This means that if with the blinds and antes there is 2.25 big blinds in the pot and we risk 2.25 chips, we are breaking even on steal attempts. Any flop we see or real hand we pick up that we can continue to play to a 3bet is a bonus. But this bonus can turn into a liability if we put in too much money as an underdog due to mistakes in our game. Or it can turn into a huge plus due to mistakes in our opponent's game and our positional advantage.
If opponent only reraises us with a 20% hand we can still continue to raise every single time from the cutoff and we do slightly better than break even 90% of the time. However, the remaining 10% of the time we can pick up a top 10% hand, put in a 4bet and be ahead of our opponent's 3bet range. The danger in 4betting if it isn't all in is that we may be basically committed to the pot with a small raise or a 5 bet all in or we may be risking proportionally too many chips relative to what our opponent risks. For that reason we may need to play a little tighter. Nevertheless, the 4bet all in can be done with 5-10% of hands and make money innormal situations. So we break even on our steals and 10% of the time we have a hand where IF our opponent 3bets we make money. So 50% of the time our opponent has a 3bet hand and of that 50% our opponents raise, 10% of the time we are raised we have a 4bet hand... or 50%*.10 or 5% overall. (technically 2.5%-5%). This 2-5% of the time is when we make our money even though we are raising with any two.
Additionally, opponents may just call, let us see a flop. We should be very cautious since our opponent has a stronger range than us preflop that they are trying to trap us, but even so, we an still size our bets and make decisions that at least manage to have a chance to pick up additional equity after the flop. If all we did was check it down we would win a percentage of what's in the middle, giving us a rebate on the 2.25 big blinds we put in. For example, if we get called and check it down and win a pot of 30% of the time, we may have equity in 30% of the 5.75big blind pot (it will be a single big blind bigger if the person on the button calls and half a big blind bigger if the small blind calls).
That translates to getting 1.725 of the 5.25 we risked back. Since we will be risking 2.25 and getting 2.25 half the time, and the other half the time that our opponent has a hand we will get some calls, this translates into 1.725 of profit. If for example it happens that our opponent calls and check sit down 10% of the time he has a hand, then 5% of the time overall we add 1.725 which is only about 0.08625 big blinds per time. However, we are more likely than not going to remain in position throughout the hand except when the button calls. So we may have opportunities to win a portion of the pot with the worst hand by checking it down, there may be opportunities to call on a draw for added equity plus implied odsd, and we may even be able to call to bluff or jst reraise bluff as well on some hands. And we may be able to bet and get called when we have a hand. Our opponent may do this as well, but if we adequately assess our hand vs his an make good decisions after the flop we should have added equity by being in position 2/3rds of the time we see a flop vs 1/3rd of the time when the button calls.
Of course, this is why it is more likely that our out of position players will 3 bet and the button player should just call more often.
Also, our opponents will probably change the range of hands they play if they see us raise every single time.
Nevertheless, if you are break even or better on all of your steal attempts and break even or better after the flop it is a very profitable situation. It pays to be the aggressor, it pays to be in position, and it pays to defend your blind more liberally than with 20% of all hands so the small blind, button and cutoff don't have the odds to steal with any two.
20% of hands might look like the following range: 55+,A2s+,A9+,K7s+,KT+,Q9s+,QJ,J9s+,T9s That's a pretty tough range to call a raise with every single time. You might see players reraise occasionally thinking that it should slow you down a little bit, but to 3bet constantly with a wider range is a little exhausting and stressful for the players. It would not be at all uncommon to find you should raise with any two during the ante stages from the button and the cutoff, especially when you add the probable fact that the positional advantage will add equity on every flop you play.
So let's examine the average percentage of hands all opponents should play in order to make steal attempts equitable with any two cards from each position.
Steals are profitable with any two cards even if you always fold your hand to any resistance or if opponent given the following conditions:
Small blind (or big blind if opponent completes 100% of the time): 50% of all hands
Button: profitable if blinds play 29.29% of all hands or less.
Cutoff: 20.63% of hands or less
Hijack:15.9101% of hands or less
5 players left to act: 12.95% of hands or less.
6 players left to act: 10.91% of hands or less.
7 players left to act: 9.43% of hands or less
UTG 9 handed: 8.2996% of hands or less
You might think that 3 players each playing 20% of all hands is the same as 1 player playing 10%, another playing 20%, and the third playing 30% since the average is 20%. You'd be wrong, but not so much that the approximation wouldn't still be valuable.
Against 3 20% players you have 51.2% chance of successful steal. Against 3 players of 10,20 and 30% you'd only have 50.4% chance of a successful steal.
Given this information I would say I would feel comfortable stealing with any two from the button and cutoff in most games. Even though some players may be a bit looser than 20% of hands to late position raiser I still have the skill and positional edge. I'm also hesitant to raise with any two 100% of the time since I don't want my opponents to know I'm raising every single time and change much from their style and I don't want to start out that way until I have confidence my opponents won't adapt enough. Plus, there's hardly any value from hands like 23,24,25,26,27,36,37,38,39,47,29,39,48,49, etc after the flop that I don't need to be playing every hand. Neverthless, I can play like 75% of hands from these positions and close to that much from the Hijack.
