something along those lines soon.

low/mid non-paired 2-tone boards: e.g. 864hh

this might be the first in a series of posts analyzing different flop textures across a variety of situations. there will be some work involved, so i want to pick good flops. in my opinion, 'good' means flops that different players approach most differently. i think there is where we will find edge.

so, i picked 864t and did some calcs for different lines/situations:

raised pot, ip w/ initiative, facing flop c/r:

• btn-or top 50% [22+, Ax, Kxs, suited 2-gap+, offsuit 1-gap+] v.
• bb-cc middle 14.3% [55-99, 50% Axs, broadways JTo-AJs, 98s-J9s]
• bb checks flop
• btn bets all hands
• bb raising ranges (folds otherwise)
• [1p+, bdfd+, gs+] = 60.9%
• [tp+, fd, oesd, 1pr+gs, 1pr+bdfd] = 22.8%
• [tp+, fd, oesd] = 15.2%

raised pot oop w/o initiative, c/r flop:

• btn-or top 50% [22+, Ax, Kxs, suited 2-gap+, offsuit 1-gap+] v.
• bb-cc middle 14.3% [55-99, 50% Axs, broadways JTo-AJs, 98s-J9s]
• bb checks flop
• btn bets all hands
• bb raises all hands
• btn continuing ranges:
• [1p+, bdfd+, gs+] = 79.6%
• [tp+, fd, oesd, 1pr+gs, 1pr+bdfd] = 46.4%
• [tp+, fd, oesd] = 35.7%

raised pot oop w/o initiative, DONK flop v. passive btn:

• btn-or top 50% [22+, Ax, Kxs, suited 2-gap+, offsuit 1-gap+] v.
• bb-cc middle 14.3% [55-99, 50% Axs, broadways JTo-AJs, 98s-J9s]
• bb leads flop w/ all hands for 5bb, EV = +0.6bb
• btn calls [overcards+, gs+, bdfd+], 97%
• bb bets all turns w/ all hands for 14bb (pot = 16.5bb), EV = +5.5bb
• btn calls [tp+, any 2-card fd, K or A 1-card fd, oesd], 45.5%, folding otherwise 54.5%
• bb checks all hands
• btn bets all hands
• bb calls w/ [2p+], 14.6%, folding otherwise, EV = +7.0bb

raised pot, cbet oop w/ initiative; raise cbet ip w/o initiative:

• mp-or top 15%,
• btn-cc speculative 15% [22-TT, A2s-AQs, suited broadways less than AK, AJo, AQo, KQo]
• mp cbets 8bb into 8.5bb w/:
• [all hands], EV = +3.1bb,
• btn raises 3x w/ [all hands], EV = +4.2bb
• mp shoves [tp+, fd, oesd], EV = +11.1bb
• btn calls [tp+, fd, oesd], EV = +4.4bb
• [1p+, fd, oesd, overs+bdfd, over+gutter, var1% of others], EV(v1=25%) = +4.8bb,
• btn raises 3x [all hands], EV(v1=25%) = +1.1bb
• mp shoves [tp+, fd, oesd], EV(v1=25%) = +14.1bb
• btn calls [>=tp, fd, oesd], EV(v1=25%) = +4.4bb,
• please take a look at the following spreadsheet and help me think about how to 1. maximally exploit an 2. play unexploitibly from each postion: http://spreadsheets.google.com/pub?key=tTyA0M_lIGVZJG0erviMftQ&output=html

some other lines i'll probably look at:

3b ip w/ initiative

3b ip w/o initiative

raised oop w/ initiative

3b oop w/ initiative

i also looked at some players i had largish samples on in my db and summarized their tendencies.

reg stats:

1. BamYeah: 445 hands 
1. cbet = 73%
2. success = 26%
3. fold to cbet = 60%
4. raise cbet = 10%
5. fold to raise = 42

1. UKFAN1687: 1550 hands
   
   
   1. cbet = 42%
   2. success = 45%
   3. fold to cbet = 51%
   4. raise cbet = 38%
   5. fold to raise = 47%
   
   
   
2. CountZer01: 1529 hands 
1. cbet = 65%
2. success = 42%
3. fold to cbet = 52%
4. raise cbet = 20%
5. fold to raise = 19%
cbboy: 459 hands


1. cbet = 39%
2. success = 29%
3. fold to cbet = 41%
4. raise cbet = 23%
5. fold to raise = 25%



nimuuuh: 1310 hands


1. cbet = 64%
2. success = 43%
3. fold to cbet = 46%
4. raise cbet = 12%
5. fold to raise = 36



Smart LAG: 695 hands


1. cbet = 66%
2. success = 26%
3. fold to cbet = 24%
4. raise cbet = 42%
5. fold to raise = 40%



Bluffsalot83: 724 hands


1. cbet = 61%
2. success = 41%
3. fold to cbet = 44%
4. raise cbet = 35%
5. fold to raise = 58%



AmexCenturian: 1058 hands


1. cbet = 75%
2. success = 31%
3. fold to cbet = 48%
4. raise cbet = 30%
5. fold to raise = 47%



beatis: 1373 hands


1. cbet = 62%
2. success = 44%
3. fold to cbet = 41%
4. raise cbet = 30%
5. fold to raise = 48%


Yongsuk Chang: 1208 hands


1. cbet = 48%
2. success = 40%
3. fold to cbet = 46%
4. raise cbet = 17%
5. fold to raise = 36%



pokerPIMP_5: 997 hands


1. cbet = 46%
2. success = 44%
3. fold to cbet = 54%
4. raise cbet = 8%
5. fold to raise = 35%

not sure what that's worth, but moving on...