whiteshark's avatar


206 points

Not really a "question" but something I would be interested in are some videos on the most popular toy games, how we can solve them and what we learn from them substantially for our game. Kind of what you did in your last The Mathematics of EV video with the nuts/air vs. bluffcatcher game AA/QQ vs. KK.

What about the AKQ game? Or the AKQJ version? What can we learn from the different versions of the [0,1] game? What is this clairvoyance term that keeps getting thrown around? Explanations for these games can be traced e.g. in the Mathematics of Poker book or other sources, but explaining these step-by-step in some video(s) would make for some great content IMO.

Sept. 21, 2021 | 7:17 a.m.

Thanks! I keep getting forwarded to Xing Yang lately, definitely gotta check that guy out.

Sept. 21, 2021 | 7:11 a.m.

This video is gold! Although I wasn't aware of it, it feels like I was waiting for just a video like that ;-)

04:20 Nice explanation of how mixed frequencies come about. I always wondered how a solver can "agree" on a specific mixing frequency when the EV of each action is the same. Why not just generate a random number then? You made it clear that the calculated EV of a hand only holds at the equilibrium frequency against an opponent who is allowed to adjust.

17:30 Great visualization of blockers. You can nicely see how it is more important to unblock bluffs than actually blocking value combos, as blocking one value and one bluff combo will remove a disproportionally larger share from the bluffing region than the value region, something I struggled with for a longer time.

24:14 It's great that you cover the nuts/air vs bluffcatcher game in such depth. Calculating the EV of the whole game for each Player was new for me. Although this might be abstract at first, I believe there is much value in understanding these EV calcs. Gonna grab pencil and paper soon and make sure I really understand them.

Am I right that from these slides we can straightforwardly derive that the larger P1 bets, the higher the EV of the overall game for him? If QQ always has an EV of 0, then the EV of the game for P1 is basically determined by the betsize of AA. I have learned from a Steve Paul video that the solution for the two-street version of this game is to bet both streets for a geometric sizing, but I would have no idea how to derive that multi street solution from formulas. Might make something for a future video.

32:20 absolutely crazy to think about how much more few counter-exploits outweigh the value of our MES vs. an opponent who deviated from his frequencies!

Thumbs up!

Sept. 20, 2021 | 8:01 p.m.

Okay so this post tabs on some general questions of how to use solvers and their output in the first place. Before I write about that, I do think it's important to outline that you should specify a game tree across all three postflop streets. From your post (especially your 1st point), it seems a bit like your betting tree would simply consist on one street (e.g. the flop), where you give the solver different sizes to choose from and specify a pot size. However, flop c-betting cannot be solved without accounting for turn c-betting or river shoves. Without specifying a suitable tree (multiple bet sizes, raise options, potentially donk bets), it's virtually impossible for the solver to learn which hands to c-bet on the flop without knowing which combos are profitable turn bets and river shoves on different board developments.

Once you have a tree, looking at different board categories is a very good idea, yes. There have been different categorizations proposed, but be sure to vary at least high cards, connectivity and pairedness. In my view, by far the best approach is to run your tree over a large number of boards (GTO+ for instance let's you use a set of 163 flops that they generated to represent the larger universe of all possible boards) and then to start by looking at aggregate reports.

In terms of what to take away from the solver output, I think there are basically two approaches. The first approach is simply summarize/simplify what the solver does, based around different hand classes. Then these strategies can basically be memorized just as you might need to drill new vocabulary when learning English. IMO, this is a really bad approach. Far better is not summarizing the actions of hand classes, but trying to come up with overall rules that explain the actions each individual hands take. The crucial difference is that once you found suitable general rules, you can apply them to any other spot that you might study. The better the rules that you find, the better you will be able to predict solver output in the future on boards you haven't studied yet.

