The raise % depends on the Value composition that you want to raise. Some players would 4bet most of QQ and JJ and don't have 22 here so they don't raise too much. Once you raise the sets, you pretty much need to raise % of those broadway cards as bluff to cover different straight complete runout in later street.

Good job! I should learn from you! GL!

I like this. Thanks for posting. I was a bully when I was younger and got bullied myself later. Can also be because of former friends that didn't let me be, or didn't appreciate me as myself when I was a young adult. Made me really uncomfortable and always had to pick my words carefully. Not hanging out with those people anymore and I'm very picky with who I dedicate time to nowadays. But obviously I'm not sure what has caused that I'm this way. I like myself as I am mostly, but sometimes it's very tough to live in my thoughts.

I'm exactly like you. Mistakes give me most tilt, losing unfortunate pots because of variance is relatively ok.

Thanks a lot buddy

Hehe. Well by now it's pretty obvious I like to educate people to the best of my ability, so I don't mind doing it. Especially when I get to rub it in, you know

You're right. This was my thought process as well and only doing this low frequency with combos I think are great for it. Would never reach the solver frequency and I don't think I need to.

Hey thanks!

A friend of mine looked at my session recording and asked me about my frequent use of the RNG. I'll give my answers here and let you guys comment them, because I'm not 100% sure I'm thinking correctly.


1. Why not try to find the best lines vs villains tendencies instead of mixing according to the solver?

If you have a read you should try to exploit your opponent, always. And that's what I try to do all the time. It's important to understand that we never should mix if we think 2 lines have different EV. We might have a situation where in GTO one combo takes a pure line, but if you nodelock villains suboptimal tendencies the combo might start mixing because vs villains "human" strategy the combo now has 2 (or more) lines with the exact same EV. So I don't see mixing as a thing that only applies in a GTO vs GTO situation, because villains tendencies (node-locked strategy) will change the solution and we start using different strategies with our combos, of which in part uses pure strategies and in part mixed strategies. We never find the perfect frequencies though, and we don't have to.

2. Isn't it rare that lines would have the same EV?

It's very common on every street that we have (close to) identical EV for different lines with a combo. There will always be combos that have a mixed strategy in a solution. When you reach the desired solver accuracy you input in the model (dEV), solver will stop, and it will leave you with mix and pure strategies. From what I've understood, solvers usually start the first iteration by giving every combo an even split of frequencies for every line, calculating the EV for every line and combo vs villains strategy (villains strategy starts off the same way with it's range, even split of frequencies for all the lines for every combo), and makes small frequency adjustments towards the higher EV line based on the EV calculation, for both players at the same time, for all the combos. And in the next iterations this step is repeated, and in the end we arrive at a solution for our desired accuracy. It might be that if we let solver do it's work to an even better accuracy, a mixed combo might become a pure one because the following iterations made the solve more accurate. But in all solutions we arrive to, we get a strategy that is the best one solver came up with to maximize EV, and it always includes some mixing! As a side note on this, you will almost always see that mixed combos show different EVs for the lines it's mixing between, this is because the solve is not really "complete", and it just stopped at an iteration. If a combo had minimal EV differences solver would then on the next iteration increase the frequency a little towards the slightly higher EV line to see if it actually increases EV vs villain after villain also has done adjustments to it's own combos. Usually when a combo is mixed, solver has tried adjusting frequencies up or down for a while but not seen a significant increase in EV by adjusting further up or down. Lol sorry if this is a mess.

3. Many good HS regs never use an RNG. So why use it?

Using an RNG is just one way of randomizing when you think lines have the same EV. There are tons and tons of spots where you're in a spot where you see 2 lines where you think they are very close in EV, so you will just "randomize" it in your head instead if you don't have an RNG. I think randomizing (in any way) is good because you don't let your frequencies get out of line. Imagine betting every combo OTT pure that you think might have potential to be good turn barrels (but you're not sure if giving up is better), you would probably end up betting too much and decent villains could just exploit that fact because you are now unbalanced and it would show in basic HUD stats or whatever.

