Math help

Hey, so I want to start learning the math side of things in poker and the first thing I want to do is learn how to calculate what the odds are in hitting a set on the flop if you have a pocket pair.....once I understand how this calculation works I can work out everything else....but I need some help because I terrible at maths and I dont understand the 'algebra' or whatever the (/&*) means in calculations....what are they and how do they work?..... Example which I copied and pasted ....... The formula you then get is: 1 - (48/50)*
(47/49)*(46/48) = 11.75 %, which
translated into odds is about 7.5 to 1.
......

What does this mean and how would I calculate this in my calculator.....a basic explanation would be great because I am a dummy when it comes to maths.....thanks

* means multiply. Is that what you're asking?

* means multiply

/ means divide

And you need to work out the stuff in the brackets first.


The formula is missing a couple of things:

1) There should be another set of brackets around the (48/50)*(47/49)*(46/48) for it to work.
2) The final result needs to be multiplied to 100 to get 11.75%.

So it should be: 1 - [(48/50)*(47/49)*(46/48)] * 100

So you get: 1 - [0.96*0.9592*0.9583] * 100

Which is: 1 - 0.8824 * 100 = 11.76

Tbh you don't really need to know how to work all that out and why it gives you 11.75% though, you just need to know what odds you need to setmine, I use the 20x rule as guideline and modify it in different situations...do you know about that 20x rule?

Please enlighten us on the 20x rule? I think Blackrain discussed the amount you should be set mining for, but maybe he has a different system.

So the idea is that you want the opponents stack to be about 20x the amount you have to call to make setmining profitable. You have approximately 1 in 8 chance of hitting your set so you might think that you need his stack needs to be 8x the amount you have to call but this doesn't account for all the times your opponent doesn't hit anything postflop and gives up and you only win a small pot. It also doesn't account for the rare times you will be coolered by a better set or beaten by a stronger hand like a flopped flush. So you actually need more than 8x to make it profitable, and 20x is a good starting point.

In general:

- It is not profitable to call 3bets to setmine with 100bb stacks
- It is not profitable to setmine vs shortstacks with less than 40bb

I adjust the 20x rule depending on opponent. For example I called a 3bet to setmine the other day when opponents stack was only about 12-15x the amount I needed to call. This was because I know he is a nit who pretty much only 3bets QQ+ and that he is likely to pay me off with those hands when he has an overpair to the flop.

micromachine said:

* means multiply

/ means divide

And you need to work out the stuff in the brackets first.


The formula is missing a couple of things:

1) There should be another set of brackets around the (48/50)*(47/49)*(46/48) for it to work.
2) The final result needs to be multiplied to 100 to get 11.75%.

So it should be: 1 - [(48/50)*(47/49)*(46/48)] * 100

So you get: 1 - [0.96*0.9592*0.9583] * 100

Which is: 1 - 0.8824 * 100 = 11.76

Tbh you don't really need to know how to work all that out and why it gives you 11.75% though, you just need to know what odds you need to setmine, I use the 20x rule as guideline and modify it in different situations...do you know about Ýuthat 20x rule?

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Cheers mate, yeahq I was thinking if I knew how to calceulqqate it then I could work out everything else assuming its the same formula?....yeah I know the x20 rule, been using that this far

What else do you want work out? I feel like you might be making things more complicated than you need to, you really don't need to know that much maths to win at poker. Andrew Seidman aka BalugaWhale admits not being particularly good at or using that much maths and he was beating high stakes 1kNL and above.

For most players at micro and small stakes, it's not especially important to know the underlying calculations as to be aware of certain odds and how they can / should affect your play. For example, it's important to know that the odds of a pocket pair hitting a set on the flop are about 1 in 8. If you know this and how to apply it by, for example, using the 20x guideline, whether you know the exact percentage and how to calculate it matter far less. so much so that some might say it doesn't matter at all.

micromachine said:

What else do you want work out? I feel like you might be making things more complicated than you need to, you really don't need to know that much maths to win at poker. Andrew Seidman aka BalugaWhale admits not being particularly good at or using that much maths and he was beating high stakes 1kNL and above.

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things like hitting an ace on the river if you have AK for example or if you have suited connectors and the odds of hitting a straight with a flush possibility....but yeah i suppose i could memorise all the probabilites < is that what you call them?...where could i find a chart on these things?....never heard of Andrew seidman lol but thats cool, if gives guys like me some hope haha

Arjonius said:

For most players at micro and small stakes, it's not especially important to know the underlying calculations as to be aware of certain odds and how they can / should affect your play. For example, it's important to know that the odds of a pocket pair hitting a set on the flop are about 1 in 8. If you know this and how to apply it by, for example, using the 20x guideline, whether you know the exact percentage and how to calculate it matter far less. so much so that some might say it doesn't matter at all.

