The 50% number is the relative size of the range that the book seems to recommend (approximately, and implicitly, not explicitly. These numbers came from analysis of real-world data -- there is no formula being proposed). That is not the same as having 50% preflop equity (which would be achieved by identical ranges) . He seems to focus more heavily on how well the hands play postflop than on preflop equity.

Your statement (that the blinds should play with less than 50% equity than the raiser, due to dead money) implies that the blinds should play looser (wider range) than the button.

It goes evem further than that. The ranges are optimal for his play against his opponents. There are errors on both sides. Solvers assume perfect play from your opponents as well as from you. In other words, his ranges are exploitative of his group of opponents (in 2004)

As you point out, the solver is recommending things that real players don't do. That is happening on both sides of the analysis! There may be exploitative plays that fare better than the solver output against the strategies that real players use.

Isn’t it also possible that the players whose data were recorded simply did not play well with the weaker parts of their ranges because their overall strategy was flawed? Or did opponent tendencies in 2004 make certain hands unprofitable to steal?

Good points, and I agree. The second point is most interesting to me around solver outputs compared to the realities of practical opponents. If we can be specific about the types of mistakes an opponent makes we can model the optimal exploitation in a solver.

For example, let's say we have a CO open vs. BB defend situation. Let's say the board comes out, 357, a board which favors the BB's range. A GTO solver model will recommend the BB donk this board with about 45% of it's range and that the CO should bet about 70% of its range when checked to. After a CO bet, the BB should check raise with about 30% of it's range. So let's refer to that as optimal play.

Now let's explore a common heuristic exploitation from normal live play, where the BB always checks the flop and the CO always continuation bets. When we force this action in the solver we see that now the BB is check raising 57% of it's range!

We can take this even one step further and look at the scenario where we allow the BB to have a donk range but we force a bet in the CO. Now the solver tells us that optimal play is to never donk and we can conclude that the optimal exploitation of opponents who do not have a check back range on this board is to always check and have a high check raise %.

Ask yourself, are you attacking these types of boards like this against opponents who always continuation bet in this spot? There are countless opportunities to model these types of exploits in your home lab if you have the time and initiative to do so.

Stepping back for a minute to think about the big picture of all this is probably a good idea. Solvers are very interesting in that they provide a view of what is optimal and unbeatable play for all opponent's involved in a hand. That said, even if you could emulate GTO perfectly in live play, it will certainly not win you the most money against imperfect opposition. You can never lose but your win rate will be lower.

To my mind the best way to use GTO knowledge in practical play is to identify errors that we and our opponents are making compared to the GTO model. From there we can infer exploitative strategies which improve our overall win rate. Without an understanding of what perfect play looks like, any exploitative strategies suggested are educated guesses until we fully understand what a solver optimization looks like in that particular non-GTO scenario.

we should expect that the postflop play of a winning player to be superior to the average player at the table if anything so the gto scenario would imply narrower open ranges for that reason, but this is likely a minor effect that could easily be dominated by their preflop tendencies.

tbh, though, my suspicion is that people would not be 3betting or defending enough out of the blinds back then (and the fact that he thought 40/20/10 was a good ratio speaks to that), and that would if anything suggest that the bottom of his then profitable opening range would not show a profit against gto opponents. would be interesting if that was the case because small changes in opening ranges would be compounded for each action following.

My mistake. I wrote my post from memory after having run the numbers the night before and only recalled the straight win %. It was actually, 26% win and 8% ties for a total 34%.

This is really a great post and a great example. It comes up all the time too.

That seems backwards. If people are under-defending don't you steal wider? Same with them not 3-betting enough, since you don't get punished as much for opening light. Against significantly overly-tight blinds a 100% steal range can be optimal. You profit more from the over-folding and can play more accurately post-flop when they call (due to their narrower range).

consider what is being said. you profit more against people who play too tight, yes. against those people you shoudl open wider than against gto players. we agree on that.

the implications of that are that because he chose to define what is a profitable open based on how the hands performed in the year 200x, if one of the errors the field was making was that they were playing too tight out of the blinds, he would be overestimating how many hands can be profitably included in an open range against a field of opponents who play closer to gto.

it's also possible that people in the past were erring in the opposite direction though so it's not particularly useful to know what hands were profitable opens in 200x.