One good upside to mixing combos on different streets, when you think the lines are very close in EV, is that you allow yourself to cover a lot of flops, turn and river cards to have good value, bluffcatchers and bluffs at least some of the time on every card. If you randomize according to the suits of the cards (like being more aggressive when you have a club in your hand or whatever, people actually do this) you would limit your value, bluffing and bluffcatching properties for certain runouts. Or another example is that you always have a pure turn strategy with your range of combos, and by leaving out marginal lines you might just never be able to have the blockers/unblockers you'd like to have in a river spot. It can be very good to not have biased randomizing strategies. But don't forget that we might have a bias in how we use the RNG too! Poker is tough.

4. Isn't it impossible to find the right solver frequencies?

Yes, but I think it's possible to get somewhat close. It's not necessary to get frequencies right if you play vs a GTO-bot, if you always (pure) pick a line that is part of a mix strategy, because the GTO-bot would never adjust to your frequencies. So you would lose 0EV by pure betting/checking/folding a mixed combo every time because the bot wouldn't adjust to your strategy, so the EVs of the lines you see would be the same no matter if you pure or mix play the lines. But most humans who like to adjust would pick up on the fact that you have out of line frequencies in different spots. You shouldn't be too worried about mixing a combo incorrectly as long as you keep your overall frequencies in check when you think EVs are close! No on knows that you fold or call KcJh 90% of the time when you should fold or call it 10% of the time etc. Stupid example but you know what I mean.

5. Humans rarely play close to optimal anyway, so why try to copy the solver?

You shouldn't copy the solver if you see a line that is higher EV than solver suggests.


But to be clear. I don't think using an RNG is a must, and it might even hurt your game if you use it wrong. And I'm positive it hurts my game in some spots too, but mostly I think it's very helpful!

I am personally using the RNG just for preflop. But as you mentioned you do some kind of randomization postflop even without the RNG (blockers, etc ). I guess as long as you use the RNG at the right step during your thought process it can be a helpful tool. Imo this step should be the last one during your decision making process.

A prime example for this would be a bluffcatching spot OTR. I see a lot of guys come to the river and they start their thought process with "I rolled high/low therefore I need to call/fold". Instead I think it is way better and more profitable to firstly take a look at the available information (HUD stats, population analysis, etc), based on the information decide how wide/narrow you want to call down and then select your best bluffcaterchers to do so (to some degree during the selection process you are already doing some kind of randomization based on blockers/suits). And if you still don´t know what to do, you can then at the end use the RNG to make a decision.

However, I think the majority of non elite players would do way better without the RNG. Mainly because they often guess the solver frequencies and dismiss very valuable information.

Main benefit of using a RNG is obviously that you can blame it after you lose the hand. So might be GTO at the end who knows

Nice post. I'm guilty of rolling too many spots according to what I think is GTO if I'm a bit on tilt, especially on earlier streets. You could argue it can't be that bad, but it is if I'm not taking in more valuable info before doing so.

in, gl ship!

Thanks buddy! :-) Feel free to roast my thought processes whenever you like. Maybe I can start battling with you a bit quicker

Theory post #1: Bet-sizing - Indifference is profitable

Poker is in many ways very complex and it's hard to find a way to simplify our thought processes to find the max EV lines in most spots. Simplifying thought process is something I'm working on constantly, and in the last couple months I've tried to "rewire" my thought process. The reason why I'm doing this is that I've noticed I juggle with too many concepts at once and it ends up in overanalyzing wrong concepts, especially when facing sizing decisions.

I still make use of all the basic concepts I know, of which nut and equity advantage are key in most spots. These are two concepts everyone should think about in all spots, because they just make sense for most of our decisions. If we have a nut advantage we just know that big sizings are generally allowed, and if we have equity advantage we know that small sizings are generally allowed. If we have both advantages we usually can't do a massive mistakes by betting big or small, but for simplicity we usually want to have one sizing and construct our betting range around that sizing.

While those two concepts are important, we also want to think about how we can make MOST of villains potential CONTINUING range indifferent on flop, turn and river. Indifference is defined as a situation where you are indifferent between doing one action over the other, so in most cases this means indifference between calling and folding. If we bet too small on a texture where villain has a ton of hands that can continue, we are giving villain too many profitable continues, in other words villain has too many +EV continues instead of many zero-EV continues. Every time we allow villain to make a ton of +EV continues we are giving away EV to villain, which means we are playing suboptimally and not maximizing our own EV.

