In part 1 of “Combating Aggressive Three-Bettors in NL Hold’em” (April issue) we took a look at countering aggressive 3 bettors with 4 bet bluffs and semi-bluff all-in raises and looked at some data to determine when it was and wasn’t profitable to do so. In part 2 we will be looking at calling a 3-bet and strategies for post-flop play.
Unfortunately, we can’t quantify what hands you should and shouldn’t play against a 3-bet with mathematical precision. We do have some loose recommendations about what hands to play in different scenarios, as well as advice on what things will encourage or discourage you from playing particular types of hands. When discussing hands we are doing so in the context of effective stacks of 100BB unless we say otherwise.
Trapping Hands: Aces and Kings always want to get all the money in the middle, but this is sometimes easier said than done. Opponents who 3-bet with wide ranges and frequently fold to 4-bets, but who play very aggressively post-flop, often firing one or two continuation bets automatically, and who are very willing to get all the money in with a one-pair hands are ideal candidates for a pre-flop call with these hands. Against opponents who you believe will raise all-in with a wide range if you 4-bet, who frequently call 4-bets, and who play passively or weakly post-flop we recommend a 4-bet. Also, we recommend 4-betting with AK under almost all circumstances. High card hands are typically poor trapping hands, as they are not disguised if you flop a pair and only flop a pair about 1/3 of the time.
High Card Hands: Against very tight 3-bettors (e.g. top 5.6% of all possible hands) hands like KQo and AJo perform quite poorly when they flop one pair hands, and we do not recommend playing them. Against wider ranges that include a large number of semi-bluffing and pot-building hands (often represented by an opponent 3-betting with 13% or more of all possible hands) we recommend taking a flop with KQo, AJo, AQo, and all suited double-broadway hands when in position.
Pocket Pairs: If your opponent will only re-raise with TT-AA and AK you should typically only attempt to go all-in pre-flop with QQ or better. Against opponents who will only re-raise with TT-AA and AQ-AK we recommend trying to get all the money in with JJ. Against aggressive 3 bettors with wider ranges we recommend getting the money in pre-flop with TT and better.
There’s an interesting tension with small pocket pairs in that as your opponent’s range becomes tighter or as your opponent becomes more aggressive the average amount of money you will win when you flop a set increases, but the value of trying to win showdowns without a set decreases, or disappears entirely. The converse is also true, wherein against looser or more passive opponents you may be able to win pots without a set, but you will win less money the times you do flop a set.
The reason it is often not possible to try and win flops without a set against aggressive opponents is because in big bet poker your opponent can correctly bluff a large percentage of the time with unpaired hands when overpairs are a large part of his range. As an example, say you are playing a game with $10 blinds and effective stacks of $1000, and you open raise to $35 with 44. The small blind re-raises to $120 and you call. You believe that the small blind’s 3-betting range consists of TT-AA and AQ-AK. The flop comes 732, missing all of your opponent’s high-card hands. Your opponent bets $200 into a pot of $250. What should you do?
Against an aggressive opponent you should typically fold. Assuming that your opponent bets the flop with all possible holdings he will hold a pocket pair 49% of the time. He is laying you 470:220 to call his flop bet. In order to call the flop, intending to fold to further action, you will need to win the pot about 31% of the time. If your opponent never bets the turn or river with an unpaired hand, this call will be profitable. If he will push all-in on the turn, however, he will be laying you 1130:880 to call both bets. To show a profit calling both bets you will need to win the pot 44% of the time.
The problem that arises here is that your opponent can bet the turn as a bluff an extremely large percentage of the time and you will not be able to call his bets profitably. Let’s look at what happens if you think your opponent bets the turn all-in with his unpaired hands a third of the time. If you call the flop bet and fold to a turn bet you will fold on the turn 70% of the time. Additionally, he will improve to a pair on the river 13% of the time if you check the turn, so calling the flop bet and folding to further action is –EV. If you call the flop and then call a turn bet (on a non ace, king or queen turn) your opponent will hold a pocket pair 74% of the time. This play is also –EV. So in this scenario you cannot call your opponent’s post-flop bets without a set profitably. It is interesting to note that with a tight range like this your opponent could bet the turn all-in as much as 90% of the time with his unpaired hands and you would still not be able to call his bets profitably without a set.
If your opponent’s range becomes wider or if his post-flop bets become smaller the ultimate outcome for these scenarios is still typically the same: against aggressive opponents who will often fire multiple bluffs post-flop there is typically no value in attempting to win pots post-flop without a set. You are about an 8:1 dog to flop a set. In the previous example you were getting about 12:1 on your pre-flop call to try and win your opponent’s stack. If you think that you can win your opponent’s stack about 66% of the time then calling pre-flop becomes profitable.
