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