ok, this can now officially be called a dumpster fire

i got football practice and a pep rally (the guys on the team are gonna run through mainstreet in our uniforms) in a in a few mins but once i get back ill continue

Football practice? How old are you? Brings back memories of mid August football camps for me...

+1, let's go wildcats

Should I post some photos to settle the dispute? Or is this too much fun?

Please post photos and make the madness stop.

I'm glad my question has all these different responses. It really shows that almost no one has any clue what GTO is (myself included).

there are plenty of situations where solver mixes, say, 33/33/33 between two sizings and a check-and NO this is not a converging issue. youre telling me its the most directly EV line to do something 33% of the time ����
so we're always taking the most +EV line..33% of the time
GTFO kid

whatever your book says i can assure you youre either misapplying or misinterpreting

^ If it mixes, it means all lines have the same ev

So not only are you illiterate when it comes to poker but you're rude as well? When shall I kick your ass at warcraft III?

could someone please explain to him that the page he posted says exactly what ive been saying all along, and actually refutes what he is saying... *facepalm*

Thanks for the picture - but we already knew Mixed frequencies were the same EV.

Where does it say - GTO takes the highest EV line all the time - always - regardless of the best strategy?

Don't mix things up, gto takes the highest ev line, always, against an optimal opponent

And an exploitative strategy does the same against an exploitable opponent

Lmao, get a room. Everyone on the first page said exactly what he was saying (and more in-depth, although with some errors) and you were calling the thread a dumpster fire, and apparently called someone a 16 year old who doesn't know anything.

I don't get what you're asking really since we agree that mixed frequencies are the same EV?

What does that leave? Non-mixed frq hands? So you're asking, if a solver checks 100% of the time, which line has the highest ev between betting and checking?

Also, coming from a mathematical persepctive it is literally impossible to have the same EV. Anybody who says there is the "same EV" doesn't understand math/probability. Similar example: Think back to what the probability of a continuous random variable is at some fixed point, or look it up (ie ZERO). That is because it takes values on a range of values, where every interval is an uncountably infinite set. So even on the set [0,1], which is very small, every P(X = xo) = 0. And it's not very intuitive, but clearly on the range that EV can take, it's obviously very big so it's impossible to have the same EV. ie EV1 = 11.257812351912481242183 is not equal to EV2 = 11.2578123519124812421839. EV2 has .000 whatever 39 higher EV so if that were true the solver would use EV2 at 100% frequency...

So IF a solver did always take the highest EV line, there would be ZERO mixing. So that in of itself already invalidates the conclusion that solvers always take the highest EV line.

ie if the EV differs by ANY epsilon greater than zero, the solver would choose the higher EV hand and use that at 100% frequency, which obviously it does not do.

ie NOT TRUE

Never really expected to have any useful applications of pure math, which can be dry and complete garbage at times but there it is. Math aside, LordPallidan is basically on point.

it's literally hilarious how people who don't know what the hell they're talking about are so openly arrogant and condescending. Welcome to poker.

indeed LMFAO

Maybe I should clarify what FD said : GTO bots playing against each others indeed take the highest ev lines. Any other line is lower ev.

Edit : was unclear

Ok, maybe you are having trouble reading the text in the picture so I'll quote "then by definition the ev of both lines against an optimal opponent still has to be equal"

Yeah, I can read, thanks.

Furthermore, I am almost certain that whoever wrote that definition is still wrong, at least from a mathematical perspective. It might be correct (or what the author is trying to say) is to say that the solver develops it strategy such that its EV is maximized/strategy is unexploitable, although the individual hands themselves have lower/higher EV in one specific instance

It's also somewhat wrong to say that one line/one individual hand has less EV than another since it's range vs range, if you did something at 100% frequency you'd drag the EV of your whole range down... it's really not that complicated. That's why mixing exists and nothing is done at 100% frequency.... Lord is literally spoonfeeding everyone here.

I hate getting into GTO dick-waving contests since I play a highly exploitative strat and care more about winning money than having a jerk-off session with other GTO nerds and belittling others who don't join, but it's hilarious when the GTO nerds themselves have no idea what they're talking about and talk **** on other posters.

Are you refering to the author of the book?

If so you can ask him here https://forumserver.twoplustwo.com/3...ssion-1668307/
I see, then why do solvers sometimes bet or check at a 100% frequency?

Yeah, i'd rather not waste my time on the interpretation of a definition, which often can be interpreted in multiple ways.

That's why i said somewhat wrong. Because technically (especially in mathematics), you can almost always find one, or multiple cases, such that whatever you're saying doesn't hold true. That is, if you made a statement about nearly infinite truths, if you found one and only one counterexample, then the statement isn't true. Yes, it's true enough to mostly accept it as true and that's how we live our lives, by going on things that are "good"/"true" enough, but "technically" it isn't. I meant in general, and in a lot of cases.

Here's one for lulz. If you rob a bank, then you go to jail. Is that false simply because people have gotten away with it before? To humans, no. that's why you don't see people running around robbing banks. To a mathematician, yes it is false.

That's very interesting but I don't think it has its place here.

Nice deflection. The type to always have the last word, I see.

Edit: Didn't mean to say nothing is done at 100% frequency, meant "a lot of hands/ranges".

No it's interesting but I don't think it has any value here. Maybe you can show me an instance where it's useful to better understand poker theory because I've never seen this stuff in any poker book, site or whatever. There's an internal contradiction in your statement, mathematicians are humans.

But let's not derail the thread :x

That was to explain why i said “somewhat wrong” and why I didn’t care about the author’s definition, since all definitions are also arbitrary and subject to interpretation. If you really wanted to nitpick at every word and every sentence in his book, you could find a lot of “technically” wrong statements. That goes for any sentence on the internet, let alone a book. That aside it’s funny how OP has a bunch of holes in poker theory understanding yet berates a lot of those who are mostly giving him right advice/information and remains steadfastly stubborn, time and time again. And he isnt even some nosebleeds player, high stakes pro or whatever.

Alright, sure there may be somewhat of a loose contradiction. If you wanted to be precise, you’d say that the statement is false from a mathematical perspective.

Okay sure because I’m pretty sure not too many people care about “math” anyway lol and hate it

You never see this type of stuff because people who study math don’t exist LOL. And by math, i mean real math. Not lol calculus/differential equations/plug-and-chug engineering math.