Obviously simplification is key, but nothing in poker is that simple. But creating good and clear decision-making processes is key. I will try to show a way to find good sizings in game without having to memorize solver lines. Memorizing solver lines just by eyeballing is OK, but you don't allow yourself to be flexible enough to find correct sizings or frequencies in spots you've never seen before by doing so. I will focus mainly on flop and turn, because river sizings can get a bit tricky and I have to admit I need to work way way more on river play.

The process:

1. Nut and equity advantage
Figure out who has advantage is equity and nut advantage. Not gonna go deeper into this here because this is easily done by studying in any program where you can input ranges and analyze them.

2. Allowed sizings
Based on nut and equity advantage you have an idea of the sizings you are allowed to use. But in terms of simplicity:

Nut advantage -> you can bet big with a narrower valuerange, but less often
Equity advantage -> you can bet small with a wider valuerange, but more often
Both -> You can do both, but picking one sizing and constructing your range accordingly is fine

Not always the case, but just in general these are good rules of thumb starting out.

3. Villains continuing range
Figure out which handclass/handclasses make up the majority of villains CONTINUING range. You don't have to do the whole combinatorics calculation, but you can easily figure out what type of hands make up a lot of combos in villains range tha are likely continuing vs a bet.

4. Pick a sizing!
Put most of villains CONTINUING range in an indifferent spot! Remember that we don't want to give easy decisions to the majority of villains continuing range when we bet. Giving easy decisions = giving away EV = not maximizing our EV.


FLOP EXAMPLE:

BTNvMP 3bet pot 100bb deep:
J32

1. Nut and equity advantage

Nuts:
-BTN has JJ and all the overpairs
-MP has some JJ combos

Equity:
-BTN has more AK combos and all the overpairs, and almost all marginal hands that MP has.
-MP is heavily weighted toward PP's and BTN has a ton of Ahi hands that missed the flop.

2. Allowed sizings
-BTN has nut advantage
-> Betting big should be allowed

-BTN has a slight equity advantage at best
-> Betting small is questionable since the EQUITY advantage is small at best. But it can't be a huge disaster since BTN is IP and has way more nutty hands in general.

3. Villains continuing range
-Villains continuing range will be heavily weighted towards medium pocket-pairs and Ahi with a backdoor straight- and flushdraws.

4. Pick a sizing!
-Since villains continuing range is mostly PP's and Ahi with backdoors we want to make this range INDIFFERENT between calling and folding with most of these.
-Betting small (33%?) would give villain too many +EV continues and an overbet (130%?) would give villain too many -EV continues.
-We need to pick a sizing that makes most of these 0 EV calls, which is the same EV of folding. So in this case betting 50-75% is probably closer to optimal because that makes villains continues way more closer to 0EV.


TURN EXAMPLE:

BTNvBB SRP 100bb deep:
943
BTN bet 33%, BB calls

Turn:
9438

1. Nut and equity advantage

Nuts:
-BTN has most overpairs and all the sets (flop is close to a range bet for BTN because of big:ish equity advantage and a general advantage in top of range)
-BB is supposed to check-raise most nutty hands OTF. In SRP it's very rare that BB slowplays a nutty range.

Equity:
-The 8 is a good card for BTN because it doesn't improve BB more than BTN. All good hands BTN had OTF are still good hands OTT. Generally BB has an equity advantage on turns when flop went bet and call, but the 8 is such a good card that BTN usually has a slight advantage still OTT. Most of the low cards 5 and lower and board paring cards are good for BB because it improves BB to 2p, sets/trips and straights. The preflop caller is generally more concentrated to smaller cards and pairs that are on the board.

2. Allowed sizings

-BTN still has an advantage in sets and overpairs
-> Betting big should be allowed
-BTN only has a small equity advantage at best
-> Betting small is questionable

3. Villains continuing range

-BB continuing range is mostly Ahi, 9x, 8x, 4x, 3x, PP's <77 and draws

4. Pick a sizing!

-BB gets many +EV calls if we bet small (33%-50%), even with 4x/3x type hands.
-BTN has a huge advantage in top pair+ hands and BB is heavily capped to 1 pair hands (because better hands mostly pure raises flop)
-BTN should leverage the advantage in all the strong hands and put villains range that mostly includes marginal hands into an indifferent spot and bet HUGE.
-Optimal sizing here should be 75%+/overbet for BTN, which also allows BTN to have many bluffs. Personally I overbet or check here since I use 1 sizing only. This should make BB indifferent with most of the continuing range!
-Notice that when SPR is high, it's very important that the uncapped player mainly bets huge OTT on blank cards. In 3bet pot it's easy to get money in even if we use <100% pot sized bets with a polarized range OTF/OTT


