I await Savy's post and hopefully that will help me out a lot. If I learn it, it better come in handy.
It's not clear to me what you mean by algebra. I wouldn't waste our time here like that.
I was only trying to point out that you already know and use algebra. You may not know of it under that title, but there it is. So be relieved that you already know a lot more than you thought you did a second ago about algebra.
If you can follow my prior post, that's really the extent of the algebra involved in poker and a direct example of how it applies.
Does anyone know any websites that will teach you how to move stuff around/manipulate the equation to find what you want? I'm comfortable mixing numbers and letters but i don't know what you can or cannot do to an equation and how to break it down, all i remember from school is if something crosses the equals sign it does the opposite but when iv been trying to figure out some of spoons algebra before this didn't even apply, example of where i get stuck;
B/(B+F) = 0.27
B = 0.27(B+F) so to get this far we take the (B+F) over the '=' sign and it comes multiply as it was divide the other side? Is that right?
B = 0.27B + 0.27F then we multiply out the brackets to get this line
0.73B = 0.27F Now i'mstuck, i just tried squaring it there because i thought theres two B's BxB is Bsquared so we have to square 0.27 as well but i comes out at 0.073 not 0.73? This example is from this thread http://www.flopturnriver.com/pokerfo...rd-192649.html
B = 0.27F/0.73
B = 0.37F
Does anyone know anywhere where i can learn these rules, i think i could learn this pretty easily only i don't know the rules.
You can do anything you want as long as you do the exact same thing to both sides of the equation. That's pretty much all you need to know.
B/(B+F) = 0.27
B = 0.27(B+F)
^ Here we just multiply both sides by (B+F). It appears to "move" to the other side. Here's another example that's a bit more practical:
2x + 5 = 13
The objective is to have x = "a number" so that we just know what x is. Note that 2x just means 2 times x. We can subtract 5 from both sides and get this:
2x = 8
Now we can divide by 2 on both sides and get this:
now use the distributive property in reverse
(1)B - 0.27B = 0.27F <-- just showing the hidden 1 that multiplies, well everything.
(1 - 0.27)B = 0.27F
simplify
0.73B = 0.27F
So if we're solving for B we want to isolate all B's and find the value of one single B? and the reverse of removing brackets is adding brackets, so do we just add the brackets to the multiplication things (terminology fail)
So if we get to the stage in an equation when we have all the B's on one side we have to use the reverse distributive property (add in brackets to breakdown that side of the equation to get us a solvable equation for a single B?
I'm aware the letters change, like if we were solving for x when we get to the stage of having all X's on one side of the equal sign we use reverse distributive proerty to enable us to actually solve for x?
Am i on the right track here?
10/10 post btw all us algebra noobs will learn from this, very instructive.
It's not clear to me what you mean by algebra. I wouldn't waste our time here like that.
I was only trying to point out that you already know and use algebra. You may not know of it under that title, but there it is. So be relieved that you already know a lot more than you thought you did a second ago about algebra.
If you can follow my prior post, that's really the extent of the algebra involved in poker and a direct example of how it applies.
Jesus Christ, how the fuck are you doing that. It just makes no sense whatsoever. I fucking hate algebra.
And try to go through the examples. It'll take you a while to get comfortable with it, you aren't going to be ableto go through the whole thing in an hour it'll take a few hours worth of effort to get through it.
And try to go through the examples. It'll take you a while to get comfortable with it, you aren't going to be ableto go through the whole thing in an hour it'll take a few hours worth of effort to get through it.
I did start writing a thread on algebra, but it'd be all over the place.
Getting comfortable with it takes most people doing a lot of examples and you will eventually get the hang of it.
I'm working on it. I don't care what anybody says, that website is not basic algebra, it's hard. Basic algebra is 2a + 3b = 5ab. ( I hope I got that right haha )
MMM's post explains it very wellimo. As long as you do whatever to both sides you should be ok and the most of it is add/subtract/multiply/divide.
Also spoons; 2x+5=13 example is a good starting point to understand the objective of algebra; turning 'x' (or whatever variable for that matter) into a number.
Just take your time and work through it line by line.
MMM's post explains it very wellimo. As long as you do whatever to both sides you should be ok and the most of it is add/subtract/multiply/divide.