To stick to your example, below is the c-betting range that GTO+ gives me for BU vs. BB SRP on AK4 two-tone when BB is forced to check and BU chooses between check/30%/70%. Rather than summarizing what each individual hand class does, we could note the following:

  • BU has a severe range and nut advantage on this board as BB will 3-bet almost all AA, KK, AK and most A4s. BU's top range is largely undisputed and ahead of BB's top range. Hence, the value hands want to go for the bigger size.
  • The bluffs take the same size as the value hands do. There are hence no small sizes used on this board. Prime bluff candidates are those which block BB's continues and, if called, have equity against the continuing range. This explains the betting of QJ/QT/JTs or suited Qx/Jx type holdings.
  • Although the board hugely favors the BU, there is a lot of checking going on. Those hands that (i) cannot go for value and simultaneously (ii) don't have an incentive for equity denial vs. overcards check back. This explains all the checks from low Aces and Kx, and also explains why JJ-77 check, whereas smaller PPs bet. The former can't get to fold any (many) overcards that have EQ vs. them, the latter can.

Now if you take these general ways of reasoning from the bullet points above, what do you predict for AKT? Or AQ3? How does AK4 differ from K74 in terms of these thoughts? What do you predict for that? How does a weak top pair on AK4 differ from one on K74? Identifying rules that predict range construction rather than trying to memorize range construction is the way to go at least in my opinion. There are just way too many spots in poker for the latter approach.

Sept. 20, 2021 | 1:53 p.m.

Hmm so maybe someone else might have a more informed opinion on this but I don't think we can do this. If we fold all hands that are mixing we reduce our overall continuing frequency quite substantially.

If you nevertheless want to choose between 0EV hands I would then give priority to those that unblock bluffs. E.g. when facing a 3-bet CO vs. BU, let's say both 33 and 66 are mixing. However 33 might be a better candidate to defend than 66, as 33 unblocks 76s/65s whereas 66 blocks these...

Sept. 14, 2021 | 9:20 a.m.

The substantive reason why you're not maximizing EV by overfolding is that you are giving up your open raise too often I guess. Failing to stack the 3-bettors overpairs on low boards is another reason I think

Sept. 14, 2021 | 7:37 a.m.

So in general, the counterstrategy A that is going to make most money against a particular other strategy B is called Maximally Exploitative Strategy (MES). When your opponent has an "ideal 3 bet frequency" we can translate this into him playing the equilibrium strategy. Against the equilibrium strategy, the MES that is maximally exploiting your opponent is responding with the equilibrium strategy as well. If your opponent plays idealy, then any deviation from the equilibrium by definition loses you EV. So no, overfolding would not maximize EV versus an ideal 3-bet frequency.

If your opponent has an ideal 3-bet frequency, maximal exploitation is reached with playing the equilibrium as well. If your opponent is 3-betting too tight, the MES will overfold. If your opponent is 3-betting too loose, the MES will overcall and 4-bet more than an equilibrium response would do.

Sept. 14, 2021 | 7:27 a.m.

Great! Any kind of input is appreciated

Sept. 13, 2021 | 5:51 p.m.

Another component to this question is whether our value-to-bluff ratio is the same when we bet compared to when we check/raise. So let's say we play BB. vs. BU and we take the very same flop where we could either donk bet or check/raise as the BB. Let's say we do so for the same relative sizing, regardless of whether we donk bet or check/raise.

Do we have the same value-to-bluff ratio in both scenarios? I know I could just look this up in the solver. But if yes: Why is that the case? At least, there will be different SPRs created. If no, why is it not the case?

Sept. 13, 2021 | 8:07 a.m.

So something that I'm asking myself for a longer while now is how to determine optimal value-to-bluff ratios on flops and turns. Across the forums, you often read some rules of thumb mentioned and they often loosely refer to Janda, but I haven't seen anything systematic yet.

