In this thread I'm analyzing what are the impacts of making a pretty wide overbet range OTR, including and excluding merged ranges, let's see what happens.

Imagine a spot like this



Ok, let's start with a villain steal range: 30%



Hero 3-bet range 10%



Villain calling range




Now, let's make a reasonable amount of hands that go down to the river for each player:

Hero: all busted flush draws, all JT, QT, all broadways with a , 98, KK, AA, AK, AJ with A AQ with A of
It's roughly 7.5% of hands, which is 75% of the initial 3-bet range(I'm assuming here a pretty aggressive post-flop player, semi-bluffing all gutshots OTT, also this board texture is good for the hero's 3-bet range).

Now to the villains' river range (we're assuming he knows about hero's tendencies and calls lightly), also K is a good card to barrel, so his river range will be like this:

OTF he folds his cards that didn't connect well, calls with the rest of his range(even sets, since slowplaying vs an opponent who is barreling a lot is optimal)
it will be roughly 11% of the total range.

OTT, he folds half of his pocket pairs and midpairs, keeps with Kx, sets, gutshots, pair+ draws, flush draws, his range will be around 7,5%


Hero Final range is 7.5%:
Air (3.2%): JTs(all combos), AQo with a , AJhh, AJo with a , AQhh, QJs QT, ATss AThh, SCs
Value range(3.3%): KQ, AK, AA, KK
Merged range(1%): KJhh, KThh, QQ, JJ

Hero's equity vs villain's range: 58.1%

Now let's make a calling range for villain: Fold the air and call with pairs+(4.5% out of 7.5%) = 40% fold, 60% call

Hero's equity vs villain's calling range: 43.9%

Always shove

Now let's make hero shove 100% of the hands OTR and calculate the EV

40% he wins the pot = 70.04*0.4 EV = 28
60% he goes in with 43.9% equity on a 294.92 bb pot = 294.92*0.439 - 112.44 = 31.09 EV * 0.6 = 18.65 EV
Total = 46.65 EV


Merged range with no bluffs

Now let's see how it goes with a merged range with no bluffs:
29.3% check-fold
70.7% shove
Villain keeps calling with 60% and folding 40%

Hero's merged range equity = 71.58(merging crushes bluffcatching pretty hard lol)
29.3% he checks-fold = 0 EV
40%*70.7% he wins the pot =19.8 EV
60%*70.7% he gets in with 71.58 equity = 41.85 EV
Total = 61.65 EV

Polarized range

Now let's see a polarized range with 1 bluff for every 2 valuebet shoving and hero check-folding his middle strength hands and rest of the air

13% medium strength hands checking
29% air checking
58% shoving

Hero has a 33% equity in his shove.

29% air showdown = 0 EV
58% shove EV = (294.92*0.33 - 112.44)*0.6*0.58 = -5.2 EV
58% shove EV that villain folds = 0.58*0.4*70.04 = 16.24 EV
Let's consider that villain is willing to valuebet half of his value range and bluff 10 shove respecting a 1/3 ratio between bluffs and valuebets = 30% betting, so hero will see showdown probably 70% of the time with his medium strength hands, let's make it like he wins 50 of those 70 and he folds always to a bet.
13% medium strength hands, 50% win at showdown = 0.13*0.5*70.04 = 4.5 EV

Total EV = 4.5 + 16.24 - 5.2 = 15.54

So, which is the best range to be shoving?
From the EV perspective, the merged range is crushing by a huge margin all the other ranges, but it considers that villain is calling with a lot of bluffcatchers, thinking that hero is unbalanced there on that spot towards bluffs. If villain adapts and stars folding his bluffcatchers and calling only with Kx+, he will call 36% of the time with 75% equity vs hero 100% shoving range, which will result in an EV of 44.83 -14.14 = 30.69 EV for hero

Vs a pure merged range I'm pretty sure the results will be lower than that when villain adapts, although it's a good exploitative range to use vs villains who love to hero call and don't have much knowledge of how your river range really is.

