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#1
07-10-2005, 09:14 AM
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Problem Solving: Dealing with the LAG who checkraises the turn
Preface:
When I started trying to solve this problem I realized that it is much harder to accurately solve than I thought. So I had made some approximations. I did my best and I believe that my results are accurate as they confirm the intuition that I had. Also this is a long post so if you want to read the hand setup and jump to the conclusion that wouldn't be a bad way to go. I always seem to run into this problem when playing against your typical loose and very aggressive opponents. The LAG in this problem is your typical $10/$20’er with stats of VPIP of 50%, PFR of 30%, aggression factor of 3. He also loves to check raise the turn, and loves to bluff. For this problem he will defend his blinds with any two cards. He will three bet with any ace or any pair and just call my raise with any other two cards. The action: Pre-Flop: Hero is in CO with A [img]/images/graemlins/club.gif[/img]2 [img]/images/graemlins/heart.gif[/img]. Villain is in Big Blind. Two folds hero open raises from the cutoff, two more folds and our LAG in the Big Blind calls. Flop: K [img]/images/graemlins/heart.gif[/img]8 [img]/images/graemlins/club.gif[/img]3 [img]/images/graemlins/heart.gif[/img]. Big blind checks, hero bets and big blind calls. This action would take place on 85% of all flops. Turn: 4 [img]/images/graemlins/club.gif[/img] Big blind again checks. At this point there are 3.5 big bets in the pot. So my question is: What action should hero to take to maximize his EV? For this problem I am going to assume that the villain will check raise with any gutshot straight draw, any flush draw, or any pair. I am going to assume villain doesn't have a set since he would three bet any pair or that he hasn’t made two pair. Also notice that domination cannot occur since the villain doesn’t have an ace, again because he would three bet any ace. So catching an ace on the river will make me a winner, since I hold the A [img]/images/graemlins/club.gif[/img] the ace will never complete a draw. If I bet Villain will fold any hand which has no draw (i.e. he will fold JT,Q7 etc.). Also villain will bluff the river/value bet with any hand if I check the turn. So I have one of two options to bet or check. Let’s see which produces the most EV. (Here is where I need to make some BIG approximations. I would appreciate feedback to make this a more complete problem): Villain will fold any non-draw hand and any non-pair hand. I approximate that this will occur 40% of the time. Villain will raise with his pair 40% of the time (Note that this is approximately the odds that two random cards will be paired by the turn). The other 20% of the time Villain will raise with a draw. I am going to assume all draws are equal and he will have 6 outs to his draw and 6 outs to his pair for a total of 12 outs against my A2. I bet and call him down He folds with no pair .4*3.5 BB = +1.4 BB He check raises with a pair and I call down with out improvement .4*.935*3 BB = -1.122 BB // .935 = 1-3/46 He check raises with a pair and I call down but improve (I don’t get an extra bet on the river because I am a wuss) .4*9.5 BB*.065 = +.247 BB // .065 = 3/46 He check raises with his draw, I call down and his draw doesn’t come in and he doesn’t make a pair. .2*9.5 BB*.74 = +1.406 BB // .74 = 1-12/46 He check raises with his draw, I call down and he hits his draw or makes a pair. .2*.26*3 BB = -.156 BB // .26 = 12/46 My total EV from calling down is 1.775 BB I bet and fold to a raise He folds with no pair .4*3.5 BB = +1.4 BB He check raises .6*1 BB = -.6BB My total EV from betting and folding to a raise is .8 BB I check and call a bet on the river He bets on the river with an already made pair without me catching an ace .4*.935*1BB = -.374BB // .935 = 1-3/46 He bets on the river with an already made pair with me catching an ace .4*.065*5.5BB = +.143BB // .065 = 3/46 He bets on the river having made his draw or catching a pair .2*.26*1BB = -.052BB // .26 = 12/46 He bets on the river having missed his draw and not catching a pair .2*.74*5.5BB = +.814BB // .74 = 1-12/46 He bets the river on a hand he would have folded without catching a pair .4*.869*5.5BB = +1.91BB // .869 = 1-6/46 He bets the river on a hand he would have folded with catching a pair .4*.130*1BB = -.052BB // .130 = 6/46 My total EV from checking and calling is 2.4BB Conclusion: From this analysis the best line is to check the turn to induce a river bluff. This result agrees with my playing results against this type of opponent. I have implemented this line in my game vs. betting the turn and I have had great results with it. I feel that the math above shows why my results have been so good with this line. I also feel that the opponent I described above is commonly found in the $10/$20 6-max game on party. Please feel free to critique my analysis. I am sure that there are some holes which I need to account for. 
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#2
07-10-2005, 03:47 PM
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Re: Problem Solving: Dealing with the LAG who checkraises the turn
This is a nice analysis- good work. I just read it quickly, but no arguments really on your assumptions.
Another tough spot is holding something like QJo against this type of player. Now that you can't really snap off bluffs on the river, it seems bet-folding is at least +EV even though it feels crappy to me getting raised so often.
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