[5NL] JJ, IP, 3bet pot, river spot.

[Cobra_1878]

Ahh, I wasn't sure about the -7 -3, earlier on I had it as -10 but decided to change my mind second time round.

Adding 7 makes much more sense. So x = 2.5

Let me have a second go;

2x + 6 = 7x - 9

We can take away 2x from each side.

2x + 6 - 2x = 7x - 9 - 2x

6 = 5x - 9

Now we can add 9 to each side

6 + 9 = 5x - 9 + 9

15 = 5x

Now we divide both sides by 5

x = 3 ( That worked out well haha )

[spoonitnow]

Ahh, I wasn't sure about the -7 -3, earlier on I had it as -10 but decided to change my mind second time round.

Adding 7 makes much more sense. So x = 2.5

Let me have a second go;

2x + 6 = 7x - 9

We can take away 2x from each side.

2x + 6 - 2x = 7x - 9 - 2x

6 = 5x - 9

Now we can add 9 to each side

6 + 9 = 5x - 9 + 9

15 = 5x

Now we divide both sides by 5

x = 3 ( That worked out well haha )

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.

Point 2

Self-quoting from http://www.flopturnriver.com/pokerfo...ad-180192.html

Part 5: The Distributive Property

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:

2x - 4 + 3x = 21
5x - 4 = 21
5x - 4 + 4 = 21 + 4
5x = 25
5x/5 = 25/5
x = 5

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.

I told you the shit was easy. Check part 8 here for an example of calculating FPP rates using what you've learned: http://www.flopturnriver.com/pokerfo...ad-180192.html

[Cobra_1878]

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.

Point 2

Self-quoting from http://www.flopturnriver.com/pokerfo...ad-180192.html



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:

2x - 4 + 3x = 21
5x - 4 = 21
5x - 4 + 4 = 21 + 4
5x = 25
5x/5 = 25/5
x = 5

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.

I told you the shit was easy. Check part 8 here for an example of calculating FPP rates using what you've learned: http://www.flopturnriver.com/pokerfo...ad-180192.html

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

[spoonitnow]

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.

[Savy]

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.

[spoonitnow]

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.

[daviddem]

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"

[DoubleJ]

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)

Both Moshman and Guerrera have sites ldo

[spoonitnow]

I might break that particular proof down in a new thread sometime as kind of a beginner's version.

I've actually decided to parlay this into my 10k post.

[MadMojoMonkey]

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.