Preflop raising decisions can be very complex. What stakes are we playing? Is it a live game or online? How strong is our hand? Which limpers will call? Will we be in position postflop?
Higher Level Poker. The following are more advanced strategy articles written by Jack Wilcox, who was a winning cash game player up to $400NL.They were originally posted on his Higher Level Poker training site for small/micro stakes players. These strategy articles make use of player stats like VPIP/PFR. Traits Of The Best 100 Big Blind Cap Game Players The 2-5 No Limit Hold'em level of cash games, is the beginning point where a significant amount of money can be made. At lower levels, the lack of stack depth and higher relative rake, cut into profits to a large degree. An intelligent player at these stakes in poker can make enough money to grind out a living if need be. Master 1 2 No Limit Holdem Strategy Most players try to end hands early when they feel like they have the best hand. 'Don't want to get drawn out on,' they think. Starting with Opening Hands. The hands that you choose to go into battle with in Texas Hold'em are.
Sometimes our decision is obvious: 'I have aces, so I'm going to raise for value here.' Sometimes it's subjective: 'I think I can force the limper to fold here.' But we should also consider what a mathematical analysis of preflop raising can teach us. When is a raise our most profitable action for the moment? When might it be the most profitable action for the hand?
Las Vegas $1/$2 NLH Stats
In order to calculate the expected value for our preflop actions accurately, we need to know certain key frequencies that are typical for our game.
Figure 1 below contains some of the most useful stats for these EV calculations for both online NL100 and $1/$2 NL live games in Las Vegas, most of them published here for the first time. (Check out Donkey Poker Volume 2: Postflop, Section 7.5 to see how these stats were generated.)
Here I define 'EP/MP' as the first four seats after the big blind on a nine-seat table. Since the vast majority of Vegas $1/$2 players are position-dumb, we can combine the results from these seats into a single stat in order to make the stat more reliable. The hijack and cutoff stats are similar to the EP/MP stats.
No Limit Holdem Sites
VPIP and PFR are the primary stats useful to determine an opponent's playing style. '35/6' means that the average Vegas player voluntarily invests in 35 percent of his dealt hands, while raising only 6 percent of them. This player would be considered a 'loose-passive' player in an online game, but he is average in a Vegas $1/$2 game.
Calling a Preflop Raise (CPFR) is a statistic that applies only when a player calls a raise after having already invested in the pot, which applies to limp-callers as well as to the blinds. This is not the same thing as Cold Calling Preflop (CCPF).
Compared to an online game, a Vegas preflop raise is fraught with more risk. Not only is our average raise size larger, our Vegas opponents are more likely to call it. Although their calling range is weaker, we often face multiple callers, which is rare online. Consequently, it is extremely important to have a solid idea of how these stats influence the profitability of our preflop action.
A Simple Example: A Big Blind Hero vs. a Single EP/MP Limper
Let's consider a situation which is relatively easy to calculate. Suppose an average player limps from one of the EP/MP positions. It folds around to Hero in the big blind who can check his option or raise.
Figure 1 indicates that that Mr. Average has a range of 35 percent, but he normally raises with 6.1 percent of this range. So we can assign his limping range as [6.1–35]. The specific card combos within his range depend on the ranking system we use. Although there is no single ranking system that is always correct, I will use the Flopzilla NLHE ranking in this column, since it is easy for anyone to access.
Suppose Hero has and decides to check. We can estimate Hero's 'Momentary Expected Value' (MEV) as...
MEVCheck = Pot0 × EWC = $5 × 0.474 = $2.37
...where Pot0 = $5 and EWC (Showdown Equity When Called) is 47.4 percent for Hero's pocket deuces when facing Villain's range. I call this his 'momentary' EV since it applies only at the moment he checks.
Suppose Hero decides to raise to $10 with the same . Figure 1 shows that an average villain will call a preflop raise after limping in EP/MP about 56 percent of the time (Row 8). This would be a Flopzilla range of [6.1–22.7].
Hero's Fold Equity is FE = (1 - 0.564) = 0.436. His showdown Equity-When-Called is EWC = 0.454. Notice that even though the villain has folded nearly half of his range, Hero's EWC is only slightly worse than when he checks. This suggests that the villain's actual limping and calling ranges are not critical in establishing Hero's MEV.
After deciding to raise, we can calculate Hero's MEV as...
MEVRaise-$8 = (FE × Pot0) + ((1-FE) × (EWC × Pot1 - Raise)) = $2.27 + $0.28 = $2.55
The first term is just the average amount earned when the villain folds. The second term is the amount earned when the villain calls. ' Pot1' is the size of the pot after he calls, minus the rake. 'Raise' is the size of our raise ($8 in this case). Since three-betting is so rare in Vegas $1/$2, and limp-three-betting is even rarer, we can ignore it for this calculation. Again, we consider this our momentary EV since it only applies at the end of the preflop action.
So Hero's raise appears to be more profitable (by $0.18) than checking. It gains nearly all of its profitability from fold equity and a just little from showdown equity. This is generally the case for heads-up battles.
However, there is a serious issue with these estimates. MEV uses showdown equity, which essentially assumes that the hand will be checked down postflop. This rarely happens in a real game, which makes its usefulness imperfect. We haven't considered such factors as skill and position, which can increase or decrease our expected profit in the hand. Hero's inferior position in this scenario suggests that his actual 'Hand EV' (HEV) will be lower than his calculated MEV. Even Hero's superior skill will not likely overcome his inferior position.
Since Hero's inferior postflop position makes it difficult to realize the full MEV of either action, it's difficult to say which action would have the higher HEV. Hero's best decision could depend on whether the villain appears more or less likely than the average villain to fold to Hero's raise. We might also consider that if both actions result in a similar HEV, the check does so with less risk.
