Even if an opponent did limp with a wide range that included strength, maybe only about 5% of all hands is going to stand up to a large raise or less. SO if they limp in with 40% of all hands and only play 5% that represents 12.5% of their holdings. So I estimate an 87.5% chance of opponents to fold plus the SB and BB playing maybe 10% and 8% of all hands or less to a large raise..
# of limps % chance all opponents fold given X limpers when you act from button
1 72.45%
2 63.39%
3 55.47%
4 48.54%
5 42.47%
6 37.16%
7 32.52%
8 28.45%
Assuming break even postflop or hand checked to river:
2x the pot requires 40% equity vs opponent's calling range if you get 1 caller 100% of the time.
2x the pot requires 35% equity vs opponent's calling range if you get 1 caller 75% of the time.
2x the pot requires 30% equity vs opponent's calling range if you get 1 caller 50% of the time.
1.5x pot requires 37.5% equity if 1 caller 100% of the time.
1.5x pot requires 31.25% equity if 1 caller 75% of the time.
1.5x pot requires 25% equity if 1 caller 50% of the time.
Should adjust the above based upon number of limpers so you can develop isolation raise/blind steal range.
Use equity against the top 5% hands to determine which hands have the equity to make the move given the number of limpers
Now let's look at given the fold percentages of the reraise over the limpers how often we need to win when called to profit (assuming opponents never raise and we check down to the river)
Assuming limp in range of 40% of hands and opponents playing only top 5% of hands to a raise with 1.5 times pot bet.
| # of Limpers | equity needed to steal |
| 1 | 19.39% |
| 2 | 21.65% |
| 3 | 23.63% |
| 4 | 25.37% |
| 5 | 26.88% |
| 6 | 28.21% |
| 7 | 29.37% |
| 8 | 30.39% |
| # of limpers | Equity needed to steal |
| 1 | 25.51% |
| 2 | 27.32% |
| 3 | 28.91% |
| 4 | 30.29% |
| 5 | 31.51% |
| 6 | 32.57% |
| 7 | 33.48% |
| 8 | 34.31% |
But just in case these assumptions are incorrect, what if opponents limp in with 25% of hands and call with 8% with big and small blind just as tight?
| 1.5x pot | 2x pot | ||
| # of limpers | equity needed | equity needed | |
| 1 | 23.42% | 28.74% | |
| 2 | 27.93% | 32.32% | |
| 3 | 30.99% | 34.79% | |
| 4 | 33.08% | 36.46% | |
| 5 | 34.49% | 37.59% | |
| 6 | 35.45% | 38.38% | |
| 7 | 36.11% | 38.89% | |
| 8 | 36.56% | 39.24% |
Now you may need to be more selective about your hand range. Having 33% equity over a 8% range is a little easier to find a raising hand than needing 33% equity over a 5% range of hands, but even still it's a bit more difficult to find a spot to raise. Either way, after representing such strength preflop and having the lead, I would be comfortable with my chances with less equity since a continuation bet may be able to take it down often enough to show a slight profit. While I'm probably not going to be able to put multiple bets in, a single bet on the flop or turn should win the flop often enough.
At the most conservative generalization 35% equity when called over say a 5% range of hand is strong enough. Once the first few limpers are in the hand range after that tends to be wider.
Let's actually go for 5.7% range of hands and define it as
99+,AQ+,AJs, KQs.
So what hand has a 35% chance of winning vs these hands?
99+,AJ+,ATs, KTs+
There are a lot of hands that are relatively close, particularly if our opponent is limping more hands and particularly if we can say he doesn't limp with AA or KK. Since we are probably making too conservative of assumptions intentionally, what about a more authentic situation?
What if opponent has 22-JJ,AJ,AQ, and any two broadway cards in his range? Sometimes he won't call with all of these hands so it wouldn't be surprising if he folds a lot of these sometimes and often times won't limp in with many of these hands either.
Now we can play A2+, K2+ and a whole lot of hands. Even Q2 gets 32.8% equity which is pretty close and if he limps in wider and folds more often that probably would be strong enough to raise. The problem with assuming 33% equity is enough is that often times opponents will limp raise, rather than just call and we may not have any equity and we may just have to fold. We probably won't have a strong enough hand to stand up to an all in. As such, I wouldn't steal with hands this weak, those types of hands may even be profitable due to positional advantage and it may get me close enough that if a few other variables align or if I have maybe moderate strength hands like Q9 and J9 I might make the play.