One last thing:

If the turn card pairs the board or completes flushes or straights, the flop bettor mainly want to use a smaller/normal bet size because the flop caller is no longer capped! In the previous example BB is still capped OTT and BTN is uncapped! When the turn card makes the flop caller uncapped, the flop bettor wants to make sure not to overpolarize and still be able to bet overpairs and top pair hands for value. Always make sure to identify how runouts affect both ranges in equity and nuts. It doesn't make too much sense for BTN to overbet overpairs on the turn 5 in the previous example, because it improves BB more than BTN and BTN has no incentive to overpolarize with the majority of his valuerange that is top pair and overpairs.

Usually on Khi flops the preflop raiser want's to bet small very frequently because the preflop raiser usually has a massive equity advantage and at least a small nut advantage. If the cbet is too big it gets too easy for the preflop caller to fold most marginal hands. This doesn't mean it's bad to bet huge in spots like this sometimes, but for the sake of simplification it's better to not split sizings and focus more on overall range construction between players.

In 3bet pots the flop bettor usually wants to bet small on the turn K, because it's usually an amazing card for the flop bettor (high EV/EQ card). If the barrel sizing is too big, it's way too easy for the flop caller to overfold the turn. Making villain indifferent between calling and folding is key.


Disclaimer: not an expert and always appreciate being corrected

Very well put and simplified Ship.
I think many, myself included find it difficult to get their heads around many concepts. They become obvious when explained well.
Thanks.

Made an account just to say thank you for writing this post. Your explanations are not only theoretically sound but also very well written. Please keep the theory posts coming!

A sign of deep understanding on a certain subject is being able to explain this subject concisely w/ an easy to understand explanation. vwp chief!

Sent from my G8441 using Tapatalk

Hey man! Really great post. You have straightforward, clear prose and do an effective job of explaining things. I have a couple questions as this post made me question my understanding of some topics. I hope you don't mind, and if you don't want this thread to be bogged down with this type of discussion feel free to let me know.

First Point/Question

Your post touches on a key concept I recall from the beginning of the Kanu course about frequencies and sizings. Basically he says:

However, my question kind of relates to the bolded, in that how does the solver decide how much of each to sizing/check to use? Obviously, a lot of spots are similar (paired boards are generally small, rangier sizes), but I'm curious if you have developed or know a heuristic to mentally wrap your head around what sizings and frequencies are preferred.

I find it easier to conceptualize and count nutted combos in many spots on flops, but I don't feel like I can accurately quickly determine who has an equity advantage deeper into the ranges on many spots, and I think my theory understanding might be limited by that.

If, you controlled for nuttyness, saying both players have the same amount of top pair plus on a given flop, will the rest of the equity advantage be more driven by things like second/third pair or draws? Is there a better way to conceptualize this?


Second Point/Question

You talk a lot here about the differences in EV between bet sizes and simplification. Scylla (GTO+ creator, but I imagine you know that) has said in the support thread many times, that bet sizes perform very similar to eachother in EV. I find in a lot of spots in my experience in GTO+, that is the case. However, obviously there will be some difference.

I'm curious, where you set the cutoff for what is acceptable EV loss for simplifying strategies. I've done some GTO work with a grinder who had ran a lot of similar DBs with more/less sizes and he said that for him, more than 2.5ish% EV loss was significant and perhaps not worth simplifying that spot. Do you agree with this? Or would you set an approach for simplifying vs when is it not a good idea to simplify?

Third Point/Question

You speak of cappedness, and that is something I've struggled to understand at 10z (and I know you were there last year, so feel free to comment on the pool in that regard if you want) is that theory vs practice doesn't really happen much at the micros, and I don't think of cappedness much or find it really a useful concept.