So against very passive opponents you will not win a stack very often when you flop a set, but will be able to call continuation bets on dry flops and show some degree of profit doing so. Against aggressive opponents you will not be able to contest flops without a set, but will win enough money when you flop a set to make playing such hands profitable. The issue does arise, however, when you are playing against a player who you do not know. Calling to spike a set against a passive player, or trying to win flops without a set against an aggressive player can be costly mistakes, and we find that the value of trying to play small pocket pairs is marginal even with very good information. And so our final say on the matter is this: Against players who you know to be either very aggressive or very passive, we recommend that you play the pocket pairs which you do not attempt to go all-in with. If you are unsure as to whether or not you are playing against a passive or aggressive opponent we recommend that you fold these hands.
Against unknown opponents with effective stacks of 125BB or deeper we recommend that you call with these hands explicitly for set value when you are in position, and 150BB when you are out of position. When the stacks are significantly smaller than 100BB we always recommend a fold with these hands rather than a call, though with short stacks these hands can become excellent candidates for an all-in semi-bluffs if your opponent’s 3-betting range is quite wide.
Suited Connectors:
As we saw when looking at pocket pairs it is often not possible to contest a 3-bet pot post-flop by calling down with pairs. Most of your opponents will naturally bluff with their unpaired hands some of the time which creates situations where you can neither call just a flop bet nor a flop and turn bet profitably. You can, however, often semi-bluff profitably.
If your opponent bets $200 into a pot of $250 with effective stacks of $1000 he will be laying you 450:880 to raise all-in. You would not be able to bluff profitably with a small pocket pair in the above example, but you would be able to raise all-in profitably as a semi-bluff with hands that have more equity against your opponent’s calling range, even if they are as weak as single pairs or gutshot straight draws.
We recommend calling a 3-bet with any suited connector 45s or higher either in or out of position. It may seem odd that we don’t distinguish between being in out of position with these hands, but as we’ve already established, there is typically either no value or very little value in trying to call down with single pairs. As we most often only intend to be either raising all-in as a semi-bluff with these hands or folding we suffer no particular positional disadvantage when playing them. In fact, we find that when opponents are in position they are more inclined to check behind their weaker hands which they would like to showdown, but will typically continuation bet unpaired hands just as often as if they were out of position. This is an attractive scenario if you are semi-bluffing.
Additional Hands:
With 100BB stacks we only recommend playing additional hands, such as offsuit connectors or other offsuit face cards if your opponent’s range is very wide and you have a specific plan for exploiting your opponent post-flop. We believe that you will not be able to play these hands profitably with a fit or fold style.
For much of the post-flop play in 3-bet pots we do not have to settle for recommendations, but can instead use hard data. Tables 4.1 and 4.2 list how often you will need your opponent to fold to an all-in semi-bluff based on your average equity when your opponent calls your raise. Both charts assume that your opponent has raised to $120 pre-flop and you have called, and that there is $10 dead blind money in the pot. You can calculate how often your opponent must fold in order for an all-in semi-bluff bet or raise to be profitable by treating your odds to bluff as (amount you win if your bluff succeeds) : (average loss when called).
4.1 $250 in pot. Opponent bets $200. $1000 stacks.
Equity When Called |
Minimum Fold % |
| 0 outs: 0% | 66.2% |
| 2 outs: 8.4% | 61.2% |
| 4 outs: 16.5% | 54.9% |
| 5 outs: 20.4% | 51.1% |
| 8 outs: 31.4% | 35.6% |
| 9 outs: 35.0% | 28.2% |
4.2 $250 in pot. Opponent bets $200. $1500 stacks.
Equity When Called |
Minimum Fold % |
| 0 outs: 0% | 75.4% |
| 2 outs: 8.4% | 71.5% |
| 4 outs: 16.5% | 66.3% |
| 5 outs: 20.4% | 63.0% |
| 8 outs: 31.4% | 49.1% |
| 9 outs: 35.0% | 42.0% |
Potentially, you can also consider a small bluff raise to combat players who often hold unpaired hands when betting the flop. We do not recommend doing this with any semi-bluffing hand that would then call an all-in raise from your opponent, as we believe it is best to simply bet these hands all-in to try and get your opponent to fold as many hands as possible. Table 4.3 lists how often a bluff raise must succeed in a re-raised pot in order to be profitable. This table ignores any equity you may have if your opponent calls your raise rather than folding or raising all-in.
4.3 $250 in pot. Opponent bets $200.
Minimum Fold % for 2x Raise |
Minimum Fold % for 2.5x Raise | Minimum Fold % for 3x Raise |
| 47.1% | 52.6% | 57.1% |
Now that you have some reference material for how often your bluffs must succeed in order to be profitable the next step is to determine how often your bluffs will succeed. Table 5.1 lists some examples of possible 3-betting ranges your opponent could hold, as well as what percentage of all possible holdings these ranges represent. We find it is quite common for many players to be unwilling to call an all-in raise with less than top pair, and so we have generated some tables to show you, based on the pre-flop ranges from table 5.1, how often your opponents do not hold top pair or better on either a jack high or 8 high flop when they continuation bet their hands which are worse than top pair 100%, 75%, 50% and 25% of the time. For the sake of simplicity we’ve ignored the times that your opponent flops middle or bottom set.