So on the river, my understanding is that the value-to-bluff ratio is completely determined by our bet size. For instance, let's assume the nuts/air vs. bluffcatcher game. If we bet pot, this implies a value-to-bluff ratio of 2:1. The defender risks 1PSB to win 2PSB and hence needs to be good 1/3 of the time to break even. In order to stop him from just folding out or calling off his entire range, the bettor hence chooses an exact ratio of 2:1 value hands to bluffs such that our value hands can get their pay-off. The bigger we bet, the more we can bluff. If we bet into an empty pot, we would always have an optimal ratio of 1:1. The bigger we overbet (say 100x or 1000x pot), the more our value-to-bluff ratio approximates this 1:1 ratio of betting into an empty pot.

Okay, but what about flops and turns? There are flops where the agressor can get away with betting range, if the equity and nut advantage is so severe that the defender fails to make the bettor's bluffs indifferent between betting/checking (see Will Tipton's first volume, chapter 4.2). So here, I guess the value-to-bluff ratio goes through the roof with bluffs heavily dominating? What does turn texture due to our value-to-bluff ratio? Is this different for static or dynamic boards? Is there a simple formula based on the bet size just as for the river for all scenarios where we can't bet range? If not, which are heuristics that help us constructing correct value-to-bluff ratios on earlier streets?

Sept. 13, 2021 | 7:55 a.m.

Yeah indeed makes a lot of sense. This explanation reconciles the two logics that I perceived as contrasting or contradicting each other.

When we perceive the club through its property of producing more fold equity/equity denial rather than through its redraw potential vs. the continuing range, then choosing (i) hands and (ii) combos within hands follows one overarching and consistent theme. Nice!

Aug. 31, 2021 | 4:29 p.m.

I've been digging deeper into blind vs. blind play recently and I have some confusion specifically about how to construct our check-raising range after we range check as the SB.


So the main boards that we can simplify to checking range as the SB PFR are low suited connected boards. There are several examples but let's take this one (GTO+ checks 75.1% here, I simplify this to checking range in game):

In general, our check-raising range is constructed around holdings that (i) can go for value and (ii) have the incentive to deny equity/protect against future board runouts. Below we see the XR range against a 30% pot size stab of the BB. We clearly see how value holdings that need to protect against overcards are raised the most (apart from the obvious nutted hands), 99-88, A7, K7 etc. Observation 1: Across hands, the driver for check-raising aggression among value hands does not seem to be equity (as then AA would raise the most out of the overpairs), but equity denial.

If we follow through with this logic, then which combinations of e.g. 99 or A7o should be check-raised the most? Well those that have the strongest incentive to protect against future board runouts for them, so the combos without a club. Those with a club can comfortably call as they'll pick up flush draws if the third club hits. Those without a club would want to get money in more quickly as their incentive for equity denial is the strongest. However, if we look at the individual combos, it seems to be exactly the opposite (see below). Observation 2: Across the combos of an individual hand, the driver for check-raising aggression among value hands seems to be equity(!), not equity denial.

This seems like a contradiction to me. When choosing hands to check-raise, we choose the driver of equity denial over equity. When choosing individual combos within a hand, we choose equity over equity denial. Feels very weird to mix these two logics in range construction. Am I not seeing something? Is there a third factor that explains this divergence?

Aug. 30, 2021 | 1:23 p.m.

nah, it's actually fine for most German players. I mean for the pros it's completely fucked up, as they can't play higher than NL200 now and also there is no more table selection possible (just random seat allocation even on regular tables). So they can't bumhunt anymore.

For the low stakes grinders, not much changed tbh, at least on Stars. You can play a maximum of 4 tables per site, but most people don't play more than that anyways. Personally, all I noticed was a rake increase of effectively about 1.5bb/100 on NL25z. And on Zoom, there is no table selection anyways. So of course it's not nice, but also doesn't change a hell lot.

Those that do their research will find the games that are least affected by the new regulations, which are still beatable

Aug. 25, 2021 | 7:26 p.m.

I don't think there is a real "solution". I guess players from Germany (like me) just have to be really careful now on which sites they are playing. Every site reacted differently to these regulations, locating themselves somewhere on a continuum ranging from placing the burden of the extra taxes fully on the individual players or covering them fully as the operating site itself.

How a site deals with these regulations now has to be the one major factor in pool selection for Germans I suppose...