Figure 2 shows the results of these calculations applied to some of the hands listed in the Donkey Poker starting hands chart. The solid symbols represent Hero's MEV when raising to $10, which is positive for each of these combos. 'JTs-' denotes 'suited connectors JTs and smaller.' Meanwhile the '+' symbols represent the difference in MEV between raising and checking.
When MEV is positive, raising is more profitable than checking, which is true for a range including approximately 22+, A2+, KT+, and QJ (i.e., any pocket pair, any ace-x hand, any two Broadway cards). This represents 27.6 percent of all starting hands.
Since we are out of position in the scenario, our HEV is probably lower than these values, so checking is probably preferable when the Delta MEV is close to zero.
Button Hero vs. One Limper
The previous scenario is rare in Vegas $1/$2 games, but it serves to illustrate the principals used for our analytical EV calculations. A more common and useful example is when the Hero is on the button with and facing a single EP/MP limper. In this case Hero can fold, limp, or raise, where folding has an EVfold = 0.
This calculation has additional complexity because we have the blinds behind us, which means we must consider their propensity to check behind or complete and their propensity to call a raise. (We will ignore their negligible three-betting frequency here.)
Suppose Hero limps and the two blinds raise 4.8 percent and 3.4 percent of the time, respectively. If the small blind completes with [4.8-50] and the big blind has a range of [3.4-100], we will have a four-way pot about 92 percent of the time.
Let's suppose the other 8 percent of the time Hero limp-folds after one of the blinds raises. (This is plausible for those hands with which Hero would actually limp.) We can also assume that the EP/MP limper has a range of [6.1-35.7]. All of these values are based on the actual Vegas stats listed in Figure 1.
We then have...
MEVLimp = 0.92 × (Pot0 × EWC-Limp) - (0.08 × Limp) = 0.92 × ($8 × 0.222 - $2) - (0.08 × $2) = -$0.38
In other words, limping on the button with is not immediately profitable.
Suppose we raise to $10 with on the button. Using the above frequencies, everyone will fold 23.1 percent of the time. A single villain will call 47.0 percent of the time, two villains will call 25.7 percent of the time, and everyone will call 4.2 percent of the time.
It turns out our EWC is nearly the same no matter which villain calls, so we can treat each villain as interchangeable. Thus, Hero's MEV is approximately...
MEVRaise = (0.231 × Pot0) + (0.47 × (EWC1 × Pot1 - Raise)) + (0.257 × (EWC2 × Pot2 - Raise)) + (0.042 × (EWC3 × Pot3 - Raise)) = $0.63
...where the various values depend on how many players called our raise. We can see that raising with our pocket deuces is much more immediately profitable than limping with them. Furthermore, our Hand EV should be better than this since we have superior position and skill and since we can leverage our profit when we flop a set.
Note that when the blinds are tight and/or passive, they are less likely to call our raise and less likely to three-bet. (Pre-loading tells are very important here.) In these situations, raising a single limper from the button is even more +MEV. And our HEV is even more enhanced since we are less likely to face multiple villains in a raised pot. (It's generally easier to outplay a single villain than three of them.)
Figure 3 depicts the MEV results for various hand types. The symbols represent the MEV for raising to $10 in a Vegas $1/$2 game. Each series represents a descending hand grouping. For example, 'T9s-' denotes 'suited connectors T9s and smaller.'
Bottom line: in low-stakes cash games such as the $1/$2 NL games in Vegas, raising is nearly always more profitable than limping (except for 63s, 53s, 65o and 54o). In fact, 33 percent of all starting combos are immediately profitable. And some of the negative-MEV combos are probably profitable for the hand due to our superior position.
Since most Vegas $1/$2 players are position-dumb, they generally limp and call with a similar frequency from the hijack and cutoff positions. So our very wide button raising range is valid for any single-limper situation when we are on the button.
Button Hero vs. Multiple Limpers
The previous single-limper scenario occurs only a small fraction of the time in Vegas $1/$2 games. We can readily extend this to multiple-limper scenarios, which are much more common. This calculation is even more complex and we are less likely to fold everyone out with a $10 button raise. This time I will spare you the gory math and show you the results below in Figure 4.
Here the top four curves represent the MEV for raising to $10 facing one, two, three, and four limpers. The smooth line represents the average MEV of limping. These curves show that our 'immediately profitable' raising range is 33.6 percent when facing a single limper, and that our range decreases to 13.4 percent when facing four limpers.
We can make several conclusions here:
- The more limpers we face, the tighter our raising range should be from the button.
- When facing one or two limpers, we should generally either raise or fold, since once raising becomes unprofitable, limping is even more unprofitable.
- When facing three or more limpers, limping is generally more profitable than raising once raising becomes unprofitable. So we now have both raising and limping ranges.
- When both raising and limping have MEVs near zero, limping may be preferable since we risk less for the same reward.
- Our slightly negative-MEV combos may still have slightly positive-EV for the hand. Our superior skill and position, coupled with our ability to leverage our big flops should increase our profit for the hand. This is combo-dependent since some combos are more likely to flop big. (22 is stronger than 54o.)
- Another way to state this is that some -MEV combos may have sufficient implied odds play. For instance, we can play a -$0.50 MEV combo if we believe our implied EV for the hand is worth more than this.
The Effect of Raise Size
A typical rule of thumb for these Vegas $1/$2 games is to raise to about 4x BB plus one additional BB for each limper. Thus we would raise to $10, $12, $14, or $16 as the number of limpers increases. The previous analysis kept the raise size constant to see the influence of the number of limpers.
A key question we would like answered is how the villains will respond to reasonable variations in raise size. Unfortunately, that data does not exist for these Vegas games. My general feeling, however, is that most Vegas $1/$2 players are not very sensitive to our raise size as long as we keep it within the table norm. So, to a first approximation, we can assume that the Figure 1 stats do not change very much when we increase our raise size incrementally.