If you compare tables 5.2 and 5.3 to the previous tables you will notice that with a one pair hand (not using a pocket pair) and stacks of 100BB you can raise all-in as a semi-bluff profitably against even very tight 3-betting ranges on most flops. The same is true of small bluff raises. If your opponent occasionally checks his weaker hands you will be able to bluff less often, but against such opponents you will be able to win many of the pots they check to you with a bet. If you choose a small bet size of half-pot your opponent would have to check-call or check-raise your bet 66% of the time in order for your bluff not to show a profit, and if he moves strong hands from his betting range to his check-calling or check-raising range then the ratio of paired to unpaired hands he holds when he bets goes back down!
What hands your opponents may or may not call you with will vary from flop to flop, and from opponent to opponent. You can determine how often your opponent holds particular hands on a flop by doing combinatorial analysis, or by using a combo-calculating software. For example, on a Q43 flop there are 55 total possible combinations within the range TT-AA and AQ-AK. 27 of these combinations are hands that make top pair or better on this flop. As a result your opponent holds top pair or better 49.1% (27/55) of the time. We recommend using the Stoxpoker Combo for quick and easy combinatorial analysis. This software is now in open beta and is available for download in the 2+2 software forum.
5.1
Opponent’s 3-Betting Range |
% of All Possible Hands |
| AK, TT-AA | 3.5% |
| AQ-AK, TT-AA | 4.7% |
| AJo-AKo, ATs-AKs, 88-AA | 7.1% |
| ATo-AKo, A9s-AKs, KQo, KTs-KQs, QJs, 22-AA | 13.1% |
| ATo-AKo, KTo-KQo, QJo, A7s-AKs, K9s-KQs, Q9s-QJs, JTs, T9s, 22-AA | 17.9% |
5.2 Opponent does not have Top Pair or Better, J high flop.
3-Betting % |
CB < TP 100% | CB < TP 75% | CB < TP 50% | CB < TP 25% |
| 3.5% | 51.2% | 44.1% | 34.4% | 20.8% |
| 4.7% | 64.6% | 57.6% | 47.5% | 31.1% |
| 7.1% | 62.1% | 55.1% | 45.0% | 29.1% |
| 13.1% | 75.5% | 69.8% | 60.6% | 43.5% |
| 17.9% | 72.1% | 66.0% | 56.4% | 39.2% |
5.3 Opponent does not have Top Pair or Better, 8 high flop.
3-Betting % |
CB < TP 100% | CB < TP 75% | CB < TP 50% | CB < TP 25% |
| 3.5% | 34.8% | 28.6% | 21.1% | 11.8% |
| 4.7% | 51.2% | 44.1% | 34.4% | 20.8% |
| 7.1% | 57.1% | 50.0% | 40.0% | 25.0% |
| 13.1% | 76.4% | 70.8% | 61.8% | 44.7% |
| 17.9% | 80.7% | 75.8% | 67.6% | 51.1% |
When you are in position one play that may also be lucrative against passive opponents is a float, wherein you call your opponent’s flop bet planning to bet the turn as a bluff if he or she checks to you. To calculate the price of a float you must add the cost of calling your opponent’s flop bet to the amount of your turn bet multiplied by the percentage of the time that betting the turn will win you the pot. Because the investment made on the flop is quite small as compared to a bluff-raise this can be a very cheap bluff if your opponent seldom check-calls or check-raises the turn.
Tables 6.1 and 6.2 list show how often a float bluff would have to succeed if you had no equity in the pot whatsoever. With unlikely draws to very strong hands, such as gutshot straight draws or sets a float play has to succeed much less often than is listed, particularly with deep stacks, as you will have excellent implied odds should you make your long-shot draw. With these sorts of draws a float play can often be preferable to making a small bluff raise if you will have to fold if your opponent re-raises all-in.
6.1 $250 in pot. Opponent bets $200. You bet $680 if checked to.
Win Turn 100% |
Win Turn 75% | Win Turn 50% | Win Turn 25% |
| 30.7% | 45.1% | 54.5% | 61.2% |
6.2 $250 in pot. Opponent bets $200. You bet $300 if checked to.
Win Turn 100% |
Win Turn 75% | Win Turn 50% | Win Turn 25% |
| 30.7% | 37.9% | 43.8% | 48.6% |
Lastly, with very strong hands, such as sets, you will find that your opponents’ ranges will often be polarized between hands that will be willing to go all-in regardless of what you do and very weak hands. In scenarios like this we suggest that you focus on choosing the line that allows you to extract the maximum from your opponent’s weak hands. Against opponents who often make turn bluffs with their unpaired hands, for example, there is often little incentive to raise with your strong hands, particularly when you are in position. Let them continue to bluff, or give them a chance to improve to a second best hand. If your opponent checks to you with a hand that he or she is intending to showdown you can still easily get all the money in with either a turn bet or a turn and river bet.
The open beta for the Stoxpoker Combo can be found here. You can get additional coaching tips from Dusty and Bryce at Stoxpoker.com.