Aug. 25, 2021 | 9:38 a.m.

Regarding your mental game: Have you checked out the free videos of Elliot Roe on this site? They are a great motivation for hard times!

Fedor Holz's Primed Mind app also has some nice free meditations to do before you start your session.

Aug. 18, 2021 | 11:43 a.m.

Flush-completing turns are a high-frequency check for your range, also your particular holding without the FD will check a decent amount of the time.

I would resort to check/call turn, check/call river.

Aug. 18, 2021 | 11:41 a.m.

19984625531 life expenses differ drastically between countries, that's the reason. E.g. compare rent prices in London and a rural city in Panama and translate these into bb/100 given a certain volume at, let's say, NL100. Obviously, the bb/100 needed to finance a flat in a rural city in Panama will be way less than if you live in London.

Aug. 12, 2021 | 1:49 p.m.

DNegs98 out of interest, which study-to-play ratio did you have in these 2.5 years?

Aug. 11, 2021 | 10:17 a.m.

Hand History | whiteshark posted in NLHE: NL25z Bluffcatching
Blinds: $0.10/$0.25 (6 Players) BN: $27.07
SB: $37.55
BB: $25.00 (Hero)
UTG: $25.00
MP: $54.75
CO: $25.00
Preflop ($0.35) Hero is BB with T K
4 folds, SB raises to $0.70, Hero calls $0.45
Flop ($1.40) J 8 8
SB bets $0.44, Hero calls $0.44
Turn ($2.28) J 8 8 6
SB bets $1.45, Hero calls $1.45
River ($5.18) J 8 8 6 T
SB bets $3.30, Hero calls $3.30

Aug. 11, 2021 | 7:46 a.m.

Hand 1:
The K32 board is actually quite good for the EP PFR I would say. You have the advantage in AA/KK/AK/KQs as for the BB these are 3-bets. Depending on whether you open 33/22 from EP or not, BB is gonna have an advantage in sets here, but still BB ranges are very wide (even vs. EP) so it's not a large portion of his range. I like the approach of betting small with a large portion of your range. This is the exactly the sizing you would want to choose with hand like KQ or KJs as you (i) get payoff from weaker Kx hands and (ii) need to deny equity vs. BB's Ax hands. Putting AK into this size seems really fine to me.

OTF and OTT you can't get away IMO. Since you c-bet small for a high frequency, BB is supposed to have quite some checkraises here. These will be constructed around sets but also FDs and BDFD+SD type of hands (such as 6c5c). The turn does not interact with BB's air range so he is supposed to polarize and go for a bigger sizing when he bets. You are on top of your range (only KK/AA are our only better holdings if we don't open 33/22). I played in the NL10 Zoom pool not so long ago and I think the population can definitely show up with bluffs here. My plan would be to call turn and decide OTR. On dynamic runouts I'm folding (since BB is likely not doing a good enough job in turn bluffing range construction to have bluffs even on dynamic rivers). On a static runout you could consider calling.

Hand 2:
In this case, I would advocate for a bigger sizing OTF as this doesn't seem like a spot to bet range here. In general, on Qxx boards equities should run closer than on Kxx boards since you 3-bet less Qx than Kx hands and the CO is also gonna have quite some suited Qx in his range. Second, the 6 and 4 interact relatively well with the PFC's defending range (though Q65 would be worse), giving 6x a pair and hands like 87s a gutshot. Third, the PFC range is shifted towards suited hands, so the two-tone nature of this board lowers the equity of your overpairs/top pairs. I would play something like 50% bet or check, with AhQc predominantly betting.

OTT with two flush draws on board, also here I'm not sure whether you can really get away, though I would be willing to find exploitative folds vs. opponents I have played with before.

Aug. 10, 2021 | 11:11 a.m.

If your primary goal is to make money, I think there are many different areas that provide you with way faster success given the same time investment than poker.

Aug. 9, 2021 | 7:47 p.m.