Every other position I would probably want to play much tighter since it's not just the preflop informational disadvantage but it's the flop,turn, and river of having to act first that is also a disadvantage.
Limp Rather Than Raise From Early Position
There are exceptions to every rule. One common rule is never limp in, always raise. But when I have say 18-30 big blinds I will limp in a lot unless my opponents are tight enough that steal attempts are more profitable. If I am raised my opponent is in a vulnerable position if I minraise as they will have to commit a lot of their stack. OR if I push all in it is not an overbet but it is enough to force them to make a difficult decision. As such, they can't raise over the limpers nearly as often as they normally would. This play works even better if my opponents are cautious/passive to any bet size but will take a stab at the pot if I check because I can represent a lot of strength by leading out with ANY bet and continue.The plan is to limp in and if reraised I will 3bet often enough to break even or more. If opponent lips behind hoping I'm slow playing and hoping to hit a big flop that's fine. I will lead out for 1/4th of the pot on the flop and if my opponent just callsand I think he is on a draw, I am leading out big on the turn say 2/3rds of the pot or the full pot on a bluff. If I am on the draw and think my opponent is slow playing I'll lead out again with maybe a 1/3rd to half size pot bet on the turn. This allows me to check to opponents who thin value bet on the river when I hit and raise, or make a very large bet on the river IF I hit my draw. small hand, small bet, big hand, big bet. That may be too predictable for good opponents so I may have to represent hitting the draw. So if I'm on a straight draw and a potential flush hits against a good opponent who will late down top pair, I might bet big or check raise.
On the other hand, if I hit a big hand on the flop like a set on a A82 board I want to see that my opponent hit enough of it to continue so I can figure out how to get the best out of it. If I am raised I might ship it right then. If I am called I may check raise the turn or call the turn then lead out as if I'm making some odd bluff that doesn't make any sense like I missed my draw.
Limp Raise Shoving Exploitative Poker Solutions
3bet exploitative math and limp raising math is similar in that you have to find opponent that plays a certain percentage OF his raising hands. The difference is that when raising, your opponent can put in a 3bet and force you to fold. With a shove, your opponent can only call or fold.If you need opponent to fold 50% of the time and he raises over limpers with 30% of hands, you might think you need him to fold to a limp raise with 15% of hands if you are risking 3 times what's in the pot. 50% of his 30% range is 15%. But it's not that easy.
You limped initially facing multiple opponents so if only the strongest raise it is very likely that at least one of them have a MUCH stronger hand.
For example if you limp with 6 players left there's a 50% chance that at least one of them has a top 11% hand. Given that there is a raise that becomes a lot more likely than 50%. So really you are playing against a stronger range even if an individual opponent may raise a lot over limpers since so might others and there's a good chance at least one of them has a good hand. A looser opponent who will always raise over limpers means you might be able to say he has a slightly wider range, but with every fold it is increasingly likely that the raiser is the one with the hand as more random bad hands are out of the deck which tend to not include face cards as often.
Even so the limp-raise represents a lot of strength from early position and opponent still may lay down mid pocket pair if they don't think you've done it much, plus you still have some equity if called. So If you think they will only call with 99+,AK,AQ and will raise with 10% of hands, you are still okay to shove. You can overbet the pot by 3 times the amount in the pot, get called 50% of the time and still end up profiting if on average when you get called you are 35% to win.
Unlike in the initial steal calculation, the all in steal has the advantage in that our opponent cannot put in another bet to force us off the hand. So our limp of 1 plus our opponent puts in 4, plus blinds and antes 2.25 make 7.25. 3 times that would be 21.75 big blinds.
In fact, the calculation says we can actually raise up to nearly 4.5 times the pot if opponent calls us half the time and we are 35% to win when called. So that means if opponent puts in 3 big blind raise after our limp we can resteal limp raise shove any two in this situation with 6.25*4.5= 28.125 big blinds. If opponent puts in 4x big blind after a limp we can resteal against this opponent with 7.25*4.5=32.625 big blinds. However I believe this assumption more than any others is most vulnerable to being wrong. If we are wrong about our opponent's steal range given a limper and it is much tighter, this can be a serious problem. Or if they call more often this is a serious problem. So you may want to use caution and only use this limp-shove a few times and do it with your premium hands as well so that on average your hand strength is stronger than 35% to win. Let them see you fold to a raise a few times at least so they don't know you do it every hand and don't call as loosely.