For example, lets say I'm BUvsBB SRP. Flop comes and lets say it is a flop where I know BB should be checkraising his nutted combos at a high freq (I'm not super studied, but let's say I know this one in GTO well, for this example). But since people in this pool don't play anywhere close to GTO (lets say 0 hud hands, so no reg/fish reads), I struggle to accept that they can be capped on turns and rivers, because they may not be raising their nutted hands at anywhere close to proper freqs, so I tend to not think people are really ever "capped" because they aren't really playing their ranges in ways that would theoretically cap them.

Final/Question


I still struggle to understand when we want to overbet turns. Is it basically that any turn that doesn't uncap BB in theory will allow us to OB to overpolarize, where as when turn uncaps them we don't want to?

Week 3: January has been good mental game training so far, dropping around 10BI in the start of every week. This week we didn't get the regrind though, hehe. Still feeling I'm playing well so let's hop onto next week with a positive attitude!




Thanks rayfox! Happy you find it helpful.

Thank you so much! :-) There will be more theory posts going forward, for sure.

I appreciate this very much. Thank you! :-)


Not sure if I can give a short answer on these questions. In the examples I gave I just focused on the majority of continuing ranges, and arrived at 1(!) sizing that will make most of that indifferent. The solver rarely uses only one sizing if it's allowed to use more, that's because solver sees everything and doesn't have to simplify to be able to execute a strategy properly. Let's say on a KJ4 board, we opened BTN and BB called. Our range is split into ~10% nut type hands, ~10% really good Kx, ~10% weak Kx, and ~10% middle pair. We also have some really good draws that can be considered value. On this board BTN has an equity advantage but also a nut advantage. Solver knows exactly how to split the range between all the sizings (in this case solver uses 1/3, 3/4 and the overbet), but we don't, and we never will. But we can still simplify a strategy to not lose too much EV. When solver overbets this flop, it's not targeting the naked 55-TT, 4x type hands, because those just mostly fold pure. In this case solver only focuses on some Jx, Kx, pair+draws and draws, and tries to maximize value vs those with the nut advantage. In the overbet value region there is very little weak <80% equity weak Kx type hands, because it doesn't make much sense because they rarely get called by worse and can never barrel for value. In the 1/3 range solver has weaker Kx, QQ, TT, 77, Jx, AJ etc. This range targets the weaker parts of villains range. In the overbet value region solver almost never uses weaker valuehands, but solver elects to mix in the strong and nut type hands in the 1/3 betting range, just to make sure that range also has strong hands and avoid getting exploited having a weak 1/3 bet range. Simplifying to flop is very good because if you start juggling 3 different sizings on all flop textures you will have a hard time playing the rest of the massive game-tree you just created.

In spots like turn probes and river bets OOP, we would usually need atleast 2 or more sizings because our range is often split into two categories that want to accomplish different things. BTNvBB, flop goes X/X, turn is 356T, BB usually has two "big" categories of hands that want to accomplish different things. BB has the protection/thin value range of 3x, 5x, 6x and low PP's that don't want to give IP a free card, which usually want to bet 33% sizing (BB should also mix in some nutty hands in this bet size). The other category is all 33,55,66,56s,35s,36s,T6s, 47s, that reeeeaaally wan't to start building the pot against BTN's check-back range that includes some overpairs, Tx, any pairs, draws etc. This range wants to bet massive vs BTN's capped range.

But to summarize you don't have to split your sizings in any flop situation, or atleast you won't lose too much EV by picking just one sizing. But on future streets it's a good idea to split your bet sizings, but not in all spots. Usually if you clearly have two bigger categories of hands that both want to accomplish different things, you should probably split.

Wrt to calculating equity advantage I'd say it's not easy, especially on turns and rivers. But playing around in GTO+ and the turn/river reports helps a lot. I don't have a quick method for this, it's just something I've tried to memorize mostly. It's also pretty easy to memorize equity advantage on various textures in different positions.

Yeah I've noticed this too. But solver knows exactly how to maximize EV using only one sizing, solving individually for all the different sizings. But it's much easier FOR YOU to play your range correctly if you pick a sizing that is logical for most of your value range vs villains continuing range. Not sure how much EV loss is too much, but the smaller it needs to be the more common the spot is. In a more uncommon spot it might be ok to have a bigger EV loss as long as it makes it easier for you to play the spot better than most of your opponennts.