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thanks Arjonius, i was thinking about learning all this stuff for when and if i get to higher limits, ive pretty much learned all the fundimentals to beat 2nl so its something else to think about and improve on while im playing the lowest limits....its good to know that its 1 in 8, but i would like to understand why it is 1 in 8 so i can work out everything else....abit like give a man a fish and it will feed him but give him a fishing rod and it will feed him for life sort of thing....but if it doesnt matter too much then thats cool, i will concentrate on things i do need to learn...thanks

AlfieAA said:

things like hitting an ace on the river if you have AK for example or if you have suited connectors and the odds of hitting a straight with a flush possibility....but yeah i suppose i could memorise all the probabilites < is that what you call them?...where could i find a chart on these things?....never heard of Andrew seidman lol but thats cool, if gives guys like me some hope haha

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You know the 2 and 4 rule? Really useful for calculating your chances of making your hand

micromachine said:

You know the 2 and 4 rule? Really useful for calculating your chances of making your hand

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yeah man i got a 4 & 2 chart...got the OESD and flush draw memorised....think i read somewhere that the first 1 to 9 outs are the most important ones to learn as outs more than 9 will be usually enough to call anything with...well within reason

Ok cool, well the 2 and 4 rule is useful for postflop. For preflop I would memorise probabilities initially rather than being too concerned with the exact calculations - although they would all be quite similar to the one above for setmining so yeah if you understand how that works you could work out others yourself.

I would say that 9 outs is not enough to call anything with, 9 outs is a FD and we shouldn't always call with a FD. For example if we are pretty sure our opponent has a set or an overpair then calling with a FD is -EV.

The other thing about the 2 and 4 rule is that is becomes less accurate when outs are higher than 9. The way to adjust it is to subtract the number of outs above 9 from the end percentage. So....for 12 outs the chances of making your hand by the river with 2 cards to come is (12*4) - 3 = 45%

Yeah agree with MM,

All you need for micros is the 2&4 rule, and an understanding of pot odds, MUCH more important is ranges, how a flop hits a range, and how our holdings play against ranges imo, theres better things to concentrate on than what % of the time you'll hit an A otr with AK!

the first step is putting an opponent on a hand...after the flop if you think you are behind,figure out your outs and multiply by 4 after the flop....then by 2 going to the river...it isnt exact but its a close,quick way to assess the situation

Sort of glad this thread got re-found;

AlfieAA said:

...its good to know that its 1 in 8, but i would like to understand why it is 1 in 8 so i can work out everything else....abit like give a man a fish and it will feed him but give him a fishing rod and it will feed him for life sort of thing....but if it doesnt matter too much then thats cool, i will concentrate on things i do need to learn...thanks

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I have never worked thru why it is 8-1 (ish), so let me give it a go;

We see our PP, and there are 50 cards preflop left that we do not know anything about. 2 of those are our gems, so that means we have a 1/25 (2/50) times 3 (flop cards) = 3/25 which works out to about 1/8.333 chance on the flop.

If we get fortunate enough to see all 5 community cards, we can figure we get to improve those original 1/8.333 odds by adding the new calcs of 2/47 (turn) [.042], and another 2/46 (river)[.043]. So, 1/(8.33 + .042 + .043) = 1/9.178 , which in my mind works out to be about 11% (10.9%).

I had always accepted the published formulas without figuring out for myself, and truthfully, I had doubted those published results. But then everyone knows dj is always wrong.....

dj11 said:

I have never worked thru why it is 8-1 (ish), so let me give it a go;

We see our PP, and there are 50 cards preflop left that we do not know anything about. 2 of those are our gems, so that means we have a 1/25 (2/50) times 3 (flop cards) = 3/25 which works out to about 1/8.333 chance on the flop.

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A 3 in 25 chance is a close approximation, yes. It's not exact because each card drawn also changes the number of cards left to draw from. The precise odds of flopping a set or better are 7.5069(4) to 1 against. This is a 1 in ~8.507 chance. Note I said set or better, as all of the math put into this topic so far has also included flopping quads (as well as boats). I can give you the probability of flopping exactly 3 of a kind with any pocket pair but it's not substantially different.

dj11 said:

If we get fortunate enough to see all 5 community cards, we can figure we get to improve those original 1/8.333 odds by adding the new calcs of 2/47 (turn) [.042], and another 2/46 (river)[.043]. So, 1/(8.33 + .042 + .043) = 1/9.178 , which in my mind works out to be about 11% (10.9%).

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You've erred here, since the odds of hitting the flop as noted above is ~11.7551%. Your work would have us believe the chances of hitting one of 5 cards are lower than the chances of hitting one of 3. The more you add into the denominator, the smaller an expression becomes.

We'll calculate the odds on a 5 card board with the same method used in this topic to calculate the odds on a 3 card board. The probability of seeing 5 cards none of which match our pair in rank is 48/50 × 47/49 × 46/48 × 45/47 × 44/46. Therefore the probability we do match our pair is 1 - 9/10 × 44/49 (the extra brackets MM inserted are redundant) if we see the board in full. This works out to be ~19.18367347%, which is almost 1 in 5. Makes sense when you consider that the odds of a pocket pair beating a larger pair are approximately 4.5 to 1 against.