Figure 5 shows what happens to MEVRaise as we increase the size of our raise when facing four limpers. We can see that that our raising range decreases slightly as we increase our raise size. This effect is fairly small and may be counterbalanced by a decreased likelihood that a villain will call a larger raise.
Here the symbols represent the MEV for raising to $10, $12, $14 or $16 in a Vegas $1/$2 game. These combos are sorted in order of MEVRaise.
The important thing to notice in this graph is that we have a much larger MEV when we raise our best hands by the maximum amount that will not result in a villain adjustment. If we have aces and the villains will call a $16 bet as often as a $10 bet, we should bet $16.
On the other hand, we should consider betting smaller with our borderline raising hands. Of course, this sets up the possibility that we could be telegraphing our hand strength. But most Vegas $1/$2 players are not paying much attention to our bet size unless the size is unusual for the table. Here we can make adjustments based on our knowledge of the players at our table.
Hero is in the Cutoff
Putting the Hero in the cutoff makes the analysis even more complex. Making some reasonable approximations, I can make a few generalizations:
- All players, including the button, are very unlikely to three-bet, so we should generally ignore this possibility when deciding to raise. (If our particular button opponent likes to three-bet, we should consider changing seats.)
- The button is less likely to cold call our cutoff raise than an EP/MP player is to call after a limp.
- Being in the cutoff facing three limpers is similar to being on the button facing four limpers. This is equivalent to the button replacing the fourth limper.
- The average button will call our cutoff raise about 22 percent of the time. We will then not have a postflop position advantage on every villain. This means that our average HEV will not be as enhanced from the cutoff as it would be from the button, and thus our cutoff raising range should be somewhat tighter that it would be from the button with one additional limper.
- If we have a tell that suggests that the button intends to fold, we can play the cutoff exactly as we would normally play the button.
Conclusions
We can't yet decide on a specific hand range for each scenario since we have not yet determined just how valuable our superior position and skill is. Nevertheless, it is clear that the more limpers we face, the tighter our raising raise should be.
Also, our raising range should be much wider than the typical Vegas player. We can also play from the cutoff facing X limpers with a similar range as from the button when facing X+1 limpers.
And of course, we should always adjust our ranges depending on the tendencies of the specific villains we face and based on specific tells we observe.
Steve Selbrede has been playing poker for 20 years and writing about it since 2012. He is the author of five books, The Statistics of Poker, Beat the Donks, Donkey Poker Volume 1: Preflop, Donkey Poker Volume 2: Postflop, and Donkey Poker Volume 3: Hand Reading.
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Update: Did you know I have a poker tells video series? Check it out here.
In the past couple of weeks (November 2012), I played a few sessions of live $1-2 NLHE with the purpose of studying what poker tell information was the most important and relevant. It'd been a while since I played $1-2 (haven't been playing much at all lately with the exception of some $2-5 and the occasional $100+ tournament), so I was kind of curious what I'd find.
Before getting to the tells, a few caveats about using tells in a live $1-2 NLHE game:
Limit Holdem Rules
- Playing in these games reminded me that, for your average live $1-2 player, thinking about poker tells is far from the best use of their time. Not that poker tells aren't present; they are, but most players' time would be much better spent studying some basic strategies and not looking for tells. So if you're a struggling live $1-2 player, long before doing something like reading one of my books on poker tells, or getting my video series, I'd instead recommend reading a basic strat book like Dan Harrington on Cash Games, James Sweeney's Dynamic Full Ring Poker, or Ed Miller's Small Stakes No Limit Hold'em. I mention this mainly because I think there are many $1-2 players who think they are better than they are, and who need a lot of work put in on basic strategy. Only when you are a decent winner at $1-2 would I recommend spending a good amount of time thinking about tells/behavior.
- Looking for poker tells can often have limited use in a game where players often do weird, goofy, illogical things, which can often be common in a live $1-2 game. For example, getting a read that a player has a weak hand doesn't do you much good if that player is weirdly going to give a lot of action with that hand. A lot of players at live $1-2 will passively call off a lot of chips with a pair and a draw, or even just a draw, even if they wouldn't bet it themselves. Many players also overvalue hands like AK and AQ, and will put a lot of chips in pre-flop with those hands. (Of course, there are also a lot of nitty players at these stakes, too, so noticing player tendencies/styles is important.)
- I usually say that post-bet tells, when they come after significant bets, are the most important tells to look for. But there are a lot of very passive players at lower stakes who only make big bets when they have strong hands. For these types of players, there are no real post-bet tells to speak of, reducing a lot of the kinds of tells you might be using more frequently in higher-stakes games where players are more aggressive/active. For many passive players, you can forget about studying them for post-bet tells, just because the likelihood of them ever making a significant bluff is highly unlikely. (This also emphasizes the idea that aggressive players are best to study for tells because you'll see them in a lot of pots.)
Decision points
Let's look at some of the most important decision points where tells can help play a role in your average live $1-2 NLHE game (with a good amount of passive/tight players):
• Deciding when to continuation bet with weak hands in multi-way pots
• Deciding when to bluff the turn
• Deciding when to bluff the river
Most of these spots will boil down to fundamental strategy and player tendencies. But every once in a while a poker tell can help you out in one of these spots.
Studying poker tells can be quite valuable for low-stakes players, not so much for the purposes of spotting other people's tells, but because they'll help you prevent leaking your own tells. Knowing the common ways information can be leaked will help you become unreadable. And I think this is the best reason for lower stakes players to study tells.
Most important tells
So what poker tells are most important at your average live $1-2 game?
• Immediate calls
• Taking a long time to check when weak
• Defensive chip handling when weak
• After cards arrive, staring at board when weak
These are mostly waiting-for-action tells, as opposed to post-bet tells, which makes sense as you'll usually be dealing with players who aren't betting that much and who are instead more passive and doing a lot of calling. I'll explain these all in order and give a couple examples.