Generally you should assume people raise their nuts on any street unless the SPR is low or whatever. Usually they cap themselves by checking back or just call on a drawy texture. If they actually slowplay in those spots sometimes, so be it, it's just good for you in the long run even if you don't adjust to it.

Yes this is true as long as you have proportionally more nutty hands than villain. Remember that when people call the flop, they usually have a marginal hand that is looking to call several streets profitable against normal bets. The flop bettor usually has more AIR than the one calling, thus BB usually has an equity advantage, but BTN mostly has a big nut advantage. This is why it doesn't make too much sense to bet small or normal on a blank turn, because we just give BB very profitable calls OTT instead of making the marginal hands indifferent when we have the top end of our range and bluffs. The marginal hands BTN has are usually not good enough to bet 3 streets anyway, even for a normal sizing, so it makes more sense to check those and bluffcatch river or bet river when checked to. So the split of only checking or overbetting turn starts making a lot of sense.


Thanks a lot mate!

In the post-match interview after the previous Dnegs vs Polk session, Dnegs really wanted to make it clear he has changed his strategy completely to the "YOLO" style, overbluffing and taking high variance spots to play big pots. Makes me think this is a bluff from Dnegs to put Polk into the lab and incorrectly adjust to this. Dnegs still has plenty of hands left vs Polk so I don't see why he would be forced to start this new strategy now? Seems a bit odd to me, but idk.

Thoughts?

I'm unconvinced. I think it would just amplify the effect of variance for the rest of the challenge. I think right now Polk is probably a slight winner vs Dnegs, thus for Dnegs to come back, he will need a massive upswing.

Thanks for the detailed reply. Regarding the bolded, is this just simply because they are taking lower EV lines?

Hi Ship, thanks so much for the detailed posts on bet sizing. Thats crazy value. Do you mind me asking how should we approach c betting when oop? I.e. hero raises LJ, CO flats and goes HU to J94r.
Do we prefer a polarized or range betting strategy in these spots?

I'd be curious to hear your thoughts on this aswell.

Yeah he probably is a pretty big winner vs Dnegs too. But just unsure if he should start the YOLO strategy this early.

There are usually slightly weaker, but strong hands you can look to protect your range with more oftenn. Not saying it's bad to slowplay sets and better sometimes and in optimal you should expect that happening at some frequency, even on drawy flops. Cappedness doesn't mean that there never is a strong hand in villains range, but just that it's rare or very low frequency.

Thanks :-)

Generally you should cbet a lot less OOP. Cold calling ranges are generally a bit stronger, and in terms of equity doing well on many flops, which makes us check a lot. It's usually a bad idea to have a flatting range in CO, because of rake etc. But let's say UTGvsBTN, the PFR should check quite a bit on many flops, especially on connected boards with cards ranging from 6-9, some of these are range checks. But on most other flops it's usually ok to bet some frequency.

On J94r we are probably mainly betting small but not for range. BTN will have some JJ, decent amount of 99 and some 44.

Thanks again ship, that would be my default strategy to be fair I just struggle with bet sizings. I usually go 2/3rds pot when I do bet a polarized range of strong hands and high equity bluffs and check marginal made hands, some draws and air. Judging by your response there are layers to this im nowhere near understanding yet. Cheers again

Interesing. In these spots where I am UTG-CO vs IP cold caller SRP HU postflop, I just 100% range check. Do you think this simplification loses to much EV? I always range check here, whether whale, fish or reg.

Subbed and gl!

You should not check your whole range even vs regs. The cbet freq. is low (~30-35%) as UTG/MP vs IP caller, but not zero. You are allowed to cbet at lower freq. especially on boards which favour your range.

The bolded part is a big mistake imo. The only reason why a solver checks at such a high frequency is because the GTO flatting range is tight. When you are playing vs fish they will have a way wider range than GTO (hands like ATo, QJo, etc). When you input such a wide range into a solver you will see that the solver cbet freq. drastically increases.

Wrt wider flatting ranges ip v EP oR. The equilibrium will often be range check for oop even on innocuous boards like A72 FD (when we nodelock for increased float flop freq', similar to BvB spots but just w/ narrow range vs narrow (condensed but capped) range or in your example a looser fish range.

Sent from my G8441 using Tapatalk