Theory Post: Reraised Blind Battles and Bluffing with Marginal Hands

[sam h]

Hi. I am a lapsed limit player trying to get back into poker and trying to get serious about learning NL, especially about examining a lot of the math underlying various situations. Hopefully I will have some dedication and be around the forum relatively frequently for a while. I have gotten a lot from lurking around here and in MSNL the last month or so, and so thought I would try to "give back" by sharing some calculations and thoughts that I have been working on.

There was a recent post where players were wondering about calling 3-bets after raising in position. I think many of us realize that we can’t call these bets if we are going to play weakly after the flop (only continue with a set or on really favorable boards) but the question of when to continue or bluff with marginal hands is tricky. Since most 100 and 200NL opponents are nits when it comes to 3-betting preflop, these situations are only applicable selectively. But those spots are still important against the more agro preflop players. And with 3-betting frequencies increasing so much as stakes rise, this seems like one of the issues that SSNL players need to figure out in order to move up.

So let’s look at a situation (Stacks=100 units) in which you raise the button 3.5 units, the SB folds, the BB bumps to 11 units, and you call. So we have 22.5 units in the pot going to the flop. The flop comes down pretty dry, leaving you with a marginal holding, and the opponont of course c-bets.

The rest of this post is going to look at the equity of bluffing on a relatively dry flop while manipulating three variables: (a) your hand – AK or 55 for simplicity’s sake (b) your opponents preflop 3-betting range and (c) your opponents range for calling a bluff if you raise. These equities can be then compared to folding, which is obviously 0 EV. Obviously, we also want to know the EV of calling given certain scenarios, but this post is so long just with bluffing that I will save that and maybe do it later if this post seems interesting to enough other posters.

You Missed, but How Often Did Your Opponent?

So let’s imagine the flop comes down T73r and your opponent makes a standard continuation bet of 16 units (into 22.5). Is raising crazy here? Well how often did he actually hit that flop hard? Let’s look at results for three preflop ranges with updated probabilities based on the flop cards. (These ranges and labels may not be accurate for many games but it captures to some degree three different ideal-typical players as far as 3-betting. I did not include a simulation for a total nit, like TT+ AK+ because intuitively I am pretty sure you don’t want to challenge this player post-flop with marginal holdings).

Two simple observations to start: (a) Your opponent’s preflop range changes things dramatically but (b) generally speaking opponents will frequently have very little on a board like this.



I think the gut reaction of many players is to fold your whiffed overcards here for sure on the T73r flop and sometimes also your small pairs. But what if you raise?

The EV of raising is going to depend on how much you are risking, his calling range and thus your fold equity (FE), and your pot equity (PE) against his calling range. A pot sized raise be a total risk of 70.5 units, which is awkward. So let’s look at the equity of a couple different bluffs – first a push for 89 units and then a small raise to 45 units.

Pushing Has to be Crazy, Right?

Let’s assume that you have AdKh and push and look at each of the preflop raising profiles based on whether they would call this push with only a very strong hand (first column in table above) or also a medium strength hand (second column in table above).

(Note that now that we have AdKh, we have to discount the chance that he has an ace or a king in his hand so the probability of calling in each situation is slightly different although not very different than the probabilities in the table above).

Your equity for each situation is going to be the sum of your FE and PE, which amounts to (1-x)(38.5) + (x)(111.5y + 89(1-y)), where x is the probability he calls and y is the probability you win against his range when called. Using pokerstove to get your PE if called by his range, here is your EV in units under those circumstances.



Wow! As long as the player is loose enough preflop but needs TPTK or better to stack off, pushing is just printing money when compared to folding. I think that a lot of “good” SSNL players, including myself, have adopted fairly laggy preflop styles but are not calling a push light here in the BB as a default play and have trouble figuring out when that’s necessary.

While AK is a hand that we would always be continuing to the flop with in these situations, an obvious implication/generalization is that other high-card hands become more playable if we can identify which flops to profitably bluff raise. So perhaps a fairly powerful general conclusion can be drawn from this specific circumstance:

<font color="red"> Take Home Point #1 – Some of the most “surprisingly exploitable” players at SSNL are those who, in trying to improve and imitate the styles of known high-limit winners, have let their preflop aggression outpace their ability to counter post-flop aggression. Against this type of player, you can profit immensely by running them over on the right dry flops. This should expand your preflop calling range if you’re really going to capitalize on these opportunities. </font>

Another interesting conclusion from this is how dramatically the EV of plays changes based on seemingly small adjustments to ranges. The only difference between the SLAG and the TAG preflop is a willingness to three-bet with AJ or KQs, and the only difference between the strong and medium calling ranges of these players is a willingness to stack off with 99 or 88. But if you push here, the difference in EV between being up against a SLAG/strong range versus a TAG/medium range is 23 units!

This may say something interesting about the notion of “changing gears.” Let’s pretend we’re the BB for a second. In some sense, changing gears is about establishing an image for your opponent of the “state of the world” being a given cell of the table above and then adjusting your play to make a different cell the de facto reality. Moving to an iterated situation or one in which you are trying to mix strategies against a range obviously involves a lot more than the simple model presented here, but I think the table above does show how profitable it can be in some situations for the BB to shift gears and trap.