So if either the equity is only 30% or the hand range is more realistic once we're called we can profitably attempt a steal with a lot more hands.
When we don't have to worry about AA and KK, A2+ and K2+ always have at least one overcard to a pair which makes them 33% to win in most situations. Many other hands that were a few percentage points off improve substantially and become profitable. Small differences in our assumptions make very large differences which makes this very tricky.
Of course, it's really hard to conclusively say that opponent always limps weak and the earlier position limps you have to be careful with. But if the first two positions have not limped I would be a lot more comfortable raising a wide range of hands. Maybe not quite as wide as A2+ and K2+ but close. Also, unless the game is incredibly passive, I'd prefer having a bit less equity in exchange for more clarity in the decision. So 56s for this reason is better than K2 by far, but perhaps neither are playable.
This is speculative but in general I might raise with A9+,any two broadway cards,A2s+,K9s+,Q8s+,J8s+,T8s+ and possibly suited connectors over limpers. I would speculate a lot less if there is a tricky or extremely tight player who never plays a hand in early position limping or early position limps in general. I would be more willing to play perhaps even a wider range if the limpers come from middle position and late position with straight forward players that don't seem to try to trap.
Even though it's possible some of the individual hands at the bottom of the range may not have equity against opponent's calling range, it's not the worst thing in the world to have some slightly unprofitable hands in your range. It certainly doesn't add a ton of value either to have them but by making you less predictable and seemingly more loose it may give you enough additional action in marginal situations to make up the difference, but the cost is that your bluffs won't be belived as much and opponents will play back at you. In any rate, it certainly is unlikely that a few extra hands will make that big of difference and typically you can find far more spots that allow higher confidence. But if you are feeling confident about your edge over your opponents (and do not have a tendency to be over confident), it's not terrible to speculate, and it may even make money, particularly if you have a lot of extra chips or very few and can make all in semibluffs on the flop without it being a massive overbet and prevent opponent chance to see showdowns
Negreanu's Take On This Play
Daniel Negreanu's has a slightly different approach with this play. As you probably would guess his approach is a bit less mathematical and more based upon table image, perception and using this move infrequently as well as the psychology behind opponents based upon their stacks, but the math is still a consideration. He also would prefer to raise with a polarized range. Either he is making a play or he has a very strong hand. That allows him to actually just limp behind or complete from SB or check from big blind when he has the hands with some value and get value out of it that way. That's perfectly fine at an aggressive table with no knowledge of you, but at a passive one it's probably better to seek out the maximum equity in case you get called.
His strategy is more about taking one single stab at the pot and giving up where as the one detailed above is more about taking one stab and then playing some poker after the flop which probably means representing that the flop hit you when it checks to you by betting fairly frequently. If you want a balanced strategy, checking behind on dry flops and high card flops just as you would with strength to induce a bluff and weaker calls and also be more believable and consistent with your style. Checking of the flops makes it more likely to get to showdown as well when hand has value but worse hands will not continue if you bet like on an ace high flop. Since the pot will probably be quite bloated it makes sense to want to check at least one street at some point.
Floating the turn or bluff raising becomes possible if you check the flop against an aggressive opponent. Floats will allow you to represent draws on a draw heavy board and slow playing a monster on no draw boards. Raises on a draw heavy board will represent a strong hand and denying free cards while raising on a dry board will represent either that you are really strong and you hope opponent has top pair or that you have top pair, weak kicker or perhaps less and are "betting for information" to avoid putting more money in by the river if you are raised while also potentially making a slightly stronger kicker or higher pair than you fold.
The minraise to set up a bluff is a good play on the turn depending on the opponent's bet size. Most drawing hands on the turn will not have the odds to call. This also looks strong on dry boards as well. It will often set up a larger bluff while raising for information on the turn. It looks like you checked to induce a bet, and raised to induce a call. On the turn it doesn't look like you are trying to buy a free card like it does on the flop. It particularly does well on boards with all low cards or a pair and low cards even though typically you will not check these boards (but on occasion you might).
Anyways, here's Daniel on the "dead money grab"
http://youtu.be/eQT8udBfhdE
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