Also spoons; 2x+5=13 example is a good starting point to understand the objective of algebra; turning 'x' (or whatever variable for that matter) into a number.
Just take your time and work through it line by line.
I understood Spoon's post so I have to be happy with that haha
Jesus Christ, how the fuck are you doing that. It just makes no sense whatsoever. I fucking hate algebra.
It's just a method of taking one true statement and making other true statements come out of it by doing identical processes to equal things.
Let's start with the simple example from earlier:
2x + 1 = 5
I just made this up, it comes from nowhere, it represents only an example to illustrate some concepts.
We want to solve for x.
Definition:
"solve for x" means we want a single x on the left hand side of the equals sign and no x's on the right hand side of the equals sign.
Here we go.
2x + 1 = 5
We're not too interested in the 5, since it is both not an x and already on the right hand side.
There's that 2 in front of the x. However, if we try to divide by 2 now, it will complicate things. I'll do it later, just to show that the steps don't have to be in a certain order.
For now, let's focus on the + 1.
I want to make the +1 go away, and the best way to do that is to make it +0.
Useful info:
I can add or subtract any number I want to as long as I do it to both sides.
I don't want to pick just any number, though. I want to pick the number that turns +1 into +0, which is - 1.
So I want to subtract 1 from both sides of the equation.
2x + 1 - 1 = 5 - 1
It's just a method of taking one true statement and making other true statements come out of it by doing identical processes to equal things.
Let's start with the simple example from earlier:
2x + 1 = 5
I just made this up, it comes from nowhere, it represents only an example to illustrate some concepts.
We want to solve for x.
Definition:
"solve for x" means we want a single x on the left hand side of the equals sign and no x's on the right hand side of the equals sign.
Here we go.
2x + 1 = 5
We're not too interested in the 5, since it is both not an x and already on the right hand side.
There's that 2 in front of the x. However, if we try to divide by 2 now, it will complicate things. I'll do it later, just to show that the steps don't have to be in a certain order.
For now, let's focus on the + 1.
I want to make the +1 go away, and the best way to do that is to make it +0.
Useful info:
I can add or subtract any number I want to as long as I do it to both sides.
I don't want to pick just any number, though. I want to pick the number that turns +1 into +0, which is - 1.
So I want to subtract 1 from both sides of the equation.
2x + 1 - 1 = 5 - 1
Do you follow so far?
I understand that x is 2 in this equation but this is a super simple one.
Your intuitive understanding of algebra is getting in the way of your intellectual understanding.
If the solution of this equation is clear to you, but the B/(B+F) = 0.27 equation is not, then just re-read that post until it makes sense. The methods and concepts are the same, except for the distributive property, which I can more clearly explain if you don't like the web sites' explanations.
i seriously cannot be assed reading the wall of text above. but i once found myself in a similar position to cobra. hated maths. reluctantly realised maths could help me get better at poker. tried to make excuses as to why i didn't need said maths. started learning. i'm still fucking attrocious at all but the simplest of maths. but i found these two resources spoonitnow gave me the most helpful.
good luck if you bother with it. it's certainly beneficial. it's also less boring learning it the second time around when you actually have a purpose for it.
The following is the easiest way I know how to explain the basics of solving equations. Please let me know if these examples help or not so that I can make better ones in the future.
We'll have to use examples with larger numbers that you can't just do in your head for this to work. In all of these examples, we're going to solve for x. (That just means figuring out what number x is.) I used some color to make it easier to see what's happening in these three examples.
The Rule You Need to Know: You can do something to one side of the equation as long as you do it to the opposite side of the equation. (The two sides are the left and right of the equals sign.)
Example 1: 372x = 36456
Remember that 372x just means 372 times x. We would like to have x = "a number," but the multiplication by 372 is keeping us from having that. We can get rid of this problem by dividing the left side of the equation by 372. To keep the equation balanced, we also have to divide the right side of the equation by 372.
372x/372 = 36456/372
x = 98
Example 2: x + 14.68 = 43.93
We would like to have x by itself on the left side of the equation. Obviously, the addition by 14.68 is keeping us from having that. We can get rid of it by subtracting 14.68 from the left side of the equation. Since we're going to do it to the left side, we also have to do it to the right side. Here's what we get:
x + 14.68 - 14.68 = 43.93 - 14.68
x = 29.25
Example 3: 2.2x + 5.467 = 25.091
This example is just barely more complicated than the first two. Again, we'll want to get x by itself. To do so, we'll need to get rid of the addition by 5.467 and the multiplication by 2.2. We can only get rid of one at a time, so we'll start with getting rid of the addition by subtracting 5.467 from both sides.