First of all I think it heavily depends on the country you live in. The threshold for playing poker professionally will be way lower in Panama or Kasachstan than for example in Great Britain.

Secondly (and many might disagree here), I don't think that playing poker professionally is a good goal when currently being on micro stakes. The thing is that you need A LOT of intrinsic motivation in order to succeeed in this game: hours of studying for many months/years, disciplined high volume grind, high efforts to achieve emotional control in downswings etc. etc.

Only those that have a genuine passion and love for the game PLUS put all of this work in will eventually make a comfortable living out of it. At micro stakes, at least if you live in an advanced industrialized country, you actually don't play for considerable amounts of money yet that have relevance in your daily life. For micro grinders that want to move up I guess it's all about developing passion for poker and living that passion, independently of monetary success. When your passion grows strong enough and your efforts are consistent over a large time frame, eventually one day the money will come. Ironically probably only when money stopped being your driver in the first place.

That's at least my take on this topic...

Aug. 9, 2021 | 7:45 p.m.

My 3-bet sizings are:

IP: 3x (except if you are up against a minopen, then you size up a bit)
OOP: 4x

Then I add another 2-3bb for every coldcaller and another 2-3bb when I'm in the BB. The reasons that we go bigger from the BB are that we 3-bet more polarized from the BB (polarized ranges prefer a larger sizing) and that there is no player left to act after us that could cold 4-bet and force us to give up our 3-bet (other than when we are in the SB). The reason that we are going bigger from oop in general is that as the oop 3-bettor you profit from lower SPRs (that come with bigger preflop sizings) as equity realization of the IP caller goes down.

Aug. 9, 2021 | 12:02 p.m.

Sundried maybe the Ace-high backdoor flush draw (clubs) gets checkraised more often on the flop whereas the Ace-high flush draw (diamonds) plays more passively? Then the Ac would be less in SB's range on the river and hence the solver prefers unblocking the Ad over the Ac.

Aug. 3, 2021 | 12:07 p.m.

I'm continuing to work through MMAsherdog's BTS Ultimate Course and in the Blind vs. Blind video he shows a pattern that I don't understand. So the spot is SB vs. BB single raised pot. We range c-bet out of the SB on a rather dry K-high board that favors the PFR and get called. The turn is a broadway card, so a high equity card for the SB c-bettor.

Of course, after a range c-bet, we check a lot, especially oop. We still have a betting range though. What I noticed is that there are two different kinds of boards that lead to completely different sizes that we choose on the turn.

Board 1: KT4 Q
Here, the SB c-bettor goes for a small sizing on the turn. This makes a lot of sense to me since a high equity card for our range will lead to quite some betting (even after a high frequency c-bet OTF oop), and since a substantial part of our range wants to bet we go for a small size.

Board 2: K52 Q
This is also a high equity card for the SB c-bettor after a high frequency c-bet OTF, but now we go for a big size when we bet. Why? Across many regions of the game tree, I have whitnessed the rule of thumb that blank (!) turns lead to large sizes (and a lot of checking) for the c-bettor, whereas high EQ cards lead to a small size and a large betting frequency. If a substantial part of our range wants to bet, why not choosing the small size?

Attempt of an answer:
Maybe it's too simple to say that high equity cards will lead to a small size and blanks lead to a big size. I was recently told that

  1. the equity of a card for our range determines our overall betting frequency
  2. the polarization of our range determines our sizing

So could we maybe say that on KT4 Q, our betting range is less polarized since BB will also have AJo/J9o and the tops of our ranges are closer together? While on K52 Q, SB's nuts are uncontested and want to go big? This is my hunch, but when I check the equity distributions of SB and BB for both spots in Flopzilla, there is few visual difference in the tops of the ranges...

What's your take on this?

Aug. 3, 2021 | 9:50 a.m.

