this was inspired by a friend of mine who plays nl50 and wanted to work out whether he should 4bet/call in a spot vs a reg. i assumed there were posts like this on 2p2, and there may well be, but my friend couldnt find them. so here is an example of mine to explain it.

its a .5/1 game and everyone at the table has $100 stacks. folded to us with JJ in the cutoff, and we open to $3. the btn and sb folds, the bb 3bets to $11. assume 50c rake.

we are considering whether we can 4bet/call JJ. now if we assume a 5bet shoving range of QQ+ and AK by the bb, we will have 36.19% equity with JJ vs his shoving range. so if we 4bet to $25 and he shoves, it will be $75 to call into a pot of $125, giving us $75/$200 (125+75) pot odds which means we need 37.5% to call. based on the assumed 5bet shoving range of him its a close fold, but the liklihood of the bb doing something spazzy or shoving a worse value hand than we assumed him to means its tough to find a fold since him having 1 bluff/TT type hand in his range would dictate we should call - im not so familiar with peoples ranges at nl100 or below, but the point of this post isnt to discuss ranges anyway.

obviously, if we know he only 3betting QQ+ and AK, we shouldnt 4bet JJ because when we get it in we arent going to have great equity. in fact the EV of getting it in can be shown by calculating:

EV of out 4bet/call = [what we stand to win if we win * chance we win] - [what we stand to lose if we lose * the chance we lose].

inputting numbers from the above scenario gives us the equation:

[100 * 0.3619] - [100 * 0.6381] = 36.19 - 63.81 = -27.62.

so we stand to lose $27.62 every time we 4bet/call after he 3bets. but does that mean a 4bet is bad? what if he is 3betting 100% of hands but folding pretty much everything when we 4bet? we can work out how often we need him to fold to break even based on what we win when he does fold (fold equity).

here is the formula for determining how much fold equity we need to break even:

let x = amount of times he folds.

[what we win when he folds * x] + [what we win when he doesnt * (1-x)] = 0.

substituting in numbers from the above calculations, we get:

14x - 27.62 (1-x) = 0..... [14 comes from his $11 3bet and our $3 initial open. -27.62 comes from the fact we lose money when he doesnt fold rather than win].

so to work out the fold equity required we simply expand the brackets and solve for x.

14x - 27.62 + 27.62x = 0. [2 double negatives determine +27.62 rather than -].
42.62x - 27.62 = 0.
42.62x = 27.62.
27.62/ 42.62 = x.
x = 0.648 or about 65%, so almost 2/3rds.

i.e. if he folds to a 4bet 65% of the time, we break even by 4bet/calling JJ vs the aforementioned range of QQ+ and AK.

now, if we assume him to 5bet all in with QQ and AK, that represents 2.6% of hands. so since we need him to fold about 2/3rds of the time to break even, that 2.6% of hands can represent 1/3rd of his 3betting range. i.e. if he 3bets (2.6*3) 7.8% then he is going to be folding 2/3rds of the time and shoving 1/3rd of the time, thus meaning we break even. if he is 3betting any more than 7.8% in this spot and only shoving QQ+ and AK, we start to make quite a lot of money by 4betting even though when we get it in we are an underdog vs his range.

however, is 4bet/calling more profitable than calling? well calculating whether we should call would require a lengthy formula because u have to consider all different flop textures, his cbet% on various textures, and his 2barrel% on various textures etc. its very time consuming.

the longer it takes to work something out, the less time u have to work other things out or to play. so spending 3 hours working out the EV of a super complicated play may not be too beneficial since it means u arent playing or working out other spots. simplying it like i have means u can start to say "ok how about if i have TT or AQ?" or "what if his shoving range is TT+ and AQ+" etc. u can also use the same formula to work out postflop spots as well such as whether you should re-raise and get it in with TPTK or the nut flush draw when you are raised on the flop. if you can work out what u shud do like i have above then u can adjust quickly in game without having to do calculations again - e.g. if i see someone 3betting 4% i know im losing money 4bet/calling JJ whereas if he is 3betting 10% then i know im making money.

hope this was useful, if i made any mistakes or you would like stuff expanded then please let me know

A+

+1....Now I just need to take the time to figure out exactly what it all means. Re-read a few times than play around with it some.