We're now one step closer to having x by itself, so we have made progress. Now we'll divide both sides by 2.2 to get rid of the multiplication.
2.2x/2.2 = 19.624/2.2
x = 8.92
If you can understand the thought process and the strategy used to get x by itself in examples like these, then you're only a couple of rules away from having a decent enough understanding of basic algebra to do things like solve for balanced strategies.
Last edited by spoonitnow; 02-19-2013 at 07:26 AM.
The following is the easiest way I know how to explain the basics of solving equations. Please let me know if these examples help or not so that I can make better ones in the future.
We'll have to use examples with larger numbers that you can't just do in your head for this to work. In all of these examples, we're going to solve for x. (That just means figuring out what number x is.) I used some color to make it easier to see what's happening in these three examples.
The Rule You Need to Know: You can do something to one side of the equation as long as you do it to the opposite side of the equation. (The two sides are the left and right of the equals sign.)
Example 1: 372x = 36456
Remember that 372x just means 372 times x. We would like to have x = "a number," but the multiplication by 372 is keeping us from having that. We can get rid of this problem by dividing the left side of the equation by 372. To keep the equation balanced, we also have to divide the right side of the equation by 372.
372x/372 = 36456/372
x = 98
Example 2: x + 14.68 = 43.93
We would like to have x by itself on the left side of the equation. Obviously, the addition by 14.68 is keeping us from having that. We can get rid of it by subtracting 14.68 from the left side of the equation. Since we're going to do it to the left side, we also have to do it to the right side. Here's what we get:
x + 14.68 - 14.68 = 43.93 - 14.68
x = 29.25
Example 3: 2.2x + 5.467 = 25.091
This example is just barely more complicated than the first two. Again, we'll want to get x by itself. To do so, we'll need to get rid of the addition by 5.467 and the multiplication by 2.2. We can only get rid of one at a time, so we'll start with getting rid of the addition by subtracting 5.467 from both sides.
We're now one step closer to having x by itself, so we have made progress. Now we'll divide both sides by 2.2 to get rid of the multiplication.
2.2x/2.2 = 19.624/2.2
x = 8.92
If you can understand the thought process and the strategy used to get x by itself in examples like these, then you're only a couple of rules away from having a decent enough understanding of basic algebra to do things like solve for balanced strategies.
YES! YES! YES! I actually understand everything you just wrote.
Let me try;
3.8x + 7.975 = 54.698
OK, so first we have to get x by itself. First thing is to get rid of the 7.975, we do this by subtracting 7.975 and we have to do this from both sides.
3.8x + 7.975 - 7.975 = 54.698 - 7.975
3.8x = 46.723
Now to get x by itself, we can divide both sides by 3.8.
Now that you got that, the only thing you need to do to solve more complicated ones is to be orderly and take it one step at a time (in the beginning).
try solving for x: 5x + 3 = 9x - 7
Spoon, do him some distribution and factoring next.
Last edited by daviddem; 02-19-2013 at 08:07 AM.
Virginity is like a bubble: one prick and it's all gone
Ignoranus (n): A person who is stupid AND an assh*le
YES! YES! YES! I actually understand everything you just wrote.
Let me try;
3.8x + 7.975 = 54.698
OK, so first we have to get x by itself. First thing is to get rid of the 7.975, we do this by subtracting 7.975 and we have to do this from both sides.
3.8x + 7.975 - 7.975 = 54.698 - 7.975
3.8x = 46.723
Now to get x by itself, we can divide both sides by 3.8.
3.8x/3.8 = 46.723/3.8
x = 12.30
I hope I have got that right.
Congrats man. Next you need to learn how to add and subtract things that have variables in them.
2a + 3a = 5a
7x - 4x = 3x
4x + 3y you can't combine, the variables have to be the same. It's like trying to add apples and oranges.
Keep in mind that x is the same thing as 1x. So x + 3x = 4x.
