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?

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.

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).

Re: 1/2 nl short stack strategy I dont think we ever see much on a real shortstack strategy for live poker due to the fact that most would rather slit their eyes with razor blades than play such a boring / low return strategy.

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...

MEV_Check = 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...

MEV_Raise-$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 EV_fold = 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...

MEV_Limp = 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...

MEV_Raise = (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 MEV_Raise 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 MEV_Raise.

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.

Live 1/2 Nl Poker Strategy

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

Poker Strategy Guide

Recently I've been struggling with the idea of moving up in stakes. I have dabbled at the higher buy in No Limit games and had mixed results. There are a few factors that come into play when I'm deciding. First is bankroll. Well, after a good summer at the WSOP and cutting down on my spending habits, my bankroll is in good shape and very sufficiently rolled to move on up to a bigger game. Next- my skill set. As poker players we all seem to think we're better than we really are. I try hard not to fall into that trap and always try to be realistic. I think my skill set is there to move up. Lastly, my mindset. This is the tough one for me. While my bankroll and skillset are ready to rock and roll, my mind isn't quite ready for the journey. The one big issue I've faced when moving up is that my mind can't handle the swings of the bigger games. If I'm in a 2/5 no limit game or a 5/10 no limit game and have $1000 in front of me I don't think about the money at all. Now, put me in a 10/20 no limit game with $2000 or $2500 and suddenly I become afraid of the money and don't play well. This is unfortunate because as I mentioned my bankroll and skill sets can support the game, but unfortunately my mind can't. So, what to do? I think the best route for me is to continue beating the games that I beat, and when I see a bigger game that looks real good and I'm upswinging in my current game, then take a shot at the bigger game. Eventually my mind will come to terms with the swings and I can move up.

So, whats this all mean for you, the reader? Well I figured if I have issues moving up you may as well, and it's mostly likely issues in making the move from 1/2 no limit to 2/5 no limit. Today I'd like to elaborate on the differences in the games to best prepare you for that move. But always remember, you need to evaluate the three things I spoke about above- bankroll, skill set, and mindset. Make sure all three are ready for the move up before giving it a shot. Also, don't be afraid to move back down if it doesn't work out or if you are uncomfortable with the new stakes.

The biggest difference between 1/2 and 2/5 is best summed up in one word- aggression. There is a lot more preflop raising and even three betting in 2/5 than there is in 1/2. Also, there is far less open limping. While it's very common in 1/2 to see four or more players limp in for $2 and the blind check taking you all to a six way flop, there is very little of this in 2/5. Most players know that it is very profitable to isolate limpers in no limit and players in 2/5 take advantage of this. You will often see a bad player open limp in 2/5, a good player from middle position raise to $25, and another good player on the button three bet to $75. What's likely happening is that the good player in middle position knows that it is profitable to isolate the bad limper, and the really good player in late position knows this, knows that the good player is likely isolating light, so now he three bets in position light to isolate the isolator. Plays like this don't always happen but are definitely more common in mid stakes games than in low limit games. It can also be taken to the extreme when the middle position player picks up on the fact that the button knew he was isolating light, so he can now four bet light to force a fold from the buttons light three bet. As you see this can easily turn into a leveling war between good players- and it all started by a bad player limping in for $5!

Apart from the three betting and open raising in 2/5, you will also see more continuation bets from the preflop raiser whether or not they hit their hand. Because of this you will have to be prepared to play post flop more with weaker hands. You can't spend all day calling raises and waiting to flop the nuts because the good players will win all the small pots from you and then shut down as soon as you show any resistance post flop. To combat this you need to learn to continue with weaker hands that haven't crushed the flop against pre flop raisers. This means calling in position more often, floating flops, and taking away pots on the turn or river. Bluffing (more like semi bluffing) becomes a more important part of the game as the limits go up. That doesn't mean that we should be bluffing every pot with no regard to what we are representing. Learning to tell a story with your hand becomes much more important. Always be thinking 'if I had X hand would I play it this way.' That will help your bets to be believable if you're telling a believable story.

With regards to online poker, I'd say this same principle holds true when moving from 50c/1 no limit games to the 1/2 no limit games. I'd also equate moving from 1/2 no limit online to 2/4 no limit online would be akin to moving from 2/5 no limit live to 5/10 no limit live. The player pool becomes much tougher and you don't get paid off as much on your big hands so learning to win countless small pots becomes much more vital.

With that said, assuming sufficient bankroll, I'd advocate dipping your toe in slowly. Start off by playing tight, observing your opponents, and then join in the fray with calculated bets and bluffs that tell a believable story about your hand. Good luck to all those who are attempting to move up in limits and make sure to post any trouble hands in Table Talk here at PokerAtlas. Good luck on the felt and most importantly, have fun!!

Comments

Winning Poker Strategy

1. Excellent article Benton! Have you ever written anything about transitioning from Limit to No Limit? If not then that is my request. I always enjoy reading what you write. Few people are able to simplify complex poker strategy and advice better than you.