<font color="red"> Take Home Point #2: If your opponent is a thinking one and has likely become suspicious of your bluffing in these situations, then you need to track any changes in his 3-betting tendencies and be careful. Because if a SLAG/strong changes gears to a TAG/medium, then a must-capitalize +EV opportunity can quickly become a big –EV mistake. </font>

What About Underpairs?

So lets get back to the main discussion. What if, instead of overcards like AKo, you have a small pair like 55? Is raising still better than folding?



Things are not quite as rosy if you hold an underpair, since your equity against his calling range decreases dramatically – the draw value of AKo is much preferable to having a pair. If you know with high probability your opponents’ 3-betting and push-calling ranges, then pushing may still be profitable. But notice how much it hurts if your assumptions are wrong. For instance, with AK we may not have a great grasp of the villain’s 3-betting range, but as long as we are relatively sure that he won’t call a push with 99 or 88 then it is hard for us to make a big mistake. With 55, pushing into the nittier preflop three betters is going to be a big mistake even if they are never calling light.

<font color=" red"> Take Home Point #3: If you are going to attempt to run the opponent over, consider not the strength of your hand currently but its equity against your opponents calling range. Basically, overcards can constitute a semi-semi-bluff. </font>

Are Small Raises Really Donk-Like?

Ok, so bluff raising dry flops looks like something that needs to be added to the arsenal in some situations. But is pushing necessarily the best idea? Small raises are often derided but may be pretty effective in SSNL games. Let’s consider a situation where you raise to 40 units and your opponent will still fold all the hands he folded to a push but will push all the hands he previously called, with you then folding to that push. What does your equity look like now? (Since you are folding to the push if it comes, having AK versus 55 only matters in so far as it slightly changes the probabilities of his holdings. These calcs assume AK.)



Behold the power of the donk raise! Of course, your opponent may be less likely to fold to this raise with a medium strength hand (and will not always push over, but that’s the simulation). But I do think many SSNL players at least will fold hands like 88 or 99 here for 24 more units, feeling that calling commits them to the pot and being unsure what to do on the turn if they call and don’t improve. If you are up against that type of player, then the donk raise in this spot is almost always better than folding no matter what you have. Also notice that, against the looser preflop 3-betters, the small raise is a winning play no matter what unless they are willing to expand their repushing range even more. The small raise also obviously has the advantage of lower variance.

<font color="red"> Take Home Point #4 – Don’t discount the power of the small bluff raise. If you can find a player that will still fold medium strength hands to a small raise or is loose enough with preflop three-bets, then a small raise on dry flops can be devastating. </font>


What About Other Flops?

For the ranges examined here, the T73r flop is pretty generalizable to other flops with three relatively low cards, no flush draw, and few straight draws. I don’t see why 962, 755, T83, etc would be much different. Even J high flops are pretty similar for players with the tighter ranges, since they won’t have many more jacks than tens. Flops with As, Ks, and Qs are a different beast. Also, flops with flush draws that are low may also play differently. The chances of your opponent having the draw are actually very slim, so it shouldn’t affect the strength of his hand that much. But we would assume that opponents are going to call raises lighter if there is a flush draw, since raising the FD in our position is so typical. Therefore, it probably makes sense to think of a T73ss flop to play roughly similar to the T73r one examined here, but that the opponent is significantly more likely to be calling with a range that includes medium-strength hands.

Ok, so that got way too long. The major caveat I would add (other than the very real possibility that my math is wrong) is that naturally our overall strategy involves mixing our range and so looking at just one isolated situation should be taken with a grain of salt. Hope this provides some fodder for discussion.

[orange]

this is a really cool post. i'm reading it again.

[Requin]

Sticky

[orange]

only thing i rarely, if ever do is the small bluff raise. i used to do it a bit, but then once i realized that i will rarely raise the flop with any hand in RR-ed pots (be it a set/TPTK/2p/etc), i sortve stopped doing it. (of course this depends on board texture...if i have JTs and the board is JTx w. 2 of a suite, of course i'm raising). but as far as dry flops, meh.

[Mjafish]

fwiw, aba20 touched upon this point you made too in his well post: when bluffing keep in mind your equity vs villains calling range. hence pushing AK is better than 55.. etc

I like this post OP. nice job.

[Austiger]

[ QUOTE ]
fwiw, aba20 touched upon this point you made too in his well post: when bluffing keep in mind your equity vs villains calling range. hence pushing AK is better than 55.. etc

I like this post OP. nice job.

[/ QUOTE ]

I thought about the aba post too when I read that.

Great post sam.

[joseki]

[ QUOTE ]
Take Home Point #1 – Some of the most “surprisingly exploitable” players at SSNL are those who, in trying to improve and imitate the styles of known high-limit winners, have let their preflop aggression outpace their ability to counter post-flop aggression. Against this type of player, you can profit immensely by running them over on the right dry flops. This should expand your preflop calling range if you’re really going to capitalize on these opportunities.

[/ QUOTE ]
...uh, that'd be me.

I really like this post. Please post the calling analysis. I feel certain it will be "interesting to enough other posters".

Posts like this also make me feel guilty for lurking around 2+2 for years.

[Robert A.]

Awesome, thanks dude

[ValarMorghulis]

Brilliant post. Thanks for sharing.

[PBJaxx]

Very nice. Thanks. Sticky.