Example: 3x = 2x + 7
Here you can subtract 2x from both sides.
3x - 2x = 2x + 7 - 2x
x = 7
Ta da. I'll come back and play with you guys later.
At any point, you can flip what's on the left and the right. For example:
2x + 3 = 7
is the same as
7 = 2x + 3
Originally Posted by Cobra_1878
I did that but it left x on the right?
5x + 3 = 9x - 7
We can take 4x from each side.
Taking 4x from each side doesn't really accomplish much. See how you're still left with an x on both sides? What if you subtract 5x from each side instead? That would get rid of the 5x on the left side.
Make sure you try and find some more examples to practice though as you want to iron out any mistakes you have.
PS - So you feel good about it, I had a chemistry teacher who had a phd in chemistry who I had to explain you could collect like variables together in an equation.
Two more points I want to make now that you've gotten this far:
Point 1
You can manipulate equations that have multiple variables, even if you aren't necessarily solving them. For example, if you had
a + b = c
You could subtract b from both sides if you felt like it and get
a + b - b = c - b
a = c - b
There are a lot of applications of this, but I just wanted to plant the idea in your head. Part 15 from http://www.flopturnriver.com/pokerfo...ad-180192.html uses this idea to show where the bet/(bet+pot) shortcut comes from.
This is something that comes up a lot and some people don't fully understand, so I'm making a special place for it here. If you have something that says 6(3+4) normally you'd add 3+4 to get 7 and have 6(7) which is 42.
Side note: If you don't know, 6(7) just means 6 times 7, and similarly 6(3+4) means six times the sum of 3 and 4.
But back when we have 6(3+4), there's another way we can work it out using a relationship between numbers that we call "the distributive property". This says that we can start figuring out 6(3+4) by doing 6*3=18 and 6*4=24 to get 18+24, and then do the addition 18+24 = 42. The name of the property comes from thinking of it as the 6 being "distributed" to the 3 and 4.
One more example. Say we have 4(2-7). Normally we'd do 2-7 to get -5, and 4(-5) = -20. With the distributive property, first we would "distribute" the 4 to get 8-28, and then do the subtraction 8-28 = -20.
Here's why this is important. Suppose you have an equation that looks something like this:
2(x - 2) + 3x = 21
It can be really hard to figure out how to make progress here. However, the distributive property tells us that we can replace 2(x-2) with 2x-4. Doing so makes the equation simple:
Ta da. The distributive property comes up an incredibly large amount of the time, so that's why you need to know it. Outside of that, you probably know enough algebra at this point to start working through EV equations.
Two more points I want to make now that you've gotten this far:
Point 1
You can manipulate equations that have multiple variables, even if you aren't necessarily solving them. For example, if you had
a + b = c
You could subtract b from both sides if you felt like it and get
a + b - b = c - b
a = c - b
There are a lot of applications of this, but I just wanted to plant the idea in your head. Part 15 from http://www.flopturnriver.com/pokerfo...ad-180192.html uses this idea to show where the bet/(bet+pot) shortcut comes from.
Here's why this is important. Suppose you have an equation that looks something like this:
2(x - 2) + 3x = 21
It can be really hard to figure out how to make progress here. However, the distributive property tells us that we can replace 2(x-2) with 2x-4. Doing so makes the equation simple:
Ta da. The distributive property comes up an incredibly large amount of the time, so that's why you need to know it. Outside of that, you probably know enough algebra at this point to start working through EV equations.
OK, I understand both points that you have made here. However, I am looking at how you worked out the bet/(bet+pot) and I can't quite fathom how you did it
0 = PF + (1-F)(-B) ~ If I understand properly here, PF is the times we win, (1-F)(-B) is the times we lose?
0 = PF - B + BF ~ So here, equity equals when we win the pot, minus our bet + the times we bet and villain folds?
0 = PF + BF - B ~ This is exactly as above, just in a different order
0 = F(P + B) - B ~ I don't quite understand what has happened here. Our EV = Times villain folds, multiplied? by the pot+bet minus our bet. Why has P+B been placed in brackets?
I can't carry on as I am not even sure I understand what has happened up to this point
OK, I understand both points that you have made here. However, I am looking at how you worked out the bet/(bet+pot) and I can't quite fathom how you did it
0 = PF + (1-F)(-B) ~ If I understand properly here, PF is the times we win, (1-F)(-B) is the times we lose?