2. Benton, I find that for lack of a better word 2/5 is more 'predictable.' For example, At the 1/2 level you see a lot of players call pre flop raises with Junk hands because it was only another $8 and 'they were suited. ' 2/5 players are less likely to make that loose preflop call. At the higher levels you get more reliable information in response to your action. As a result players with good hand reading skills can thrive at the higher levels.

   While in the long run it's profitable to play against the loose passive 1/2 players that doesn't make it feel better when your AA gets cracked by J4 flopping bottom two pair.

3. Good read and something I need to make the effort to do. I've mainly played 1/3 lately so the transition might be a bit easier.

   I just wish the nearest good cash game wasn't two hours away!

4. @GameChanger Very kind words. I appreciate it. I don't think I've ever written about transitioning from limit to no limit. That might make for an interesting article, although I don't know how useful considering most limit players have already made the switch or they refuse to ever make the switch. I did write an article about playing limit poker. I personally started as a limit player in 2001 and made the transition to no limit in 2004-2005. Let me think about how to approach that article. Thanks for the suggestion.

5. @zourah You and me both! 2.5 hours to Lake Charles. At least I get Vegas once a month tho so I shouldn't complain. Good luck with the transition.

6. Great article Benton, and perfect timing for me. Off to Vegas in a couple weeks to take some shots at 2/5, as I'm a bit hesitant to do so at my local yet, since they'd know I was just moving up and I'm afraid I'd be a bit exploitable until I'm more comfortable. Any reccomendations on best Vegas rooms to play 2/5? Heard Bellagio is a solid go to. Thanks!

7. Wait, so VegasMikey doesn't live in Vegas? Hmmmm we will have to investigate this in our member screenname policy. hahaha I'm kidding. As long as LasVegasMichael doesn't have a problem with it, I don't either ;).

   Bellagio, Aria, Venetian, and Wynn I think are probably known to have the most 2/5 NL games to choose from. Others often have games, but not on as regular of a basis. From my experience, they're all pretty similar to one another, so it just comes down to which room you feel the most comfortable in.

   BTW, excellent article Benton. I agree with GameChanger. Would be a very interesting piece....and maybe the reason more Limit players don't switch to NL is because you haven't given them appropriate guidance on how to do so? I'm guessing that is the case.

8. I'd echo Krusherlaw's comment. In my brief move up to 2/5 (back down again due to bankroll considerations) I definitely felt more comfortable at the 2/5 game due to predictability. I felt I understood bets, and hands played out as expected which I enjoyed, even though I eventually felt overmatched more times than not in these games.

9. @VegasMikey Good luck with your trip! I'd recommend Bellagio if you're just making the transition. It's a $500 max buy in there and the game is typically softer than the $1k max at Venetian or $1500 max at Wynn. Plus at Bellagio there are regular 5/10 and 10/20 NL games so it makes sense that the 2/5 would be softer than Venetian and Wynn which don't run regular bigger games daily. Aria is an option at $1k max but also tends to be tougher than Bellagio, yet as states by others it is a bit predictable as the players are all competent.

10. Not sure where you are located or what your buyins are but a great alternative to a 2/5 game assuming your buying in for at least 100bb, is the Wynn 1/3 game. (500 max buyin) on a most tables plays like a 2/5 game. Just like the article states, very few limpers, pretty aggressive games. Plus since the blinds are smaller, its like a jr step before a true 2/5 game.

11. Thanks for the help and advice guys. Looking forward to getting down there on Sunday. As for my VegasMikey handle Jon, it's just from my friends after a rather memorable trip (aren't they always) a few years back. I'll for sure give Bellagio a whirl (plus the 1/3 at Wynn), and I might take a stab at Aria too, since it's my favorite room in town (mmm burgers and watermelon juice at the table). Also looking forward to the 'ATB hold em' game at TI. Hoping that's still going Sunday night!

    Cheers!

12. Anybody remember limit poker? It was the only game in town for a lot of years. Sort of like $2-5 today. I play a lot @ Bellagio because they have a lot of limit games. The $10 20 limit game, which is rare on the strip is relaxing for me after $2-5 unlimited. I predict limit will make a come back; especially at at the higher limits.

13. Hey Benton nice article you help me out and in turn I teach military tactics for 12 years ever try meditating before a big poker game .I know people say what meditating brings your life energy back in your body all it takes is 5 minutes listen nice music takes deep breaths though the mouth exhale thru the nose sit in chair spine erect .This will help your mind game.I think you will do well in 2/5 games since you can grind them 1/2 games and make a profit.Good luck and look forward too more poker articles ..Team Pitbull Fighting Ptsd one poker hand at a time..

14. super interesting article. I actually feel exactly the same but the cutoff depend how I am running :
    running good 2/5 --> 5/10 is my cuttoff,
    running bad it is from 1/3 to 2/5.

    Any ideas / tips how to get thru this psychological leak ?

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