Some Additional Applications of Blockers

Almost a year ago I finally sat down and wrote out a post describing different ways hand combinations work in holdem (link). The information in that post is pretty important and you'll need to understand it before you can really get the following. Here I'm going to elaborate on some other ideas having to do with blockers that sort of go together but don't really belong anywhere else, so I threw them all together.

Blockers That Raise Your Fold Equity

Quoted from the post I linked to above:

Quote:

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Suppose that in some preflop scenario, we hold A3s and Villain's range is {QQ+, AK}. That gives him 12 possible combinations of AK, 6 of QQ, 6 of KK and 3 of AA, for a total of 27, and 33.33% of that range is KK+. If instead, we held JJ, then Villain would have 16 possible combinations of AK, 6 of QQ, 6 of KK and 6 of AA, for a total of 34, and 35.3% of that range would be KK+. The point is that blockers have the potential to weaken our opponents' ranges significantly.

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This is what most people think of when the topic of blockers comes up, which is why I've copy/pasted it here. Now consider the following:

Blockers That Lower Your Fold Equity

Generally when we think of blockers we consider cards that reduce our opponent's continuing range to some bet or raise or whatever. But this isn't always the case.

Suppose an EP opponent in full ring opens {77+, AQ+}, they continue with {JJ+, AK} and we 3-bet bluff them with 43s (no blockers). His opening range is 80 combinations, and his continuing range is 40 combinations, so he folds 50% of the time. Now suppose that instead, we 3-bet bluff with AJo (Ace and Jack block his continuing range, a.k.a. they are blockers). Then his opening range is 66 combinations, his continuing range is 30 combinations, and so he now folds 54.5% of the time, a small improvement. Finally, suppose we 3-bet with 87s (Eight and Seven block his opening range without blocking his continuing range). Now his opening range is 74 combinations, and his continuing range is 40 combinations, so he folds only 45.9% of the time.

In scenarios where we would like to have some fold equity, our hand can have three possible effects on our opponent’s ranges. First, it can have no effect at all. Second, it can serve as a blocker for the continuing range. Third, it can serve as a blocker for the betting range, but not the continuing range. When our hand is in the second category, we will have more fold equity than if it was in the first category, and we typically refer to this phenomenon as having blockers. When our hand is in the third category, however, we will have less fold equity than if it was in the first category, and I've suggested calling this having "reverse blockers".

To give just one application of this, in full ring NL games right now people are discovering that a lot of the regulars have EP ranges that are very exploitable to 3-bet bluffs. This idea shows that hands like ATs will have a lot more fold equity than hands like T8s.

Blocking Draws

The cards we hold can "block" other combinations our opponent could hold in many other situations besides preflop bluffing scenarios. While these bluffing scenarios are usually brought up to illustrate the basic points because of their ease of use and understanding, they are far from the only use for blockers in holdem.

Suppose a fairly tight player opens in EP, you call with A :s: K :h: in position, and the flop comes K :s: 8 :s: 7 :d:. You might need to consider what draws your opponent could likely have at some point in the hand, but because you hold the A :s:, almost none of his likely flush draw combinations (besides some SCs) are available.

Along the same lines, suppose you hold JJ on a board of Q93, and have to consider that your opponent may have JT. It's half as likely now because of your Jack blockers.

So yeah there you go, I'm finished typing for now.

Not so much to say on the topic because spoon's post is pretty complete - forums are fantastic for asking questions and getting discussions going, but article/publish quality content like this doesn't really invite discussion so much.

By this I mean - if they aren't already caught I hope posts like these get added to the Poker Articles section of the site or at the very least captured in the digests.

And now to actually comment - I thought something funny while I was reading this. It's common for poker players to have continuation ranges that in the case of unpaired hands heavily favour suited cards. An example could be that we play ATs+ and ATo+ and we decide that we can probably justify playing another 32 hand combinations for raggy aces without too greatly hurting our balance. There most of us would tend to pick A9s-A2s rather than A9-A8.

What struck me as funny is when you 3bet with a hand that is not purely for value - where you would welcome some folds you might end up in a situation where you prefer the offsuit variety as both cards can be blockers to the suited hands that are most likely to continue against us.

As an example a preflop raiser may raise a hand like AJ from a middle position, but when we 3bet him from the BTN he might decide to raise 25%, flat 25% and fold 50%. To make up those percentages he might flat suited, raise if the two cards are the same colour (red/black) and fold if the two cards are different colours. It's probably better EV for him to follow this type of procedure with AT+, KQ-KJ, QJ and JT or whatever his continuation range is instead of being predictable and always raise AK/AQ and always flat AJ/KQ or whatever he might be considering as an alternative. The question is whether he should be preferring the suited cards for the flat call or for the 4bet, but since the 4bet has fold equity I'd probably prefer to lean towards flatting the suited variety and 4betting the unsuited variety.

While the process for determining our 3bet range could go along the exact same lines, if we have two high cards we could also go along the lines of considering which hand has most blockers to his continuation range. If we 3bet AQs we're blocking only one combination each of ATs+, KQs and QJs (and none of KJs and JTs). If we 3bet AQo we're blocking two combinations of each of these (effectively halving this part of his flat calling range). Similarly with offsuit hands, if we're 3betting AQo with heart/diamond we're blocking just one 4betting hand (heart/diamond) whereas if we 3bet AQo with red/black (heart/spade) we're blocking two of the four 4betting hands (heart/diamond and club/spade blocked. diamond/heart and spade/club going ahead).

Whether this is useful - I won't pretend to say. I just thought it was funny. And dramatic - ignoring the paired hands if the opponent tendency is reliably like this we don't just shave a few percent off but greatly reduce his continuation range by picking AsQd rather than 7s6s for the 3bet. Of course, the wider his continuation range is to begin with the smaller the impact is measured as a percentage of his continuation range.

Even if this is completely true, I still think there's a case for using the 76s type hands for 3betting some of the time. Simply put it's the A85 rainbow flop type of situations where the PFR and 3bet caller might have the A and he will stack off when the straight completes. The 76s type hands tend to have strong implied odds when they do hit a big hand and worry less about domination than some high card based hands. The fact that cbets (and flop bets in general) tend to (correctly, I believe) be smaller in 3bet pots helps the drawing hand getting something quite near to immediate odds with super strong implied odds.