simple maths question with implied odds

Since no-one is up for any basic maths, I will explain what I am trying to do.

We calculate pot-odds needed to make the call. We then calculate our pot-equity. We realise we then have insufficient pot-equity. We then use our pot-equity to calculate how big we'd need the pot to be given our actual pot-equity. We then subtract the actual pot-size from our desired pot-size to calculate how much we'd need to make on the river.

Is it for certain that one of these steps isn't redundant. For example, is there no relationship between how much equity you need and how much you have that would allow you to calculate the amount needed on the river without first having to calculate how big you'd need the pot-size to be for it to be possible??

I'm simply trying to maximise efficiency, but not fully convinced the method outlined in the strategy article is the most efficient where mental arithmetic is involved. I'm not saying for certain it isn't, I would just like convincing.

Check this link below:

https://forums.pokerstrategy.com/forum/thread.php?threadid=134183

I believe this is what you're looking for.

Edit: check my post on page 2. Unfortunately they both use odds not equity.

Thanks for the link.

I'm mainly looking for a specific answer to the question in my second post however. Maybe it's somewhere there, I'll have a look.

EDIT - Seems I did find something semi-useful. But not complete for my purposes. Posted below.

Implied Odds (:1): *odds to make hand - pot odds*
Amount Needed on River: *amount to call * implied odds*
(20%) 4(:1) - (30%) 2.333333r(:1) = 1.66666666r

$15 * 1.6666666r = $25

which is the correct answer

Ok, I just need to work out how this works in %, like the OP of that post also wanted.

So.....20(function)30 = x
x(function)$15 = $25

Any help guys? Thanks.

it's easy. to pay $15 with 20% equity you need 1:4 = 15:60, i.e. you need to profit 60 when you win the pot to make the times you lose 15 worth it.
right now there are $35 in the pot that you will profit if you win, so you need villain to put in at least an extra $25 on later streets, then you have 15:35+25=1:4
that's how i calculate during a hand

Originally posted by Kruppe
it's easy. to pay $15 with 20% equity you need 1:4 = 15:60, i.e. you need to profit 60 when you win the pot to make the times you lose 15 worth it.
right now there are $35 in the pot that you will profit if you win, so you need villain to put in at least an extra $25 on later streets, then you have 15:35+25=1:4
that's how i calculate during a hand

Thanks a lot. But that is not really what the post is now asking.

Implied Odds (:1): *odds to make hand - pot odds*
Amount Needed on River: *amount to call * implied odds*

I want to modify this formula so that it works with %s instead of ratios.

i answered exactly what your original post asked, and gave you a very simple method. why are you not happy with that? do you want a formula so you can program a bot?

Originally posted by Kruppe
i answered exactly what your original post asked, and gave you a very simple method. why are you not happy with that? do you want a formula so you can program a bot?

You are correct. You answered my initial question. Thanks for that.

I know how to calculate implied odds however. If you read the rest of the thread you will see the real question I am asking. And I would be grateful for further insights.

The problem I'm having is, the formula I found from the other thread subtracts ratios. For example, you take 4:1 and then 2.33333r:1 and subtract the left sides to give the number 1.333333, which you use in your next calculation.

The problem is, I'm not sure what is exactly happening to the ratios. The formula is calling it "subtraction", but it seems quite clear to me the ratios are going through a different function which isn't subtraction.

Originally posted by Wolfjustice
I want to modify this formula so that it works with %s instead of ratios.

Kruppe gave you simple answer, and now you would like someone to solve you basic math? (under/(over + under)) *100

Originally posted by doctorkgb

Originally posted by Wolfjustice
I want to modify this formula so that it works with %s instead of ratios.

Kruppe gave you simple answer, and now you would like someone to solve you basic math? (under/(over + under)) *100

If you read the thread you will see it is not a case of converting ratios to percentages. The formula given works ONLY for ratios, seeing as it appears to break some of the basic laws of maths. (i.e, just taking one side of the ratio, using it for subtraction, and disregarding the rest. What is the equivalent for a percentage??)

I want to convert that formula to one that can work with percentages.

I don't think you could ever find that formula. Percentage aren't exactly correct math, you're gonna have to convert those to floats like 0.25(25%) - which is a hassle in my opinion. I tried it before, in the end I ended up having the percentage converted into odds.

Why not use this one,
( call amount * odds ) - total pot = 9
( 2 * 7 ) - 5 = 9

it's less percentage to odds conversion. You could use Kruppe methods, or mine.
You could convert your equity to odds,
(100 - equity) / equity
100 - 25% / 25%
=> 3 : 1

PS: If you find the formula, please post it here. I'm really interested

Here's my post from the link I gave you. I think this one are easy to understand.

after trying to understand what pyure's formula is.
i think i just stumbled to a faster formula.

total pot: 5
call amount: 2
odds: 7:1
pot odds: 2.5:1

pyure's formula:

call amount * ( odds - pot odds ) = 9
2 * ( 7 - 2.5 ) = 9

faster formula:

( call amount * odds ) - total pot = 9
( 2 * 7 ) - 5 = 9

Well it probably doesn't matter since it only omits pot odds calculation.
But less odds less percentage to ratio conversion, right.

Originally posted by cpers
Percentage aren't exactly correct math

I don't understand what you are saying. Percentages are just as accurate as ratios.

Just taking one side of a ratio and subtracting it from another doesn't appear to be "correct maths", that's the whole cause of the problem I'm having. Sure, it works, but how can I use that formula for anything other than a ratio?

Originally posted by cpers
Why not use this one,
( call amount * odds ) - total pot = 9
( 2 * 7 ) - 5 = 9

It doesn't seem to work with percentages either. Only ratios.

Originally posted by cpers
You could convert your equity to odds,

Yeah, this would be logical. But the whole point of this exercise is to avoid using ratios. You can calculate how much you need to make on later streets with percentages just fine, i.e by calculating the size of the pot you WOULD need given that you are contributing x% of the pot. However, the formula above makes that step redundant if you are using ratios. There must also be a way to make that step redundant using percentages also with a modified formula.

What in essence is that formula doing by only subtracting one side of two ratios. What function are those ratios being put through? That is the question.

Ok, could it be that multiplying the numerator of two fractions is the equivalent to subtracting one side of two ratios? (although an inverse function)

4:1 - 2.6666667:1 = 1.6666666666

20% function 30% =

2/10 " * " 3/10 = 60% (reciprocal of 1.666666)

$15 divided by (because it's 1/x) 0.6 = $25

Notice I put the * in inverted commas, because this is also an illegal operation. 2*3 is 6, but (2/10 * 3/10) is NOT 6/10, just like (4:1 - 2.66666:1) is NOT 1.66666:1

I need to turn it on it's head somehow, because I don't feel dividing by decimals like 0.6 is appropriate for mental arithmetic.

I also need to check this theory with some other examples to see whether it's just a coincidence. Rather than multiplying the numerators of two fractions together you might be able to just multiply both percentages (as numbers) and divide by 10.

Ok, just a coincidence I think.

I guess I give up for now.

I should have just focused on creating my own formula from scratch. That formula from the other thread is causing me a whole bunch of problems.

Actually when I see this calculation is extra to the other method, this method is probably no quicker than just calculating the required pot size and subtracting.

It'd still be interesting to know how you can just subtract one side of two ratios and what this actually represents mathematically.

Implied Odds (:1): *odds to make hand - pot odds*
Amount Needed on River: *amount to call * implied odds*

Like, how the hell was this formula derived. You have to subtract two ratios incorrectly in order for it to work.