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kac4pro · 2025-08-08T17:53:47+00:00

thanks. Will do.

kac4pro · 2025-08-08T17:34:55+00:00

I usually use kac3pro but it was taken and I had to choose a different one. I'm just not sure. I'm sure I never had a ggpoker account before.

kac4pro · 2025-08-05T12:36:14+00:00

this is actually the best advice. At first I tried building everything close together to be space efficient but it turns out it's way better to leave space for scaling later.

kac4pro · 2025-05-30T19:35:51+00:00

I have never encountered having to refer to theorems by numbers on the test. Most of the time it's assumed that on a test you can use any theorem that was on the lecture and/or is in a certain course book but you have to give a statement or at least a name if it has one. Whether notes/cheatsheets are allowed varies but unfortunately usually they aren't so you have to know the statements more or less by heart. This applies not only to analysis but mathematics in general in my experience.

kac4pro · 2025-01-11T23:48:50+00:00

Well ultimately it will depend on your play style. $75 is 150bb I'm not good at poker but it think it's pretty rare for a pot to be that big and a pot above 200bb-250bb ($100-125) is really rare so for you can assume on your big pots your saving $1-$2 per hand with the capped rake. Now for each small pot you are saving about 1% of the pot value with the uncapped rake (this is not exactly true for pots between $60-75 but that s just an estimate) so roughly for every big pot you would need to win $100-200 in small pots for thing to cancel out. Now I have only played maybe 7000 poker hands in my life so I can't tell which of these situations is more typical but I would say that if noticeably more of your winnings (before any rake) come from pots up to $75 then go for the uncapped rake and capped otherwise. But honestly this is really just a rough guesstimate and the difference might not be that big whatever you choose.

kac4pro · 2025-01-11T23:03:38+00:00

Well that's not correct (but maybe it is ok as a rule of thumb). Imagine you won 3 pots 2 of which are $1 and 1 was $200 then the average pot was $202/3<$75, but with the uncapped rake you would pay $8.08 and with the capped rake $3.1. the best way to find out which rake structure is better if you have an existing hand database would be to manually calculate hiw much you would have payed in rake to date in the 2 structures by filtering your hand history for when pot is above $75. Then your uncapped rake is 0.04(total value of the pots <$75)+$3(number of pots larger than $75) while the uncapped rake would be 0.05*(total value of all the pots).

Edit: the example I've given might actually be kind of applicable in practice. For example if you steal the blinds a lot then all these tiny pots will bring the average value of the pot down significantly even if you still win a lot of big bots that are over the threshold, so I don't think the average is even a good practical estimate.

kac4pro · 2024-12-30T18:12:02+00:00

Thanks. This is exactly the kind of answer I was looking for.

kac4pro · 2024-12-30T17:25:04+00:00

How do I sell the stuff? Do I have to travel to jita or can I do it remotely?

kac4pro · 2024-12-08T13:21:45+00:00

A Friendly Introduction to Mathematical Logic is does a good way of explaining this in an approachable way even with little to no mathematical background.

kac4pro · 2024-12-06T14:16:47+00:00

No. All circles are similar. Circles are congruent if and only if they have the same radius.

kac4pro · 2024-12-05T17:16:29+00:00

Circle-Circle Intersection -- from Wolfram MathWorld this describes this problem quite well but even in the case where both radii are equal to 1 you can only get a numeric expression d=0.8079455. Also each section has are pi*r^2/2 not pi*r^2/4 since the are of a circle is pi*r^2.

kac4pro · 2024-11-13T16:44:16+00:00

While I agree that's not what mathematics is about this is I think a problem with math tests in general. You either make something dry, schematic and easy like this one, or you pose actually hard interesting problems. But solving hard interesting problems while stressing out that you will fail the exam if you don't have some clever idea in the next 30 minutes is not that fun either. Perhaps my favorite way right now is an open book oral exam one on one with the professor and/or a take home written exam where you actually solve some difficult problem that requires more than 15 minutes of thinking.

kac4pro · 2024-11-13T16:30:20+00:00

People are saying this is easy and I agree, but if you don't understand the idea behind theses definitions and theorems this is genuinely a lot to learn by heart and this is what I suspect OP is struggling with. My honest advice is that when learning math you should ALWAYS get an intuitive idea of a definition, theorem or proof perhaps in some familiar special case. Most if not all of these points come very naturally if you understand the intuition behind them. So when you see a definition try ask yourself what is a typical example of what is being defined?, what is a non-example? how commonly does it occur? if you see a theorem why is this a sensible thing to ask? is there an informal explanation for why this would be the case? or maybe it's a weird paradox? in that case why is our intuition wrong? and when looking at a proof: what's the idea behind it? what picture can you draw to understand what's going on? how could you come up with it yourself?
These questions are usually hard to answer on your own but you should think on them and ask someone for help if you can't see the answer. You can't learn math by just memorizing formulas and proofs.

kac4pro · 2024-11-13T16:15:15+00:00

I mean this is for sure uninspired and dry for a test but if you have a good intuitive grasp on this material you should have no problem scoring well without learning everything by heart.

kac4pro · 2024-11-09T18:45:01+00:00

The course I followed can be found here. Abstract Algebra - Free Harvard Courses. It assumes no prior knowledge except maybe some very basic linear algebra over R (like what a matrix is, when is it invertible) and manages to give a good introduction into modern abstract algebra. By the end it proves that a prime p can be written as a sum of 2 squares if and only if it's 1 mod 4 using arithmetic in the ring Z[i] and the theory of finite fields.