Yes I suck at math.

thank you

nice calculation, thanks.

so basically, if villain is 3betting 7.8% or more, 4bet/calling with JJ is profitable and if he's doing it less, we should fold ?

well assuming his range is QQ+ and AK when he shoves. i mean if he is 3betting 7.8% but then going with his whole range, u should be fistpump getting in JJ every time because he will have like 99/AJ etc.


btw yeah, anyone wanting the math explained in more detail just quote a section or create ur own example and ill do my best to explain. i appreciate a lot of people really struggle with the maths in poker, im not an expert by any means but i know about the basics.

good post

bump

So you think all about this while you make a decision? That's gonna be a long pokersession! And I'm not good in calculating all this stuff in my head.

what about 55c rake

if u read the bottom paragraph u will see that what i am saying is once u have calculated away from the table, u can apply it super easily at the poker table. u have to put in time studying anyway if u want to move up levels, you arent going to just grind up to small-mid stakes by watching videos. this sort of thing is what u should be doing in those hour or two that u leave aside to study. once u have learnt these formula u can take it and apply it to any situation pre flop or post flop, u just have to change the numbers around. i can post a postflop example if u like too.

by using the math u can prove your logic as either right or wrong and it will help u make good decisions quickly. like i say in OP, my logic would dictate getting JJ in vs a 4% 3bettor is bad, whilst against a 10% 3bettor is standard. i can then go ahead and prove my logic using math, which gives me more confidence whilst playing, and i can find the exact cutoff points whereby i am either making money or losing money by 4betting the JJ there.

i used the small blind as rake if u re-read the original calculations they account for 50c of rake. its pretty negligable anyway.

nice poast, really helped me!

NH - should definitely go in the digest, if anyone is working on one. Some things worth repeating/elaborating on:

This is really crucial - what determines whether you can 4-bet profitably is the gap between what Villain will 3-bet with and what he will shove with. If the gap is narrow or non-existent, you have little/no FE and your equity will be poor when you are called. So it pays to identify the players who will never 3-bet light/wide and the players who will 3-bet bluff (or turn hands like AJ into bluffs).

As jack noted in his example, JJ has ~36% equity against Villain's shoving range. This is the equivalent of having 9-10 outs on the flop when called, and the math shows why semi-bluffing is so powerful. Like in the preflop example, you need to think about the gap between Villain's raising range and his range for stacking off.

Could this be a beginners approach to maths?
1.Evaluating opponents range
2.doing random calculations
3.memorizing basic percentages when dealing with common situations(straight draws,TPTK,pocket pairs to suited broadways)
4.????
5.Start over
What charts can we incorporate in order to have a hard copy of relevant percentages ?Bond 18 on tworags.com has a series of useful charts with common situations ,are these relevant ?
What I am trying to do is understand the maths by going at it from a theory /textbook approach is this making any sense or am I totally off the mark?

Hi there i just stumbled across this and think i found an error but wanted to make sure with you guys -

This suggests that when we win, we win the same amount as when we lose i.e $100. However this is not the case. When we win, we win the existing money i.e. our raise and the sb as well, and when we lose we just lose the money left behind. So when we win we win 103.5 but when we lose we lose 97

so the ev of this play is not:
[100 * 0.3619] - [100 * 0.6381] = 36.19 - 63.81 = -27.62.

but rather :

[103.5 * 0.3619] - [97 * 0.6381] = 37.456 - 61.896 = -24.44.

Is that correct?

Yes, you are correct.

Could I ask for a complete dummies guide to these calculations?Whether it is explained step by step including where and how the values are collated assuming that the reader is a total poker illiterate , or labelled in the initial stages describing where the values come from and how they are extracted for use.Several examples may be invaluable in that I and I believe various others will benefit greatly from them.Two plus Two have enormous content but whether it is my inability to apply the theory or my inexperience this could avoid some major headaches for the 2+2 colective audience as I may well be silenced once and for all.

Excellent post and ty for your efforts.One thing i would like to ask you is that i am playing at 25nl and soon going to 50nl.However i have a big leak in 3b section of strategy.Can you please give me some advice on how should i improve it because the regs at 50nl will rip me off by constantly 3betting me.
Ty.

correct, yes

Hey Jack , I just watched a couple of your session vids from the pokerbank . Just wanted to say that I found them useful ,Love the accent too Thank you

thanks man

I don't make videos there any more, but i do have some free videos and articles here http://www.higherlevelpoker.com/ you just have to select the filter to 'only free videos' or 'only free articles'

Cool , Thanks , I will deffinitely check them out .

awesome