Immediate calls
Immediate calls are one of the most useful bet-timing tells. When someone makes an immediate call, it means they've quickly decided not raise. Because players with strong hands tend to at least consider a raise (even if they end up calling), this means almost all immediate calls are made with weak and medium-strength hands and draws. This tell is rampant in low-stakes games.
For instance, in a few hands, players called my continuation-bet on the flop immediately. This tells me that, almost all of the time, they are on the weaker side of their range. If I am bluffing or semi-bluffing, I will continue bluffing on the turn most of the time with this read. For example, I raise pre-flop with KJo and get heads-up. The board is T -7-4 rainbow. I bet and the player immediately calls. I will usually continue betting the turn and maybe even the river, because I think the player will most often have, at most, a ten, and often a lot of hands like 99 and 88 or 98.
I would also you want to be choosy about who you're attempting to bluff. I wouldn't want to do this against a calling station, because you could be completely correct in reading them for a weak hand but they still may call you down or even just shove in with their hand. So you want to ideally be focusing on players you know are capable of folding.
Master 1 2 No Limit Hold'em Strategy
Also, board texture is a factor in understanding immediate calls. For more aggressive players, immediate calls will also mean that it's very unlikely they have a strong flush draw. For example, you continuation-bet a board of Kh 9h 3s and your opponent immediately calls you. If this player is capable of bluffing at all, this immediate call will make strong draws like Ax of hearts and QT of hearts very unlikely, because that player would probably at least consider a raise, even if he ended up deciding to call. So in a lot of cases, immediate calls can help you define a player's range a bit more than usual.
Taking a long time to check when weak
Some players will take a long time to check to the aggressor when they hold weak hands. Don't use this tell generally, though, because most players will vary their bet- and check-timing enough (both consciously and because there can be a lot of thought-inducing situations with many different types of hands) that it's hard to get a good read. But against some players it can be very useful information.
For example, let's say a player calls your pre-flop raise, hits a medium pair on the flop, checks to you and calls your flop bet. The turn card comes, doesn't improve him, and he then takes like ten seconds to check to you. Whereas if he had a top-pair hand or better, where he knew he was probably going to be calling, he would only take a couple of seconds to check.
I'm not saying this is extremely useful information, because sometimes, with a medium-strength hand, $1-2 players will call you anyway. It's going to be mainly useful against the most nitty players; the ones you know are scared to carry on without very strong hands. Those are the ones who you might bet off the hand on the turn if you get some sense of weakness.
Along with taking a long time to check, a player might look very studious in studying the board, as if trying to figure out what to do. That combined behavior is usually a sign of a vulnerable hand. As is the following tell, which you can sometimes see in concert with these:
Defensive chip handling when weak
The gist of this one is that players will often try to make you think they're interested in calling by handling their chips in a defensive manner when it's your turn to act. They might hold their chips in their hand, as if ready to put them in. They might start cutting out chips as if ready to call. Basically, any chip handling action that looks vaguely defensive in nature, even if it's quite subtle, is usually a sign that the player holds a vulnerable hand. When a player holds a strong hand, they want to give no impediment to your bet, no matter how small.
This is a very useful one; it's one that came up a handful of times in hands I was in, making me feel better about making a large river bluff. In one hand in particular, I had been betting first to act on the flop and turn, and I thought it was quite possible my opponent had flopped the flush draw. When a low flush card came on the river, I probably usually would have given up on the bluff, except for the fact I saw him riffling his chips in his hand while he stared at me (staring at an opponent when they're waiting to act can also be a sign of weakness), so I bet $100 and he folded.
Two other hands went down very similarly to that. In one three-bet pot, where I'd three-bet and whiffed with AQ, an opponent called the flop, but I pushed all-in on a turn of 9JK3 based on my opponent grabbing his chips and holding them up defensively as he checked to me. It wasn't usually a spot I would have felt so comfortable in.
Again, even if this tell is only 75% reliable, that's still a great reason to carry through on a bluff that's already got a lot of logic behind it; in my experience, though, this tell is more reliable than that for most players.
Staring at hole cards and board cards when weak
When players stare at cards, whether it's their own hole cards or the board cards, it will generally mean they don't have a strong hand. I had forgotten how much the staring-at-cards when weak type of tells apply to low stakes.
Why is this a pattern? Players who look at strong hands tend to look away quickly. There's an instinct to 'hide their treasure' from their enemies or competitors. This accounts for the common tendency of players to look at pocket aces and immediately put them down. Whereas players with weak hands don't have a reason to look away.
Pre-flop, this can be useful when you spot limpers or players behind you looking for a second or two or longer at their cards. When you see this, and if you've decided it's a reliable tell for those players, you can choose to become more aggressive in the hand. For example, you see a few limpers staring at their cards before they call, and you decide to raise pre-flop lighter than you normally would. Or you see a late-position player staring at his cards for a few seconds and he ends up raising. You might decide to call him or 3-bet him lighter than normal.
Of course, players are still capable of calling you with their weaker hands, and then you'll have to play some post-flop poker. But because the read is generally reliable (and sometimes very reliable for some specific players), you'll be putting yourself in a lot of profitable post-flop situations where a flop bet will often take down the pot.
Sometimes players look back at their hole cards after the flop, too, and the longer they look at their cards the more it becomes likely they're weak.
For communal cards, it's the same basic idea: players who connect well (like top pair or better) tend to look away from the board when the cards come out. This can be seen as an involuntarily, unconscious attempt to distract attention away from their 'treasure.' Staring at communal cards, with no looking away, will tend to mean the player had no real reason to look away or be thoughtful about the hand.
Playing some $1-2 again, I got back into the habit of trying to watch everyone in the hand during multi-way flops, trying to see if anyone looked away immediately. Mainly I tried to watch the player or players behind me, because that is more valuable information than what the players in front of me do.