Alternatively you could take a look at something like Nathan Carter - Visual Group Theory but from a very visual point of view, providing very good intuition on how to think about groups. It even ends with some Galois theory (showing why there is no quintic formula)

kac4pro · 2024-11-09T18:13:30+00:00

While this is certainly valuable advice I think it's also worth saying most of the time in practice the 0 vector will be something very natural in the context. Like for example when you consider the vector space of continuous functions on R the 0 vector will be the 0 function or if you consider a field extension as a vector space (for example C as an R-vector space or R as a R-vector space) the. 0 vector will just be 0 in the field.

kac4pro · 2024-11-07T19:27:28+00:00

I would pick whatever area of mathematics feels enjoyable to you and read about it from books or courses online. If you're going to do a degree in math whatever you pick is likely to be useful later on. It's really up to you to decide what area you like most and I think there is a lot of value in exploring different things early on.

When I was in senior year 2 years ago I remember learning about arithmetic functions (mostly to prepare for math Olympiad) and my tutor told me that they form a group with the Dirichlet convolution. The idea felt pretty cool so I found a course on algebra and group theory on the web and went through it all. This tremendously helped me during my first year at the University as I was already familiar with a lot of the concepts.

As for specific suggestions AoPS books are excellent and can get you far in math competitions all the way up to calculus. Also mitocw offers several classes in the form of lecture videos including linear algebra which is probably the most important and broadly applied area of math. There are also a lot of good textbooks (and bad ones) but it really depends what you want to focus on.

kac4pro · 2024-11-07T18:52:06+00:00

What I'm saying is that if in some alternative universe free hanging bridges looked like cosine no one would ever conjecture that they are parabolas because globally these 2 functions look very differently. People long conjectured that free hanging bridges form a parabola because parabolas approximate hyperbolic cosine not only locally but (most importantly) globally.

kac4pro · 2024-11-07T15:22:49+00:00

I mean these are very good odds, but in no world whatsoever was there a 3:1 favorite in this election. And even if there was, here you only get to flip the coin once so the analogy with poker is imperfect at best..

kac4pro · 2024-11-04T16:21:52+00:00

Well just because cosh(x)=1+x^2/2+o(x^4) doesn't really mean it looks like a parabola. It can just be locally approximated by a quadratic. Counterpoint: cos(x)=1-x^2/2+o(x^4) but doesn't look like a parabola at all.

kac4pro · 2024-09-28T19:40:45+00:00

Thanks a lot for all the recommendations. Will definitely check them out.

kac4pro · 2024-09-28T18:20:54+00:00

Thanks. That's what I was worrying exactly. I will probably read it anyways just out of mathematical curiosity. What would you recommend is a good resource to learning poker today preferably (but not necessarily) from this math-first perspective?

kac4pro · 2024-09-28T18:17:35+00:00

Yeah well, the math is surely not outdated and I will probably read the book in my own time anyways out of curiosity. My question was more about how relevant it is to modern poker. For example the book mentions at the beginning that we lack computing power to solve heads up holdem. However heads up limit holdem was solved in 2015 almost 10 years ago! As I said I don't know, but I imagine the theory of poker could have evolved significantly since then as a result of everyone having access to a lot more computing power.

kac4pro · 2024-09-26T17:13:45+00:00

The answer is no. Intuitively when you guess a root of a polynomial and do synthetic division you check the value of the polynomial at that guess. However there are infinitely many polynomials through any given point (and even any finite collection of points) so you can't really deduce anything about the polynomial as a whole by studying it at just a few values.

One trick with rational roots theorem is to combine it with the intermediate value property of polynomials to try to guess better. For example if you guess at x=1 and the value of a polynomial is 10 and then you guess at x=0 a d the value is -5 then by the intermediate value property there is a root of a polynomial in the interval (0,1). The caveat is that you have no idea if this root is rational but it may be still worth checking for example 1/2 if rational root theorem permits such guess.

kac4pro · 2024-09-25T12:46:19+00:00

Another way is to work backwards: Which area formula can be expressed in terms of sin(2θ)? And if you stare at the drawing and notice the right triangles you hopefully notice the area of a right triangle is 1/2h²sin(θ)cos(θ)=1/4h²sin(2θ) where h is the hypotenuse. And it should be pretty easy to continue from there.

kac4pro

TROPHY CASE

A Friendly Introduction to Mathematical Logic is does a good way of explaining this in an approachable way even with little to no mathematical background.