Limp Shove Hand Range
If our opponent calls our shove with 5.55% of hands (88+,AQ) and raises with 11% of hands, how loose exactly can we limp-shove to still maintain an average of 35% equity vs his range of hands? 22+,AT+,KQ,K9s+,Q8s+,J7s+,T8s+,96s+,86s+,75s+,54s,34s Any pair, Ace Ten or better, KQ, and suited one and two gappers. That's a pretty wide range to be able to limp in with in the first place from early position. That means we can limp in with nearly 22% of our hands and shove to any raise with 33 big blinds and less. That doesn't mean we SHOULD play it that way, just that we could.Actually, it probably would be more ideal to only play individual hands with 35% equity since even though the RANGE of hands we are representing force opponent to call with the range we think he will, if we don't think he'll adjust, the individual hands that are more than 35% vs our opponents calling range will be more profitable and the overall hand range on average that we push with will be much stronger. However, if we believe our opponent is more likely to fold too much, pushing with a wider range is better. That range would probably be 44+AQ+. However, if we had shallower stacks what we win when our opponent folds to our push would be much larger compared to what's at risk when we get called so that range would widen quite considerably as we paid a few more big blinds or if blinds went up another level to any pair, most suited aces and a few suited connectors and then quickly to A2s+,K2s+, any 2 broadway, any suited two cards 6 or higher and any suited 1 and 2 gapper.
For a quick solution to situations solving for individual hands that are profitable, use the ShortStacking app. You can push wish more hands and on the average still be profitable but your profit goes down if you assume the calling range remains the same. But if initial raising range tightens up and opponent's calling range loosens up he can make a lot of your pushing hands unprofitable. Conversely, if opponent's initial raising range loosens up and his calling range tightens up it's profitable to steal with a lot more hands. Either decision to push frequently or less frequently may influence your opponent's strategy so keep that in mind and ANTICIPATE.
Call, Limp, Shove: Depends On Stacks Sizes
With more chips the larger overbet should represent better hands so that our equity is better than 35% but can still be done. With more than 30 big blinds though I prefer to minraise up to 40 big blinds. At 40 big blinds my raise will increase a little so that my 4 bet shove is right where I want it and so that my opponent to 3bet shove has to put in a huge overbet which allows me to be more patient about calling his all in.With 40 big blinds I could fold to a shove and give up 3 big blinds 8 times for a total cost of 24, call all in on the 9th and even if I was only 65% to win, I'd be able to yield a greater expectation than 24 big blinds so I would be making money. Of course I also have to keep up with the blinds so I may have to call a little more often than that, but to find a 65% favorite hand over my opponent's range should be easy if I can fold several times, plus I can adjust so that I am raising with fewer hands if need be.
On the other hand, if I am 3bet minraised to 6big blinds I can see a flop with plenty behind to bust my opponent if he has AA and I have 55 and he is willing to risk it all. I am calling 3 big blinds with a greater than 10% chance to hit and I will probably get greater than 10 times 30 if I call and hit a set or quads. I also will have 10 outs if the flop gives me a pair and open ended straight draw such as 467,234,346,678. If my opponent gets tricky and slowplays, I also may get the turn and a 4% chance to catch a set on the turn.
Alternatively, if my opponent puts in a reraise/3bet of 9 or 10 big blinds I can shove for 40 to 50 and my opponent won't have the luxury of being able to wait very long to call. In other words, he cannot 3bet me very frequently with these stack sizes without being exploitable.
Squeeze Play Trapping
For this same reason you should be hesitant to 3bet someone when they have 40 big blinds and you have more, or when they or you have less than 40 big blinds and you don't have an all in hand. So you can start flat calling raises with 40 big blinds and hoping someone puts on the "squeeze play" where you can get all your chips in when you have a hand. Otherwise you can fold many times before shoving. With deeper stacks but under 100 big blinds, you can shove to the squeeze play as there will probably be a lot in the pot but it will probably succeed much less often and probably get called so you need a real hand here. Nevertheless, you are only giving up 3 big blinds when someone raises big and you fold, and you are either getting a ton, nearly 20 OR getting your money in with a pretty strong hand.
So you can easily afford to give up 5 or 6 pots and shove on the 6 or 7th while your opponent won't be able to be that patient waiting around for a hand if he squeeze plays too often with under 100 big blinds. If you only want to 4 bet shove over a squeeze play with AA and KK which is 0.90% of hands, then you can flat call raises with 5%-7% of hands and still not be exploited by the squeeze play. Actually you can be much looser than that since opponent has to respect two players so he can't just do it 100% of the time and because you can always adjust AFTER you get squeezed a few times. So you could probably flat call 11% of the time and only move all in when you have AA or KK. Once your opponents know that about you, you could potentially try a bluff but trying to work out opponent's hand ranges with any reliability in this spot is much more difficult.
The issue though is this math carries with it the assumption that it is a repeatable play. If an opponent only does it once or twice every 6 hours, you won't probably be able to adjust to him specifically. But you can however play in a way that your entire table won't be able to realize you are exploitable as you can tighten up about flat calling raises.
The great thing about flat calling raises is you often will have position on your opponent and the pot size will be a good size to get a lot of chips or win a small pot and not risk too much.
Other plays:
Being on the other side of any of these plays mentioned is fine, but you probably shouldn't do it when your chipstack is vulnerable to someone being able to push all in for 3 to 6 times the pot unless you rarely ever use that "move" without a hand that can stand up to an all in.
So raising over a bunch of limpers is a good tactic provided the amount you risk PLUS the money in the pot is less than 1/6th and ideally 1/10th of your stack in addition to opponents not being short stacked. You can do it on an all in move, but then the math is different and the risks are higher.
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