Here:

BTN 3b versus MP flat

MP flat: {44-QQ,AJs-ATs,KTs+,QTs+,65s+}
BTN 3b: {QQ+, AKs, AKo, A5s, 87s, 76s}

Flop: J65r

MP equity: 45%
BTN equity: 55%

So BTN has the range advantage.

However, MP can have all sets and two pair, while BTN can have none.

So MP has the nut advantage.

Let me try to translate here.

These ranges are a mess. that is what Doodoo refers to as a toy game and cherry picking. it is like picking random hands. Doodoo says if both players use reasonable ranges this will lead to the fact that the player with the nutadvantage will also have a range advantage.

example used before

Range 1 AA
Range 2 AA/KK

This makes no sense. Because Player 2 would never continure with KK if player 1 only has AA.

It is a complicated topic and i dont really have an opinion on the topic.

MP defend range has like 2.5x as much combos as btn 3 bet range. many hands are supposed to be pure folds vs a btn 3 bet range like that. Just for the fun of it remove all Suited broadways from MP´s calling range because they would get r**** by a QQ+/AK value 3 bet range and just continue with all the pockets and SC. and then check for MP equity.

BTN 3 bet range {QQ+, AKs, AKo, A5s, 87s, 76s}

more reasonable MP flatting range {44-QQ,AQs,T9s-65s}

Okay, I cleaned up the ranges and switched to a slightly different example. These ranges are taken from Ki Lee's Fast Track Series on Crush Live Poker.

Situation is BTN 3b versus UTG1 flat. Flop is T86r

Ki suggests that BTN 3bs with {QQ+,AKo,AKs} (100%) and partials of {AJs+,JJ,87s+,A5s}. For simplicity in this example (as it barely affects equities), we can contract the partials and say that
BTN 3b = {QQ+,AKo+,AQs+,KQs,98s,87s} (3.77%).

Ki suggests that UTG1 opens {77+, all suited broadways, A5s-A4s,A9s,J9s,87s+,AKo,AQo} (10.6%). Let's assume UTG1 4bets the BTN 3b with {KK+, AKo, A5s} (2.11%) and UTG1 folds {KJs, KTs, QTs, J9s, A4s, A9s} (1.81%), Then UTG1's flatting range to the BTN 3b is
UTG1 flat = {77-QQ, AQo, ATs+,87s+} (6.64%).

Altogether, UTG1 defends 8.7% of their original 10.6% opening range. Note that if BTN 3bets with a 1x pot raise then UTG is supposed to defend with at least 65% of their range. Here they are defending with 8.7/10.6=81% of their range, which is probably reasonable if stacks are fairly deep.


With those ranges the BTN has a 52.5-47.5% equity edge over UTG1.

However, BTN is capped at 1 pair, while UTG1 can have two sets {TT, 88}.

These situations will arise quite often in 3bet pots when there is a middling flop. We will often expect the 3bettor to have a tight range with an overpair advantage leading to an equity edge, while the caller has a ton of missed suited broadways, but an advantage in flopped sets.

I don't understand why anyone would find such a basic fact to be controversial.

I played a hand the other day where I raised $15 in CO with K9s, button and bb called. Flop AA6r, bb checks, I bet $15, button folds, bb shows me KK and folds. People do weird things in live poker. Never say never.

No opinion needed when it's a math question.

Is this specifically A5s or A5s+?

76s and all the suited no-gap connectors or higher, or just 87s and 76s?

So MP would flat T9s but folds JTs and KQs?

AQs+ I assume. What about AQo+

Why are 22 and 33 eliminated?

Another example:

5h, Kc, 9d flop:

Range 1: 66+
Range 2: 99+, ATs+, KTs, QTs+, JTs, ATo+, KTo+, QTo+, JTo

Range 1 has range advantage of 54.7% vs 45.3%.

One more:

Range 1: AA, QQ - 66
Range 2: 99+, ATs+, KTs, QTs+, JTs, ATo+, KTo+, QTo+, JTo

Range 1 is still 52.5% vs 47.5%.

No opinion needed. Premise is clear and result is clear.

When there are more junks in a range, the value of that range will be lowered, irregardless whether there are bunch of nutted hands.

I didnt come up with the ranges and i dont like them. BUT
yes. against someone who 3 bets mostly QQ+/AK we want to rather call T9 than KQ or JT or AJ.

I didnt eliminate 22/33, they were never in the range. AQo is garbage.

Those are not my ranges. i just tried to make the defend range more reasonable vs that specific 3 bet range


I can not believe i am actually posting in the live poker forum.

Good luck guys.

So classic. Thanks.

run a tight UTG range against a tight SB flat range and the run a board like As5s6s...who has more flopped flushes and sets? but yeah the two concepts are pretty correlated otherwise...I don't feel like reading like 3 pages are arguments, why are we concerned about the difference?

There's always the possibility that they 3bet QQ/TT cause they "love ladies" and "always flop sets with tens". Also everyone knows that pocket kings are "ace magnets", and who doesn't "hate jacks"? Sorry, just amazed at how often I hear these spoken with no shame at 1/3 and 2/5.

This thread is a prove itself that poker is alive.
This post just enforces it.
And let’s just 3Bet 72o to have the chance to show it when everybody folds and see how cool I’m.

Ultimately it comes down to the fundamentals of understanding how combinatorics and expected values work.

If you are collecting $5 from your best hands but you are also losing $2 from bunch of losing hands, you are probably going to be less profitable than someone who may only be collecting $3 from best hands but isn't losing any money.

Actually, the proof is everywhere.

The fact that you need to illustrate that a range with more junks has less value than another range without junks is mind blowing.

2009: Should I 3bet my KK vs an MP raise?