For example, in most three-way (or more) pots, if I'm the pre-flop raiser, I usually will shut down if the board comes down pretty scary and I haven't connected. Like if I raise pre-flop and the board is 9TQ or something similar, I generally check if I raised with 6-7 suited, or AK, or something that missed completely, because those are the types of boards that hit right in the range of most players who call a raise. Whereas on a really dry board, like K-7-3 rainbow, I will usually bet my misses into two other players (but not usually three other players).
But looking for opponents who are staring at the flop can make me feel more comfortable about betting into a multi-way pot. It happened several times in three-way and four-way pots where I wouldn't usually have bet from a fundamental strategy perspective, but the amount of staring going on by my opponents made me feel safer. Occasionally, I would still get one caller out of the bunch, but that still put me in more profitable spots than not betting, and I felt more confident, based on their staring, that they had weak hands.
Again, this is not something you want to use to make very large decisions. Good players are capable of staring consistently at the flop whether they hit or not. And even for the people who exhibit this tell very reliably, it won't always be accurate. This will mainly be useful for determining fairly borderline situations, like when you decide to get aggressive and follow through on flop bets in multiway pots, or follow through on turn bets. Or, when you see people looking away from the board cards, for deciding to take a more passive line. There are a lot of fairly borderline situations where checking or betting or raising could go either way, so a little extra information can go a long way.
Conclusions
All in all, I never want to give the impression that tells are something that will let you crush microstakes, or any game for that matter. I think they can give you little hints here and there for the best action to take, but these are often actions that are dictated by fundamental strategy. Occasionally, you can get really obvious signs from some players that dictate a very specific course of action, but you shouldn't try too hard to look for those spots. Those are spots that will come to you naturally, the more comfortable you get with tells.
Hero's Fold Equity is FE = (1 - 0.564) = 0.436. His showdown Equity-When-Called is EWC = 0.454. Notice that even though the villain has folded nearly half of his range, Hero's EWC is only slightly worse than when he checks. This suggests that the villain's actual limping and calling ranges are not critical in establishing Hero's MEV.
After deciding to raise, we can calculate Hero's MEV as...
MEVRaise-$8 = (FE × Pot0) + ((1-FE) × (EWC × Pot1 - Raise)) = $2.27 + $0.28 = $2.55
The first term is just the average amount earned when the villain folds. The second term is the amount earned when the villain calls. ' Pot1' is the size of the pot after he calls, minus the rake. 'Raise' is the size of our raise ($8 in this case). Since three-betting is so rare in Vegas $1/$2, and limp-three-betting is even rarer, we can ignore it for this calculation. Again, we consider this our momentary EV since it only applies at the end of the preflop action.
So Hero's raise appears to be more profitable (by $0.18) than checking. It gains nearly all of its profitability from fold equity and a just little from showdown equity. This is generally the case for heads-up battles.
However, there is a serious issue with these estimates. MEV uses showdown equity, which essentially assumes that the hand will be checked down postflop. This rarely happens in a real game, which makes its usefulness imperfect. We haven't considered such factors as skill and position, which can increase or decrease our expected profit in the hand. Hero's inferior position in this scenario suggests that his actual 'Hand EV' (HEV) will be lower than his calculated MEV. Even Hero's superior skill will not likely overcome his inferior position.
Since Hero's inferior postflop position makes it difficult to realize the full MEV of either action, it's difficult to say which action would have the higher HEV. Hero's best decision could depend on whether the villain appears more or less likely than the average villain to fold to Hero's raise. We might also consider that if both actions result in a similar HEV, the check does so with less risk.
Figure 2 shows the results of these calculations applied to some of the hands listed in the Donkey Poker starting hands chart. The solid symbols represent Hero's MEV when raising to $10, which is positive for each of these combos. 'JTs-' denotes 'suited connectors JTs and smaller.' Meanwhile the '+' symbols represent the difference in MEV between raising and checking.
When MEV is positive, raising is more profitable than checking, which is true for a range including approximately 22+, A2+, KT+, and QJ (i.e., any pocket pair, any ace-x hand, any two Broadway cards). This represents 27.6 percent of all starting hands.
Since we are out of position in the scenario, our HEV is probably lower than these values, so checking is probably preferable when the Delta MEV is close to zero.
Button Hero vs. One Limper
The previous scenario is rare in Vegas $1/$2 games, but it serves to illustrate the principals used for our analytical EV calculations. A more common and useful example is when the Hero is on the button with and facing a single EP/MP limper. In this case Hero can fold, limp, or raise, where folding has an EVfold = 0.
This calculation has additional complexity because we have the blinds behind us, which means we must consider their propensity to check behind or complete and their propensity to call a raise. (We will ignore their negligible three-betting frequency here.)
Suppose Hero limps and the two blinds raise 4.8 percent and 3.4 percent of the time, respectively. If the small blind completes with [4.8-50] and the big blind has a range of [3.4-100], we will have a four-way pot about 92 percent of the time.
Let's suppose the other 8 percent of the time Hero limp-folds after one of the blinds raises. (This is plausible for those hands with which Hero would actually limp.) We can also assume that the EP/MP limper has a range of [6.1-35.7]. All of these values are based on the actual Vegas stats listed in Figure 1.
We then have...
MEVLimp = 0.92 × (Pot0 × EWC-Limp) - (0.08 × Limp) = 0.92 × ($8 × 0.222 - $2) - (0.08 × $2) = -$0.38
In other words, limping on the button with is not immediately profitable.
Suppose we raise to $10 with on the button. Using the above frequencies, everyone will fold 23.1 percent of the time. A single villain will call 47.0 percent of the time, two villains will call 25.7 percent of the time, and everyone will call 4.2 percent of the time.
It turns out our EWC is nearly the same no matter which villain calls, so we can treat each villain as interchangeable. Thus, Hero's MEV is approximately...
