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MATH : Issue while creating 3/5 bet ranges

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Posted by posted in Mid Stakes

MATH : Issue while creating 3/5 bet ranges

hello
i m working on my preflop game and i got a problem,
When i create ranges that cant be exploitable in regard of betsizing it does not take in account opponent range, so finally i feel it s not usefull

exemple
i have a 3bet range 7.2% i want a 5 bet range so that oppoent can not 4bet me and win money

effectiv stacks 100bb
blindes 1.5bb
he opens to 3bb
we 3bet to 9bb
he 4 bets to 23bb

vs a 4 bet our defense will be a 5 bet
minimum defensive frequency vs 4bet :1-A where A=R/(R+1) where R = his bet / pot size
here his bet = 20, pot=13.5 so MDF = 40.3%
so i have to 5bet 40.3% of my 3bet range to avoid being exploited
because we 3bet 7.2% we need to 5bet 2.9% which could be JJ+,AKs,AKo
(if we 3bet 9% we need to 5bet 3.6% which could be TT+,AKs,AKo)

thats seems great BUT
**if he only 4bet AA i will lose money wiht my 5bet range, even if i did math that i have to defend this % !!!
**given different call 5bet ranges we have different equity with different 5 bet ranges and that math does not take it into accoutn !

i m not sure to be clear but if i sum up
i want to work my ranges with math
i dont understand when we speak of GTO we only speak of besizing (minimu defensive frequency) and we dont take range in account
so in my exemple is these ranges really good becasue not exploitable? 3 bet 7.2% / 5 bet 4.3%?

thanks for your help because i took the most basic exemple but i also want to do it with 4bet% and 3 bet %

have a nice day

17 Comments

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thedoors 12 years, 1 month ago
sorry i missread your post, how would you use it?
i mean we have his 1st open stats but that does not say what he 4bet bluffs and 4bet call
mike 12 years, 1 month ago
if you are building a "GTO" range what you have is a OK start but you need to think about opponents opening range like jame's said. you can't 3B the same range vs UTG(15%) of hands as BUT(50%)

if opponent opens decent range and only 4Bs AA you should use exploitative 3B plan - ie if he is never calling 3B bluff him tons and flat your good hands - of course this extreme never happens in game but the point is when opponent is playing in a way we can easily exploit we should deviate from a "GTO game plan"

overall keep in mind that any GTO range is just our best estimate because we don't know opponents exact RFI and their exact range construction
thedoors 12 years, 1 month ago
thanks i will abuse of 3bets and then switch to my "GTO" ranges only if they 4bet a lot then
really like this forum!
have a nice day
Aleksandra ZenFish 12 years, 1 month ago
GTo range is math correct only versus opponent who plays perfect GTO game as well
Since opponents are different you adjust ranges accordingly, if they 4 bet AA only you 4 bet them to death but as Mike said its very unlikely, so versus such opponent you widen 4 bet range and 5 bet call or make 5 bet only very tight range AA KK only ( not even kk if you are sure he 5 bets AA only, tho i cant see any player doing only AA 5 bet but hypothetically )
Against player who is playing wider 4 bet range and correct 5 bet range unexploitable according to GTO you play according to maths, but you cant make a fixed 4 bet 5 bet range or you would be exploitable i suggest you take it as an approximate and tune it depending the opponent and situation
BigFiszh 12 years, 1 month ago
"[...] you cant make a fixed 4 bet 5 bet range or you would be exploitable [...]"

I don´t understand that sentence. If we play a fixed GTO-4/5-bet-range, we´re unexploitable by definition. It might be that we don´t play for maximal EV, but we definitely are not exploitable. Even if we 4b/call KK, "knowing" that Villain only shoves AA, he doesn´t exploit our overall-range because he´s folding too often to our 4-bet.
Awesome Dawg 12 years, 1 month ago
to BigFiszh: Any GTO range is exploitable by some sides of opponents unbalanced parts. For example - lets imagine that we have optimal cbet range compared with particular board. Let it be 55%-55%-55%. So, we might that opponent folding optimal, but he dont - he folds too much flop (imagine that he call or fold, never raise) . Than we have next problem - we lost EV by betting the same range flop (but it`s ok, we still unexploitable), and we bets too much turn ,even if it`s compare with our optimal range, because villian have stronger diapason , that makes our optimal bet turn exploitable. In fact, playing optimal line this spot, villian lost EV on flop by folding too much, we lost EV on turn by betting too much (compared to this opponent) and it`s seems like exploitable for us not on flop but on turn. If we have any information - we have to change our optimal strategy, this is called edje. I think so..
cold7betfold 12 years, 1 month ago
"[...] GTO range is math correct only versus opponent who plays perfect GTO game as well[...]"
Thats not true. GTO is a play that makes money no matter what your opponent does. (doesn't mean it is maxEV of course)
thedoors 12 years, 1 month ago
thanks aleks quite clear
BigFiszh 12 years, 1 month ago
@awesome: this is not correct. The term "optimal" in GTO is not equal to "maximum EV". Even though that´s confusing, GTO oftentimes does not maximize EV vs. non-optimally-playing opponents.