So you're saying that shoving your entire range has more EV than played balanced in that spot?
No. First, I made this spot out of my head, and maybe built that polarized range poorly. Second: These calculations consider hero playing poorly, like not knowing when to hero call and outplay an opponent, also villain's range should be larger than hero's, which increases the EV of a polarized shove OTR and showdown value with his midpairs.

Also these calculations are pretty simplistic and considering that 75% of the range OTF for both players would go to the river is pretty optimistic, although I forced that scenario because it simulates well 2 regs fighting really hard for the pot, so it's possible. On tighter ranges with more folds OTT and other board textures, the calculations here will have other results, increasing/decreasing the EV the different river actions for hero.

what do we get from this?

Hand merging is a really strong move, it has been proven that a lot of GTO ranges will have medium-strength hands valuebetting on that spot, I don't know which frequency though. But you should be shoving KT/KJ OTR almost always rather than check-calling those hands.

Advantages of hand merging
1- Makes the game easy for you
2- Makes the game hard for your opponent
3- Denies position advantage OTR
4- Put better villains on check(better villains will always show up with a looser range vs you, specially IP)
5- Makes your opponent play more careful and straightforward vs you
6- Variance becomes insanely high, which is also good for dealing vs better opponents: they will take a lot of time to realize what you're doing and probably will take a huge sample size to start adapting properly.

Why does hero only have 33% equity when he shoves a polarized/balanced range? You said he balanced 2:1 in favour of value, didn't you?

it is 2:1, but some parts of villain's calling range is stronger than hero's value range, also in that spot villain has more sets than hero, which may have a great impact on the calculations

how much EV should hero have vs villain's calling range? 50%?

Well in theory, if hero was making a pot-sized bet (not an overbet), he needs 66.7% equity against the calling range to make villain indifferent and to have an EV of pot. I think that if villain's calling range is so strong that he wins much more than 50% of the time when he calls, hero is betting too often. (Except when villain also folds way too often, allowing us to make many profitable bluffs, such that more of our EV comes from fold equity than hand equity).
One of the problems with your "strategy" is that you're assuming that villain doesn't adjust and always calls with the same range. Obviously if you merge (and have zero bluffs), your EV will be higher than if you balance and bluff a third of the time. But if villain has a huge range advantage, we shouldn't be betting very often at all in the first place, as we're just value-owning ourselves.
That said, if you know villain's precise (and unchanging) calling range, then you could calculate a "max exploit" bet-size and range that completely crushes him while minimizing your own losses.

The whole analysis can be simplified into one line: vs calling station, value bets thin and don't bluff.

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Not stations only, depending of the dynamics, some regs may call river shoves even wider than whales.
If there's a spot that would be too bluff-heavy for your range, you should merge more to exploit bluffcatching. Most villains won't have enough stats on you to adapt their calling range, so you can jam midpairs, TPWK, sets/2p on 1-to straight boards, low flushes on 4- to a flush board.

Also this kind of play is really annoying to play against: we hate when we have no decision to make. It restricts the opponent gameplay a lot.
Also it's common to see a lot of regs playing way looser than they should during reg battles, like guys double floating with crap just to steal OTR.

One thing I learned in the time I played hearthstone is that even though losing value and tempo overall, limiting enemy resources and options is really important: in dynamic games, the more options you have, more value you can get off things.

Just think about why people make more money IP than OOP and why your range is way wider when you're IP than OOP. Most people give up value for position: look at your calling range when you raised from UTG and BB 3-bets you: his range is probably the strongest 3-bet range possible, and sometimes you flat SCs which have a small equity vs that range, but play pretty well post-flop, specially IP. You're basically trading EV for playability.
So trading EV when you merge the river to deny position advantage imo is a good option.

From those ranges, the "always shove" version is probably the most annoying to play against in the long run. Even though it's -EV compared to better ranges in theory, it's easy to do and it reduces the edge advantage from better players.

Of course, they should fold more turns and play tighter, but if you turned an annoying good reg into a nit, then you will be fine, when you realize he is folding a lot OTT, just reduce ur river jam range to the nuts only.