MEVRaise = (0.231 × Pot0) + (0.47 × (EWC1 × Pot1 - Raise)) + (0.257 × (EWC2 × Pot2 - Raise)) + (0.042 × (EWC3 × Pot3 - Raise)) = $0.63
...where the various values depend on how many players called our raise. We can see that raising with our pocket deuces is much more immediately profitable than limping with them. Furthermore, our Hand EV should be better than this since we have superior position and skill and since we can leverage our profit when we flop a set.
Note that when the blinds are tight and/or passive, they are less likely to call our raise and less likely to three-bet. (Pre-loading tells are very important here.) In these situations, raising a single limper from the button is even more +MEV. And our HEV is even more enhanced since we are less likely to face multiple villains in a raised pot. (It's generally easier to outplay a single villain than three of them.)
Figure 3 depicts the MEV results for various hand types. The symbols represent the MEV for raising to $10 in a Vegas $1/$2 game. Each series represents a descending hand grouping. For example, 'T9s-' denotes 'suited connectors T9s and smaller.'
Bottom line: in low-stakes cash games such as the $1/$2 NL games in Vegas, raising is nearly always more profitable than limping (except for 63s, 53s, 65o and 54o). In fact, 33 percent of all starting combos are immediately profitable. And some of the negative-MEV combos are probably profitable for the hand due to our superior position.
Since most Vegas $1/$2 players are position-dumb, they generally limp and call with a similar frequency from the hijack and cutoff positions. So our very wide button raising range is valid for any single-limper situation when we are on the button.
Button Hero vs. Multiple Limpers
The previous single-limper scenario occurs only a small fraction of the time in Vegas $1/$2 games. We can readily extend this to multiple-limper scenarios, which are much more common. This calculation is even more complex and we are less likely to fold everyone out with a $10 button raise. This time I will spare you the gory math and show you the results below in Figure 4.
Here the top four curves represent the MEV for raising to $10 facing one, two, three, and four limpers. The smooth line represents the average MEV of limping. These curves show that our 'immediately profitable' raising range is 33.6 percent when facing a single limper, and that our range decreases to 13.4 percent when facing four limpers.
We can make several conclusions here:
- The more limpers we face, the tighter our raising range should be from the button.
- When facing one or two limpers, we should generally either raise or fold, since once raising becomes unprofitable, limping is even more unprofitable.
- When facing three or more limpers, limping is generally more profitable than raising once raising becomes unprofitable. So we now have both raising and limping ranges.
- When both raising and limping have MEVs near zero, limping may be preferable since we risk less for the same reward.
- Our slightly negative-MEV combos may still have slightly positive-EV for the hand. Our superior skill and position, coupled with our ability to leverage our big flops should increase our profit for the hand. This is combo-dependent since some combos are more likely to flop big. (22 is stronger than 54o.)
- Another way to state this is that some -MEV combos may have sufficient implied odds play. For instance, we can play a -$0.50 MEV combo if we believe our implied EV for the hand is worth more than this.
The Effect of Raise Size
A typical rule of thumb for these Vegas $1/$2 games is to raise to about 4x BB plus one additional BB for each limper. Thus we would raise to $10, $12, $14, or $16 as the number of limpers increases. The previous analysis kept the raise size constant to see the influence of the number of limpers.
A key question we would like answered is how the villains will respond to reasonable variations in raise size. Unfortunately, that data does not exist for these Vegas games. My general feeling, however, is that most Vegas $1/$2 players are not very sensitive to our raise size as long as we keep it within the table norm. So, to a first approximation, we can assume that the Figure 1 stats do not change very much when we increase our raise size incrementally.
Figure 5 shows what happens to MEVRaise as we increase the size of our raise when facing four limpers. We can see that that our raising range decreases slightly as we increase our raise size. This effect is fairly small and may be counterbalanced by a decreased likelihood that a villain will call a larger raise.
Here the symbols represent the MEV for raising to $10, $12, $14 or $16 in a Vegas $1/$2 game. These combos are sorted in order of MEVRaise.
The important thing to notice in this graph is that we have a much larger MEV when we raise our best hands by the maximum amount that will not result in a villain adjustment. If we have aces and the villains will call a $16 bet as often as a $10 bet, we should bet $16.
On the other hand, we should consider betting smaller with our borderline raising hands. Of course, this sets up the possibility that we could be telegraphing our hand strength. But most Vegas $1/$2 players are not paying much attention to our bet size unless the size is unusual for the table. Here we can make adjustments based on our knowledge of the players at our table.
Hero is in the Cutoff
Putting the Hero in the cutoff makes the analysis even more complex. Making some reasonable approximations, I can make a few generalizations:
- All players, including the button, are very unlikely to three-bet, so we should generally ignore this possibility when deciding to raise. (If our particular button opponent likes to three-bet, we should consider changing seats.)
- The button is less likely to cold call our cutoff raise than an EP/MP player is to call after a limp.
- Being in the cutoff facing three limpers is similar to being on the button facing four limpers. This is equivalent to the button replacing the fourth limper.
- The average button will call our cutoff raise about 22 percent of the time. We will then not have a postflop position advantage on every villain. This means that our average HEV will not be as enhanced from the cutoff as it would be from the button, and thus our cutoff raising range should be somewhat tighter that it would be from the button with one additional limper.
- If we have a tell that suggests that the button intends to fold, we can play the cutoff exactly as we would normally play the button.
Conclusions
We can't yet decide on a specific hand range for each scenario since we have not yet determined just how valuable our superior position and skill is. Nevertheless, it is clear that the more limpers we face, the tighter our raising raise should be.
Also, our raising range should be much wider than the typical Vegas player. We can also play from the cutoff facing X limpers with a similar range as from the button when facing X+1 limpers.
And of course, we should always adjust our ranges depending on the tendencies of the specific villains we face and based on specific tells we observe.