2019: Are there any ranges that have a range advantage but not the nut advantage?

POKER IS ALIVE!

PS. Also, insulting other posters who have a different opinion or seem to be less strong players is not nice and is in fact counter-productive because it makes people afraid to post.

Great post.

Quite aside from the fact that you can use toy games to illustrate a point, and that people like Bill Chen and Jerrod Ankemann, to say nothing of Andrew Brokos, have done so.

Old Man Coffee opens in the cutoff with a range of {88+, AQs+, AQo+}. Lucy Gousee hasn't been paying attention, and calls in the big blind with her usual range of {JJ-22,AQs-A2s, K7s+, Q8s+ ,J8s+, T7s+, 97s+, 86s+, 76s, 65s, 54s, A9o+, K9o+, Q9o, J9o+, T9o, 98o} (She is three-betting QQ+ and AK, so when she flats, her range is capped.)

I think we can agree that these ranges are realistic for the sort of players we are talking about.

The flop comes 6h 5s 4s.

Run these ranges and this board into Equilab, and we see that Old Man Coffee is a 2:1 favorite overall. Lucy has tons of air in her range, while the old man has only AQ and AK -- and his air is significantly ahead of her air.


Board: 456
*******Equity*****Win*****Tie
CO*****66.91%**64.61%***2.30%*{ 88+, AQs+, AQo+ }
BB*****33.09%**30.80%***2.30%*{ JJ-22, AQs-A2s, K7s+, Q8s+, J8s+, T7s+, 97s+, 86s+, 76s, 65s, 54s, A9o+, K9o+, Q9o, J9o+, T9o, 98o }


However:

The old man has no sixes, fives, or fours in his range at all. The only suited connectors in his range are AKs. Lucy, on the other hand has 76s in her range, and all the sets. She also has many, many more flush draws than he does.

Old Man Coffee has a huge range advantage over Lucy Gousee. However, Lucy has a tremendous nut advantage over the old man.

Range advantage and nut advantage are two different things. If you do not understand this, you play deep-stacked NLHE at your peril.

So both OMC and LG are not playing anywhere close to optimal ranges. At equilibrium, there is no distinction between nut advantage and range advantage.

It only exists against players with serious preflop leaks as you illustrated above.

When you study poker you should study the optimal solution first - then any deviation would be your exploit. So saying there is a difference between range advantage and nut advantage is an exploitative concept. It doesn't exist at GTO.

That was my only nit pick I had with Jarretman's post. We are never at a range disadvantage when we open in the LJ and BTN/SB/BB calls preflop and the board comes KJ8. Theoretically we have the strongest range.

You would need a solver to prove your point valid. Equilab is not robust enough software.

What are your ranges for UTG 9max open, BTN 3bet, UTG flat? What are their equities on 986r and 986tt? For the ranges I am using, this example illustrates a contrast between range and nut advantage.

"Range advantage and nut advantage are the same thing at equilibrium" is a very different statement from "Range advantage and nut advantage are the same thing."

At equilibrium, the EV for calling the villain's river bet is the same as folding to it. This does not mean that the EV for calling river bets and folding to them are the same in general.

I think we can agree that calling and folding are different things, yes?

I don't have optimal 9 max ranges but I understand what you are getting at.

If UTG has all 66/88/99/98s then he has more nut combos but not a "range advantage" over BTN

But this is most likely incorrect. UTG would have the range advantage here because BTN has more AK/AQs hands while UTG does not.

Just because you have a stronger range preflop doesn't automatically give you a range advantage on the flop.

This would also most likely be a 100% Donk Lead spot for UTG for the reasons I gave.

Run the example I gave earlier with A-high monotone flop with a tight UTG range against a SB call range... you could make it a 4-bet and call range if you play 3-bet only from SB, or want to use the UTG range you posted earlier..the point is that sometimes it happens where the caller will have a nut advantage but not the range advantage...I will agree that it is pretty uncommon

But that is not at equilibrium, so of course it doesn't count.

Solvers don’t even find the true NE, so DooDoo is making an unverifiable and unfalsifiable claim when he says polarity advantage never exists without equity advantage at equilibrium. It is senseless to argue about such a thing.

What is special about poker that doesn’t exist in toy games? Is it because poker ranges start off symmetrical? Would a toy game example with symmetrical starting ranges suffice?

Polarity advantage is also hazily defined. If it is just “more nuts” then a player with 2% nuts, no second nuts and a lot of middling strength hands has a polarity advantage over a player who has 1/3 second nuts and 2/3 air, which doesn’t seem right to me.

These are all strong points. I just want to mention it's not just flop play, but also how equities can shift across turns on KJ8tt if the flop is x/r'ed (say) and the turn is card X in the following scenarios: (A) BTN vs SB 4bet pot and (B) UTG vs BTN 4bet pot. The scenarios branch even further, as preflop 4bet ranges may look very different at 100bb and 200bb effective stacks. Nobody has done enough solver work to make definitive statements that two different range v. range indicators are 100% identical to each for all possible preflop and flop betting lines, against all possible turn cards, and at all possible stack depths. There's literally thousands of different scenarios to evaluate just for this one flop.

All of this is a moot point anyway. Nobody has access to the absolute correct equilibrium 3/4/5bet ranges for position X v position Y, because those ranges will look very different for 100bb effective stacks and for 500bb effective stacks (never mind all the depths inbetween). Never mind the fact that even for any fixed stack depth, you would need a supercomputer to compute optimal preflop ranges using PIOsolver. Mere mortals like us only have access to very rough approximations of optimal ranges built using crude tricks like flop batching.

Tl;dr None of us have access to equilibrium preflop ranges even just for the 15 different HU spots within 6max, so this argument is dumb.