Sorry, I'm not trying to be an ass here; i legitimately don't understand what you're saying.

The book suggested opening from the button with a little over 40% of hands (41.2% if I remember correctly). This was just based on which hands showed a profit from his data set. However, you are suggesting that players under-defended, which makes a wider range of hands profitable. That implies that he was able to see a profit with hands that would not be profitable if his opponents defended correctly (in the book, he even said that most of the profit comes from the blinds folding, and you should open less against people who defend more).

All this implies that the GTO range is narrower than 41.2%. But, isn't the point being made in this thread that it's actually wider? That's what has me confused.

He has a dataset with his own poor pre and post flop play. (I was equally sucky back then). Sucking post-flop hurts a lot.

The game is so much more advanced than it was in 2007 and you'd be better off never opening it again as it's quite misguided.

Well I don't play $200/$400, or anything remotely close. In my crappy $20/$40 game the concepts are quite useful.

11/1/2019 i realized i was getting trolled.

nice

i agree it's counterintuitive. i also don't put that much stock in the idea of him playing worse post flop necessitating a tighter range because for as bad as he may have been, other people must have been at least as bad since he was winning in the games.

im a solver newb though so i don't even know what gto opens are. probably should actually buy a solver at some point.

Might just call pre. Capping beats folding for sure.

As played that’s a good card to fire on the turn. We have a surprising amount of equity (A, K, Q all often give us the winner), he sometimes folds A hi that has us notched too.

I do think betting the river is mostly lighting it on fire. So I like the check fold.

Also, if you wanna crush higher stakes in 2019, going off Stox’s 2007 charts is not the way to do it.


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Agree that the game has changed a lot since 2007, and you should not bother reading any "advanced" LHE strategy books from that era.

One good example is checking behind on flops. Barely happened at all in 2007, nowadays that's a common move when it appears opponent(s) probably hit flop better than you (and also in some other trickier spots).

So books which don't account for your opponents doing stuff like that aren't really useful in 2019. That's just one example.

Regarding this hand, I'm still not a big hand of capping hands like Ac3c out of the BB 3-handed. I understand why it's done, and I understand what you can gain from doing so (including making your cap less readable in future hands), but I am still of the opinion it's on the spewy side. This especially seems true if one or both opponents just won't lay down a pair or ace high no matter what, which I've seen often shorthanded.

100% agree that folding Ac3c from the BB 3-handed is awful, though. Absolutely can't do that if you want to play 3-handed LHE.

As played, postflop looks fine to me.

uhhh, 3 handed lhe and lhe where it's folded to the button are the same game. Yes in the latter there is a TINY amount of card removal but it's so so minute it doesn't matter.

When one talks about the Stox book it’s important to always differentiate between advice and charts based upon thinking it through and those based upon cold hard data. And in the book there were three different players with differing win rates.

No one would argue the game hasn’t changed since 2007 and while some advice may be considered bad the data is still based upon players holding a skill edge over their opponents. It’s hard to beat cold hard data, I would more trust data from 1977 as opposed to a preflop solution based upon both players playing perfectly for four streets.

Perhaps you think your edge is higher and/or the changes from 2007 lead to differences where you can play more hands. And it very well may be true. But if the goal is to make the most money possible you should be honest and diligent going about that rationale.

The mindsets of the players involved are often different thus creating different dynamics

Hi Everyone:

I'm getting to this thread a little late, but thought I would address one of the questions that has been raised. And the question is, assuming you're going to play the Ac3c in the big blind, should you raise or call.