Steve Selbrede has been playing poker for 20 years and writing about it since 2012. He is the author of five books, The Statistics of Poker, Beat the Donks, Donkey Poker Volume 1: Preflop, Donkey Poker Volume 2: Postflop, and Donkey Poker Volume 3: Hand Reading.
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cash game strategyno-limit hold'empreflop strategystarting hand selectionpositionbet sizingpot oddslive pokertells
Update: Did you know I have a poker tells video series? Check it out here.
In the past couple of weeks (November 2012), I played a few sessions of live $1-2 NLHE with the purpose of studying what poker tell information was the most important and relevant. It'd been a while since I played $1-2 (haven't been playing much at all lately with the exception of some $2-5 and the occasional $100+ tournament), so I was kind of curious what I'd find.
Before getting to the tells, a few caveats about using tells in a live $1-2 NLHE game:
Limit Holdem Rules
- Playing in these games reminded me that, for your average live $1-2 player, thinking about poker tells is far from the best use of their time. Not that poker tells aren't present; they are, but most players' time would be much better spent studying some basic strategies and not looking for tells. So if you're a struggling live $1-2 player, long before doing something like reading one of my books on poker tells, or getting my video series, I'd instead recommend reading a basic strat book like Dan Harrington on Cash Games, James Sweeney's Dynamic Full Ring Poker, or Ed Miller's Small Stakes No Limit Hold'em. I mention this mainly because I think there are many $1-2 players who think they are better than they are, and who need a lot of work put in on basic strategy. Only when you are a decent winner at $1-2 would I recommend spending a good amount of time thinking about tells/behavior.
- Looking for poker tells can often have limited use in a game where players often do weird, goofy, illogical things, which can often be common in a live $1-2 game. For example, getting a read that a player has a weak hand doesn't do you much good if that player is weirdly going to give a lot of action with that hand. A lot of players at live $1-2 will passively call off a lot of chips with a pair and a draw, or even just a draw, even if they wouldn't bet it themselves. Many players also overvalue hands like AK and AQ, and will put a lot of chips in pre-flop with those hands. (Of course, there are also a lot of nitty players at these stakes, too, so noticing player tendencies/styles is important.)
- I usually say that post-bet tells, when they come after significant bets, are the most important tells to look for. But there are a lot of very passive players at lower stakes who only make big bets when they have strong hands. For these types of players, there are no real post-bet tells to speak of, reducing a lot of the kinds of tells you might be using more frequently in higher-stakes games where players are more aggressive/active. For many passive players, you can forget about studying them for post-bet tells, just because the likelihood of them ever making a significant bluff is highly unlikely. (This also emphasizes the idea that aggressive players are best to study for tells because you'll see them in a lot of pots.)
Decision points
Let's look at some of the most important decision points where tells can help play a role in your average live $1-2 NLHE game (with a good amount of passive/tight players):
• Deciding when to continuation bet with weak hands in multi-way pots
• Deciding when to bluff the turn
• Deciding when to bluff the river
Most of these spots will boil down to fundamental strategy and player tendencies. But every once in a while a poker tell can help you out in one of these spots.
Studying poker tells can be quite valuable for low-stakes players, not so much for the purposes of spotting other people's tells, but because they'll help you prevent leaking your own tells. Knowing the common ways information can be leaked will help you become unreadable. And I think this is the best reason for lower stakes players to study tells.
Most important tells
So what poker tells are most important at your average live $1-2 game?
• Immediate calls
• Taking a long time to check when weak
• Defensive chip handling when weak
• After cards arrive, staring at board when weak
These are mostly waiting-for-action tells, as opposed to post-bet tells, which makes sense as you'll usually be dealing with players who aren't betting that much and who are instead more passive and doing a lot of calling. I'll explain these all in order and give a couple examples.
Immediate calls
Immediate calls are one of the most useful bet-timing tells. When someone makes an immediate call, it means they've quickly decided not raise. Because players with strong hands tend to at least consider a raise (even if they end up calling), this means almost all immediate calls are made with weak and medium-strength hands and draws. This tell is rampant in low-stakes games.
For instance, in a few hands, players called my continuation-bet on the flop immediately. This tells me that, almost all of the time, they are on the weaker side of their range. If I am bluffing or semi-bluffing, I will continue bluffing on the turn most of the time with this read. For example, I raise pre-flop with KJo and get heads-up. The board is T -7-4 rainbow. I bet and the player immediately calls. I will usually continue betting the turn and maybe even the river, because I think the player will most often have, at most, a ten, and often a lot of hands like 99 and 88 or 98.
I would also you want to be choosy about who you're attempting to bluff. I wouldn't want to do this against a calling station, because you could be completely correct in reading them for a weak hand but they still may call you down or even just shove in with their hand. So you want to ideally be focusing on players you know are capable of folding.
Master 1 2 No Limit Hold'em Strategy
Also, board texture is a factor in understanding immediate calls. For more aggressive players, immediate calls will also mean that it's very unlikely they have a strong flush draw. For example, you continuation-bet a board of Kh 9h 3s and your opponent immediately calls you. If this player is capable of bluffing at all, this immediate call will make strong draws like Ax of hearts and QT of hearts very unlikely, because that player would probably at least consider a raise, even if he ended up deciding to call. So in a lot of cases, immediate calls can help you define a player's range a bit more than usual.
Taking a long time to check when weak
Some players will take a long time to check to the aggressor when they hold weak hands. Don't use this tell generally, though, because most players will vary their bet- and check-timing enough (both consciously and because there can be a lot of thought-inducing situations with many different types of hands) that it's hard to get a good read. But against some players it can be very useful information.
For example, let's say a player calls your pre-flop raise, hits a medium pair on the flop, checks to you and calls your flop bet. The turn card comes, doesn't improve him, and he then takes like ten seconds to check to you. Whereas if he had a top-pair hand or better, where he knew he was probably going to be calling, he would only take a couple of seconds to check.
