Range Wars – Part 3

Dave Roemer | 1 month ago in Poker Theory and Concepts

So far we’ve defined what range advantage and nut advantage means, when to think in these terms in game, and looked at a basic example to illustrate the concept. Now take a look at a real world example.

This hand was posted in the Pokerstars Discord school_handreviews for feedback. We are playing in a 6-max 10NL game and it folds to us on the button. We are 100 BB deep and elect to open to 3x with 76o. The SB folds and the BB player defends with a call. The flop comes: 7♣6♦2♦

Who has the range advantage here, and who has the nut advantage? One of the responders to the hand said this flop favors the caller’s range, but is that actually the case? It’s not, although it’s an easy mistake to make if you’re not looking critically at the ranges. What people generally mean when they say this is that the big blind defending range hits this board while the PFR’s range does not. But when you think about it, is that true? No, it’s not. For sure the big blind is defending with a call with 77, 66, 22, 76s at the very least. Maybe 76o? Probably not 72 or 62 for a 3x raise on 100bb effective. So there’s no question that the big blind defending range includes a number of holdings that hit this flop hard.

But so does the preflop raiser! Can’t the preflop raiser flop sets on this board? Certainly, they are opening all pocket pairs. They are opening 76s. Although I personally think their actual open was a bit too wide, clearly they can have all the combos of 76o here as well as that was their actual open this hand. I doubt they’re opening any 2 cards on the button, so we can rule out 72o and 62o, but the big blind is almost certainly folding those preflop as well. In short, all those hands that the big blind defending range hits this board hard with are also hands in the button’s PFR range as well. So the reality is, neither player has a nut advantage here.

What about a pure range advantage though? Both ranges realistically can have all the 2 pair+ holdings on this flop, but the preflop raiser has a distinct advantage in strong 1 pair hands. Think about it. The PFR has literally all the overpairs in their range, but the big blind defender does not as they would likely 3-bet many of the strongest pocket pair combos preflop. So their preflop calling range excludes many of these.

Thus we would expect the PFR to actually have a range advantage in this spot. Both ranges can have the nutted hands, and have numerous draws possible in their ranges, as well as plenty of air. But the PFR will have the advantage in 1 pair hands.

If we take a look at the ranges visually, our PFR is probably doing something akin to this:

That is roughly 55% of starting hands.

While we can never be sure precisely what the big blind defending range is, for the purpose of this article we’ll approximate it as something like this:

Notice we’ve excluded big pairs and AK/AQ/AJs from their preflop calling range, putting those hands in their preflop 3-betting range. We’ve also included some Ax suited combos as 3-bets. We’ve not included any suited connectors, and left them all in the calling range. Clearly this is an inexact science. They might call pre with 99. They may include 76s in their 3B bluff range on 100bb effective. But this is a reasonable approximation. Running the equities, we find:

So our PFR’s range has an equity advantage, positional advantage, and initiative in the hand. Neither range has a nut advantage. Over all, this is a good spot for the PFR to be in, and a poor spot for the big blind defender.

What are some of the things the big blind can do to counter this effect? They may include some stronger combos in their calling range preflop, so their range as a whole is stronger post flop. But the first adjustment I would make as the big blind player is to 3-bet this opponent’s button opens more frequently. We have them opening 55% from the BU, just based off the fact that they opened 76o here and all the hands that applies. This is way too wide to defend properly against a 3-bet out of the blinds, so confront them with more 3-bets. That doesn’t mean a super wide button opening range can’t work in your favor. But rather, it exposes you to being 3-bet wide as an exploit. If your opponents don’t 3-bet much from the blinds because they’re weak or passive or just fun players wanting to see flops, then this strategy is okay because they’re not exploiting you. They’re not making you pay for getting out of line with your button steals, so you can see a lot of flops against the big blind defender with an advantageous post flop situation. If they 3-bet, what is the button continuing with? Something like this?

I’ve included all suited ace combos, we kept out the smallest pairs, etc. We’ve not differentiated between button 4-bets or flat calls of the 3-bet, just estimating a continuing range facing the 3-bet. This particular range is about 13% of starting hands. So if the button opens 55%, and continues against a 3B with 13%, they are folding to the 3-bet 76% of the time. In reality it’s probably a bit tighter/higher fold %. If we 3-bet to 4x out of position, making it 12 to go, we are risking 11 (we already had 1 blind posted) to win 4.5 blinds. This has to work 71% of the time or more to make us an immediate profit by them folding. Because they’re opening so wide to start, we’ve determined they are folding well more than 71% of the time. They’re forced into a mistake, either folding too much so we turn an immediate profit, or continuing too much so their range heading to the flop is saturated with too many weak hands for 3-bet pots.

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