But not playing "maximum EV" does not mean that we´re exploitable either. Being exploitable means that Villain can maximize his EV by deviating from GTO himself. That is not given - by definition - if we play GTO, because then his maximum EV comes from playing exactly GTO himself. Hope that got clear.
BigFiszh 12 years, 1 month ago
Simple example: say we got to the river with 100 combos. 10 of them are nuts - and 90 are airballs. There´s $100 in the pot. Now say we always bet the river potsize with our nuts and x/f all of our air-balls. This is an exploitable strategy. Villain´s correct adjustment is to fold 100%. So we win 10 / 100 times the pot of $100 - which makes an average profit of $10 per hand. Now, let´s say we´re betting our 10 nut combos AND additionally 10 bluff combos. Now we bet 20 / 100. And again we´re exploitable - because our betting-range is too bluff-heavy. Now, Villain´s adjustment is simply to ALWAYS call. So we win $200 in 10 / 100 times and lose $100 in 10 / 100 times. Summarized we make 1.000 in 100 times, which again is $10 / hand.

Now, say we´re betting our 10 nut-combos and 5 bluff-combos. Now we play GTO. Villain can do whatever he wants, he can always call, never call or throw a dice and decide if to call. If he never calls, we win $100 in 15/100 (for an average of $15/hand), if he always calls, we win $200 in 10 times and lose $100 in 5 times for a total of $1.500 over 100 hands, which again makes $15/hand. If he does anything in between we still win $15/hand. => Villain can do whatever he wants, we win exactly $15 per hand. This is GTO.

Now, if we knew (!) that Villain never calls - our adjustment would be easy - we would bluff 100%, so we don´t win the pot 15/100 times but 100/100 times. Obviously the result exceeds our GTO-approach by far, but now WE are exploitable ourselves (Villain just had to start calling 100% and would print money himself).

You see, playing GTO is not exploitable. In contrast - we have to play exploitable ourselves to exploit our opponent´s non-optimal tendencies. And we can do that (hopefully) - because Villain does not recognize that we got exploitable while we take his money.
thedoors 12 years, 1 month ago
nice post it really helps me to understand the witch betwen 2 mods : exploitative and GTO
if i undestood well my 3/5 bet constructions only helps me when vilain ajust ot my 3 bet exploitative mod
then i go to my 3/5 GTO mod to be sure he does not exploit me with his 4bets
thanks
mike 12 years, 1 month ago
there is another option - if you think opponent is adjusting in a unbalanced way you can just change your exploitative strategy. ie you have been 3B a guy like crazy you might anticipate he is going to start 4B spewing so you tighten up your 3B range so you can 5B jam a bunch of hands.

i only take a GTO approach to other good regs who are already balanced but vs weaker players a good exploitative strategy will make you a lot more money :)
d2themfi 12 years, 1 month ago
you cant just pick a 3bet range, figure out what range you need to 5bet and assume thats GTO or even balanced. I think in general its better to think a bit exploitatively with preflop decisions because so much of the game tree is unknown at that point in the hand that you have to make potentially very inaccurate estimates about what is optimal postflop for both players, or worse yet make guesses at what % of a hands equity it realizes in various postflop scenarios. When we are playing we almost always have a decent sample for preflop stats, and if we have some postflop stats even better. For 3betting, obviously theres things like open %+fold to 3bet%+4bet% and his fold/raise cbet stats in 3bet pots, but you also have to factor in how he plays in SRP, since that can change your thresholds for which hands you want to flat and 3bet. Add in figuring out thresholds b/w 5betting and flatting 4bets, and you've got a complex problem, that you only get an acceptable answer to by modeling

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