You are correct that I did that wrong... I am seeking the logical connect but it is early, and I am under caffeinated.

I really have problem understanding this, maybe this questions would look stupid but no madder how much i read articles and this tread over and over i still dont get it, maybe because i still have problem with the implied odds and stuff

Here is the question, we know that chances of hitting a set are 8:1, se to justify a call we need pot odds better than 8:1 and we dont get them on flop but we still cal, because on later street we might get better pot odds because there will be more money in the pot is that what implied odds mean?

again im sorry for popping with what night be stupid question but i really feel that this part of my game is the biggest reason that i cant beat cash tables

& means add, or plus , equal to + in maths

the pocket pair hit a set is from possibility [combinations and permutations]calculation!

u got a pair, there are 2 cards in the deck
u need at least 1 show up on the flop!

if cards are dealt, u got 2 cards, have about 50 cards left on the deck.
possiblity 1 cards show on flop
2/50*48/49*47/48*3=0.115
2 cards show on flop
2/50*1/50=0.0008

add together 0.1158 , appox1: 7.5 odds

DrazaFFT said:

I really have problem understanding this, maybe this questions would look stupid but no madder how much i read articles and this tread over and over i still dont get it, maybe because i still have problem with the implied odds and stuff

Here is the question, we know that chances of hitting a set are 8:1, se to justify a call we need pot odds better than 8:1 and we dont get them on flop but we still cal, because on later street we might get better pot odds because there will be more money in the pot is that what implied odds mean?

again im sorry for popping with what night be stupid question but i really feel that this part of my game is the biggest reason that i cant beat cash tables

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Implied odds are adjusted pot odd that take into account (as an estimate) betting that may occur on later streets.

Lets say you flop a flush draw. The pot odds may tell you that calling a flop bet to try and hit your flush is mathematically incorrect. However, if you think your opponent will put more money into the pot later in the hand, then calling good. In this situation you could say that you have good implied odds. Often you will have better implied odds with straight draws than flush draws; it's less obvious when you hit so it's more likely that subsequent betting will occur.

Now if i get it right, im in the drawing hand and after a flop my opponent hits top pair and he bets half of the pot that makes my pot odds 3:1, right? now for oesd i need pot odds about 5:1 to call but i assume that he will bet again and if i hit on the turn ill make money and my call on flop will now be justified but what if i miss the turn, should i still call his bet to chase my hand or if i fold wouldn't that be loosing money if i do it every time or that way when i hit ill took more than i lose before... again im sorry if im still talking nonsense after you've explained this to me but im really have troubles figuring this out...

DrazaFFT said:

Now if i get it right, im in the drawing hand and after a flop my opponent hits top pair and he bets half of the pot that makes my pot odds 3:1, right? now for oesd i need pot odds about 5:1 to call but i assume that he will bet again and if i hit on the turn ill make money and my call on flop will now be justified but what if i miss the turn, should i still call his bet to chase my hand or if i fold wouldn't that be loosing money if i do it every time or that way when i hit ill took more than i lose before... again im sorry if im still talking nonsense after you've explained this to me but im really have troubles figuring this out...

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If you miss and he bets the turn you'll need to reassess. Whether to call will depend on pot odds and your reassessment of your implied odds.

Your implied odds will be affected by several things like what the effective stack size is, what kind of player your opponent is (will he pay you off if you hit?), was the turn card a scary card for him (could it be an overcard to his pair?), could the river card scare him (did a flush draw come on the turn?) and how well disguised is your hand (when you have one or two gapper pocket cards your straight will be better concealed).

Generally, calling turn bets to chase draws is worse than calling flop bets to chase draws because yo only have one chance to hit, because the bets get bigger and the implied odds go down. I see quite a few villains raising the turn with draws, not a bad move since calling often sucks and you have some pot equity with your draw and often quite a bit of fold equity too (cash regs know about Balugas theorem, which says you should consider coding your TPTK type hands if you get raised on the turn).

Can i imply this as a general rule, of course considering that if i hit a draw hand that ill had nuts and if i know that opponent will push again and if i think that his hand is top pair, and calling flop bet without good pot odds,and then as you said re think if i miss the turn. would that be a profitable, long term?

I wouldn't apply it as a general rule...you will never know for certain whether your opponent will bet again, or whether his hand is top pair...it better to decide what to do according to the situation at the table.

Like sometimes I might call a 1/2 or 2/3 pot sized bet with an OESD on the flop if I think my opponent is a fish who will stack off with top pair on a later street. But against a more competent villain who won't stack off and who c-bets quite a few flops I would be more likely to raise my OESD.

Ultimately, calling to chase draws is often unprofitable, so raising or folding will often be better.