Hand History | whiteshark posted in NLHE: NL25z AhJc on 7h 4h 3h
Blinds: $0.10/$0.25 (6 Players) BN: $33.75
SB: $25.66 (Hero)
BB: $26.69
UTG: $25.00
MP: $25.35
CO: $50.25
Preflop ($0.35) Hero is SB with J A
3 folds, BN raises to $0.50, Hero raises to $2.05, BB folds, BN calls $1.55
Flop ($4.35) 4 7 3
Hero bets $1.20, BN calls $1.20
Turn ($6.75) 4 7 3 9
Hero bets $3.40, BN raises to $7.55, Hero raises to $22.41 and is all in

Aug. 2, 2021 | 7:15 a.m.

July 31, 2021 | 8:54 p.m.

So against a better reg where we are using a polarized float betting strategy, it makes sense to go with a bigger bet

I don't fully remember anymore how float betting is introduced in FTGU, but my float bet sizing will almost exclusively depend on flop texture. From your post it seems a bit like you would make this dependent on the player type you're up against, with having bigger sizes versus stronger regs?

If you call out of the BB and SB checks to you, I would choose one of two strategies: On boards that are good for the PFR (let's say AT3ss), you check back a lot, bet a polarized range, and go for a 70%-ish sizing. On boards that are bad for the PFR (let's say 653ss), you bet a lot and go really small (I do 33% but I agree with fishcheckmate that we could go even smaller).

In general I wouldn't be afraid to go for small sizes in spots that favor your range. I think an important thing to understand is that overfolding is usually going to be more severe the smaller your size is. The reason is that vs. a big size, your opponent has to defend less hands in theory in order to remain unexploitable. Even if the board connects poorly to this range overall, he often will be able to find enough of these hands. When you bet small though, your opponent would in theory have to defend a ton of hands in order to stop you from just betting more and more, but can't do so since he simply is lacking enough suitable holdings and many of the potential continues would just get crushed if they continue. AlvinTeachesPoker has a nice video on this: https://www.youtube.com/watch?v=9j-CYqIoPBU

So to drive the general tendency home: When you're a vast range favorite, don't be afraid to bet really small, as large parts of your range will profit from the overfolding that's gonna happen, e.g. SB vs. BB after SB checked to you on 653ss. An exception to this rule is when you have a severe nut advantage to go with your range advantage. So when you're holding all the nuts on a board and Villain cannot have the nuts, your nutted hands are uncontested and have the incentive to bet really big. This could happen e.g. on AK4rb BU vs. BB SRP, where the BU can go for really large c-bet sizes. Note how this spot conceptionally differs quite a lot from the 653ss SB vs. BB, where the SB will also still have all 66, 55, 33, so the tops of your ranges are pretty equal.

July 30, 2021 | 7:14 a.m.

Hand History | whiteshark posted in NLHE: NL25z Turning JJ into a bluff?
Blinds: $0.10/$0.25 (6 Players) BN: $40.96
SB: $38.97
BB: $38.63
UTG: $49.96
MP: $22.29
CO: $25.00 (Hero)
Preflop ($0.35) Hero is CO with J J
2 folds, Hero raises to $0.62, BN calls $0.62, SB folds, BB raises to $2.58, Hero raises to $5.87, BN folds, BB calls $3.29
Flop ($12.46) 8 T 5
BB checks, Hero bets $3.93, BB calls $3.93
Turn ($20.32) 8 T 5 A
BB checks, Hero

July 27, 2021 | 7:23 a.m.

Comment | whiteshark commented on 3b sizing

Agree with Shaun Pauwels that we 3-bet bigger out of the BB than out of the SB. Maybe there are more reasons mentioned in the video, but the one I am aware of is that when you 3-bet out of the SB you will sometimes need to surrender your 3-bet amount if the BB 4-bets and you are low in your range, which is a quite horrible outcome. Hence we risk less if we 3-bet a little smaller. Out of the BB we don't have this problem and can go bigger.

I'm not sure of what comes next, but I could imagine that another reason lies in the BB 3-betting range being more polarized than the linear SB range. Polarized ranges tend to increase their bet sizing across the whole game tree as far as I am aware of.

July 26, 2021 | 11:58 a.m.

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