I'm not saying this is extremely useful information, because sometimes, with a medium-strength hand, $1-2 players will call you anyway. It's going to be mainly useful against the most nitty players; the ones you know are scared to carry on without very strong hands. Those are the ones who you might bet off the hand on the turn if you get some sense of weakness.
Along with taking a long time to check, a player might look very studious in studying the board, as if trying to figure out what to do. That combined behavior is usually a sign of a vulnerable hand. As is the following tell, which you can sometimes see in concert with these:
Defensive chip handling when weak
The gist of this one is that players will often try to make you think they're interested in calling by handling their chips in a defensive manner when it's your turn to act. They might hold their chips in their hand, as if ready to put them in. They might start cutting out chips as if ready to call. Basically, any chip handling action that looks vaguely defensive in nature, even if it's quite subtle, is usually a sign that the player holds a vulnerable hand. When a player holds a strong hand, they want to give no impediment to your bet, no matter how small.
This is a very useful one; it's one that came up a handful of times in hands I was in, making me feel better about making a large river bluff. In one hand in particular, I had been betting first to act on the flop and turn, and I thought it was quite possible my opponent had flopped the flush draw. When a low flush card came on the river, I probably usually would have given up on the bluff, except for the fact I saw him riffling his chips in his hand while he stared at me (staring at an opponent when they're waiting to act can also be a sign of weakness), so I bet $100 and he folded.
Two other hands went down very similarly to that. In one three-bet pot, where I'd three-bet and whiffed with AQ, an opponent called the flop, but I pushed all-in on a turn of 9JK3 based on my opponent grabbing his chips and holding them up defensively as he checked to me. It wasn't usually a spot I would have felt so comfortable in.
Again, even if this tell is only 75% reliable, that's still a great reason to carry through on a bluff that's already got a lot of logic behind it; in my experience, though, this tell is more reliable than that for most players.
Staring at hole cards and board cards when weak
When players stare at cards, whether it's their own hole cards or the board cards, it will generally mean they don't have a strong hand. I had forgotten how much the staring-at-cards when weak type of tells apply to low stakes.
Why is this a pattern? Players who look at strong hands tend to look away quickly. There's an instinct to 'hide their treasure' from their enemies or competitors. This accounts for the common tendency of players to look at pocket aces and immediately put them down. Whereas players with weak hands don't have a reason to look away.
Pre-flop, this can be useful when you spot limpers or players behind you looking for a second or two or longer at their cards. When you see this, and if you've decided it's a reliable tell for those players, you can choose to become more aggressive in the hand. For example, you see a few limpers staring at their cards before they call, and you decide to raise pre-flop lighter than you normally would. Or you see a late-position player staring at his cards for a few seconds and he ends up raising. You might decide to call him or 3-bet him lighter than normal.
Of course, players are still capable of calling you with their weaker hands, and then you'll have to play some post-flop poker. But because the read is generally reliable (and sometimes very reliable for some specific players), you'll be putting yourself in a lot of profitable post-flop situations where a flop bet will often take down the pot.
Sometimes players look back at their hole cards after the flop, too, and the longer they look at their cards the more it becomes likely they're weak.
For communal cards, it's the same basic idea: players who connect well (like top pair or better) tend to look away from the board when the cards come out. This can be seen as an involuntarily, unconscious attempt to distract attention away from their 'treasure.' Staring at communal cards, with no looking away, will tend to mean the player had no real reason to look away or be thoughtful about the hand.
Playing some $1-2 again, I got back into the habit of trying to watch everyone in the hand during multi-way flops, trying to see if anyone looked away immediately. Mainly I tried to watch the player or players behind me, because that is more valuable information than what the players in front of me do.
For example, in most three-way (or more) pots, if I'm the pre-flop raiser, I usually will shut down if the board comes down pretty scary and I haven't connected. Like if I raise pre-flop and the board is 9TQ or something similar, I generally check if I raised with 6-7 suited, or AK, or something that missed completely, because those are the types of boards that hit right in the range of most players who call a raise. Whereas on a really dry board, like K-7-3 rainbow, I will usually bet my misses into two other players (but not usually three other players).
But looking for opponents who are staring at the flop can make me feel more comfortable about betting into a multi-way pot. It happened several times in three-way and four-way pots where I wouldn't usually have bet from a fundamental strategy perspective, but the amount of staring going on by my opponents made me feel safer. Occasionally, I would still get one caller out of the bunch, but that still put me in more profitable spots than not betting, and I felt more confident, based on their staring, that they had weak hands.
Again, this is not something you want to use to make very large decisions. Good players are capable of staring consistently at the flop whether they hit or not. And even for the people who exhibit this tell very reliably, it won't always be accurate. This will mainly be useful for determining fairly borderline situations, like when you decide to get aggressive and follow through on flop bets in multiway pots, or follow through on turn bets. Or, when you see people looking away from the board cards, for deciding to take a more passive line. There are a lot of fairly borderline situations where checking or betting or raising could go either way, so a little extra information can go a long way.
Conclusions
All in all, I never want to give the impression that tells are something that will let you crush microstakes, or any game for that matter. I think they can give you little hints here and there for the best action to take, but these are often actions that are dictated by fundamental strategy. Occasionally, you can get really obvious signs from some players that dictate a very specific course of action, but you shouldn't try too hard to look for those spots. Those are spots that will come to you naturally, the more comfortable you get with tells.
Want to learn more about Poker Tells in $1-2 No-Limit Cash Games?
$1-2 No-Limit Hold'em cash games are one of the most popular forms of poker played today. In this short ebook, Zachary Elwood examines 35 actual $1-2 NLHE hands, finding meaning in opponents' physical and verbal behavior.
The ebook bundle comes with the book in 3 formats: PDF, EPUB, and MOBI (Kindle). (It's easy to sync third-party files with your Kindle reader.