Well, since there's objection to our 2007 book, how about one from 2011, The Intelligent Poker Player by Philip Newall. In "Part One Strategy; Rules for Preflop Limit Hold 'em" on page 36 we have:

The next logical situation to consider is when two players have voluntarily entered the pot, the first raised, the second reraised (since we have decided that, in general, it would be a mistake for the second player not to reraise), and we are not in the big blind. You can probably guess by now that my advice is to cap-or-fold. It’s true that letting the big blind in cheap is less of a concern now that the betting is already at three bets, but I feel that showing aggression here preflop will have a number of benefits postflop. Most importantly, it will make your postflop decisions easier as now you will be the “preflop aggressor,” and will get a cheap shot at seeing how your opponents react to your probable bet on the flop. So in the absence of any compelling reason to call, my choice in this spot is to play cap-or-fold

Also on page 36 and 37 we have:

So far, things have been very simple as my advice at every eventuality covered is to have a basic game-plan of raising-or-folding. However, the big blind hasn’t been mentioned yet, and this is because my advice here is the mirror image of what we have covered thus far. In the situations we’ve been looking at, the choice was to raise because the majority of our playable hands have benefitted from this strategy. Specifically, raising benefits so many of our profitable hands that it’s the natural umbrella to hide information under. But the situation is reversed when you are in the big blind heads-up against an in-position raiser. Getting immediate odds of 3.5-to-1 on a call, the vast majority of your playable hands will be worth a call, but no more. For example, against a button open raise, hands as weak as the 7h4d should have enough equity to call and see the flop. On the other hand, the range of hands we could profitably reraise with is much smaller than the range of hands we can make plus-EV calls with. This means that the logical way to hide information in this spot is by always calling.


Also, on page 37 we have:

I play similarly in the big blind against a raise and a reraise. Here, my strategy is again to call-or-fold. (Of course, we must play a much tighter range against two raises rather than one.) Until recently, my strategy was to cap-or-fold because if there is any chance of getting the original raiser to fold, then capping will be the better option since the benefits of creating a heads-up pot with lots of dead money are massive. However, it has become increasingly rare to see players raise first-in and then fold to two more bets, and this is an example of how the general standard of play has increased in recent years.

By the way, this is an absolutely great book for limit hold 'em, and his other book Further Limit Hold 'em has a lot of value as well.

Best wishes,
Mason

I apologize profusely but I am still trying to understand the logic behind the 3 way cap preflop with A3s. I have read this thread multiple times and thought about it for hours.

Here is the way I see it (please feel free to brutally correct me!): If we happily cap we are ok getting 2 to 1 assuming everyone calls which I think is a safe assumption. That means we need 33% equity to break even. But we're out of position so I would think that maybe 40% equity is reasonable. I played around with the ranges of the button and small blind and couldn't get us 40% equity. Even when I put them on playing 100% of their hands our equity is only 39.7% while theirs is 30.1% and 30.2%. Is that enough equity to make a 4 bet the right choice? What if a 5 bet was the cap? Would we have still 4 bet? I used a program that calculates the hand all the way to the river (any suggestions for one that can look at equities after just the flop?) so I would think that is some area where I am making a mistake?

So, how can getting 2 to 1 on a bet when we're out of position and not a 2 to 1 favorite be the right thing? I am excluding deception and balancing from my analysis.

Thank you!!


Ps. This is WAY above my pay grade. The biggest I have played is 30/60 with overs. But I usually play much smaller (6/12 to 20/40).

how many bets do you have to put in to cap from the bb? hint, it's not 4.

otherwise, consider range vs range instead of hand vs range. add a few hands at the margins of hero's range and recalculate. iterate as necessary.

1) we are in position against the stronger of the two ranges. Not oop to both

2) if we magically knew our equity is exactly 33.3% we could put in our whole bankroll and be breaking even / fair gamble. This 40% threshold you decided on is arbitrary and meaningless.

3) modern poker aka dream machine aka solvers tell us that implied odds is an overrated concept in limit poker. Players’ EV is often quite close to the equity of their range vs the other ranges.

Hey DD, I don't have a dream machine and am still using an abacus to calculate EV and figure out my poker decisions

I saw it touched on, but am curious what your thoughts are on flatting 100% from bb here? This is what I do, but it's only because I'm not good enough to properly split my range in this spot and remain as opaque as I'd like. I feel like having relative position on sb makes this okay. So is this strictly a cap or fold decision? Anyone?

I used to flat there but now I think cap is better. We are ahead of the Btn's opening range, we don't mind bloating the pot vs SB, sometimes the button folds for two more bets which is awesome!