0 = PF - B + BF ~ So here, equity equals when we win the pot, minus our bet + the times we bet and villain folds?
0 = PF + BF - B ~ This is exactly as above, just in a different order
0 = F(P + B) - B ~ I don't quite understand what has happened here. Our EV = Times villain folds, multiplied? by the pot+bet minus our bet. Why has P+B been placed in brackets?
I can't carry on as I am not even sure I understand what has happened up to this point
Don't worry so much about what it means. You can learn that by following through the thread. I just wanted to show you the example of how the variables can be moved around in a useful way without having to solve for one of them.
PF is the size of the pot times the % of times he folds. This is the EV we get from him folding.
(1-F)(-B) is the amount of time he doesn't fold (1-F), which just means 100% - his fold %, and (-B) means we lose our bet
I might break that particular proof down in a new thread sometime as kind of a beginner's version.
Last edited by spoonitnow; 02-19-2013 at 06:46 PM.
Don't worry so much about what it means. You can learn that by following through the thread. I just wanted to show you the example of how the variables can be moved around in a useful way without having to solve for one of them.
Off topic again ,but I'm a cunt. Any suggestions for a book/site on math which goes very deep into the game?
I have a very good grasp on math (almost a finished degree) and I'd like to understand the game a bit better through that as understanding how a system works is how I do best.
I'm quite happy to put a lot of work in if it involves it.
OK, I understand both points that you have made here. However, I am looking at how you worked out the bet/(bet+pot) and I can't quite fathom how you did it
0 = PF + (1-F)(-B) ~ If I understand properly here, PF is the times we win, (1-F)(-B) is the times we lose?
0 = PF - B + BF ~ So here, equity equals when we win the pot, minus our bet + the times we bet and villain folds?
0 = PF + BF - B ~ This is exactly as above, just in a different order
0 = F(P + B) - B ~ I don't quite understand what has happened here. Our EV = Times villain folds, multiplied? by the pot+bet minus our bet. Why has P+B been placed in brackets?
I can't carry on as I am not even sure I understand what has happened up to this point
The cool thing is that every line is exactly as above, just in a different order.
Trying to interpret the meaning of the intermediate steps can be interesting or not... you never know, but it is fun to do the exercise you did where you tried to see the meaning at every subtle change. Cool stuff.
Off topic again ,but I'm a cunt. Any suggestions for a book/site on math which goes very deep into the game?
I have a very good grasp on math (almost a finished degree) and I'd like to understand the game a bit better through that as understanding how a system works is how I do best.
I'm quite happy to put a lot of work in if it involves it.
Mathematics of Poker is a good place to start, but it's more of the difficulty of a textbook than a typical poker book, so have fun.
Off topic again ,but I'm a cunt. Any suggestions for a book/site on math which goes very deep into the game?
I have a very good grasp on math (almost a finished degree) and I'd like to understand the game a bit better through that as understanding how a system works is how I do best.
I'm quite happy to put a lot of work in if it involves it.
Mathematics of Poker by Bill Chen & Jerrod Ankenman
Otherwise for all the EV calculations and probabilities etc, Sklansky's "No limit theory and practice"
Virginity is like a bubble: one prick and it's all gone
Ignoranus (n): A person who is stupid AND an assh*le
I remember taking a finite maths course in university that was disguised as a computer science course. I wish I had paid more attention.
I probably would have, if they used poker examples instead of "how many different combinations of baker's dozen's bagels can be created using 11 types of bagels?"
Any suggestions for a book/site on math which goes very deep into the game?
I like "Killer Poker by the Numbers" by tiny Tony Guerrera, and "The Math of Hold 'Em" by Collin Moshman and Douglas Zare (although haven't got deep into this one yet)
I thought I would chime in that I'm working on something for my 10k post that should make complicated EV calculations and situation modeling accessible to anyone who understands Cobra-level math shown in this thread.
I thought I would chime in that I'm working on something for my 10k post that should make complicated EV calculations and situation modeling accessible to anyone who understands Cobra-level math shown in this thread.
...I'm working on something for my 10k post that should make complicated EV calculations and situation modeling accessible to anyone who understands Cobra-level math...