ok so the recent cepheus thread got me interested in playing it again. kinda rambly post as it's my thoughts, but i was interested so i thought others might be.

here's a hand:

Hand #31 of 100 dealt by Cepheus, Cepheus pays SB (5), uhbw pays BB (10)
Cepheus calls and raises (#1 of 3)
uhbw calls (10) with A4o
8♦8♠9♣ are revealed.
uhbw checks (i'm doing black/red k/r vs. call w/ Ahighs on favorable flops so this time was k/c. red-> k/r)
Cepheus bets
uhbw calls (10) (plan is to simply call down)
3♣ is revealed.
uhbw checks
Cepheus bets
uhbw calls (20)
5♣ is revealed.
uhbw checks
Cepheus bets
uhbw calls (20)
uhbw shows pair of eights with ace, nine, and five
Cepheus shows pair of eights with ace, nine, and seven [Cepheus won w/ A7o]

what i'm most interested in is cepheus's river bet. and more interestingly, how it approaches the river?

is cepheus bluffing? or is it value betting? i'm like virtually certain this is a value bet due to the insane # of bluffs it can have.

buuut, some of those value bets will check the turn. cepheus has a very balanced range and puts some bet/bet/bet hands in either the check/bet/bet bucket or the bet/check/bet bucket (though admittedly this one is small). so not ALL his value bets are ALL there on the river.

as a result, he has to include more value bets than i guess we'd think since it has to make up for the fact that there's a loootttt of bluffs that fall into the 11% bluffing frequency it needs to hit on the river.

i'll be honest, i was surprised to lose this pot. it seemed most likely he had any number of busted draws rather than value and i assumed he'd check any better ace behind vs. bet for value. ofc, i shouldn't be thinking like that and instead thinking about what my range of hands is and how far up A4o is in it. offhand it seems like it's way too far up to fold even though he's only bluffing 11% of the time.

last thought on this part-> aren't there SOOO many bluffs he can have here (oesd, gutshots +overcards, etc.) that he'd have to be checking back the river a lot? of the 89%, he has to be checking like 50% of those, right? does this mean if i play my draws mostly aggressively that i can fold even a hand this high up in my call/call/call range? EDIT: no i can't ever fold this. even if my c/c/c range is made stronger and smaller by playing draws generally aggressively, he's still bluffing lots. he'd have to check like 2:1 check/value bet the river for me to start considering folding hands like this imo

secondarily, cepheus doesn't follow the fundamental theorem of poker since WHEN CALLED, cepheus loses more than 50% for sure. instead, it's developing ranges solely based on pot size and the decision trees that eliminate the possibility of being exploited vs. getting the most money out of each bet.

in order to follow the FTOP, it would have to reduce the value bet frequency, which would then also reduce the bluff frequency, which means it would be giving up on too many bluffs.

what do you guys think here? agree it's a clear value bet? agree it's not following FTOP? other thoughts?

I think the turn is a low frequency value bet in position, followed by a 100% value bet on the river.

my 2 cents.

so you think it'd check the turn more? it def has to bluff more on the turn than on the river (3:1 vs. 6:1 --> OOPS lol just realized i was using 8:1 vs. 6:1 on the river. it's not 11% bluffs it's 15% bluffs, which makes more sense to me now)

so the breakdown is something like 2 checks and 1 value bet and 1 bluff on the turn?

i must be bluffing WAY too infrequently:

Hand #1 of 100 dealt by Cepheus, Cepheus pays SB (5), uhbw pays BB (10)
Cepheus calls and raises (#1 of 3)
uhbw calls (10) with Jd8d
8♥K♦K♣ are revealed.
uhbw checks
Cepheus bets
uhbw calls and raises (#2 of 4)
Cepheus calls (10)
K♠ is revealed.
uhbw bets
Cepheus calls (20)
7♦ is revealed.
uhbw bets
Cepheus calls (20)
uhbw shows kings full of eights
Cepheus shows trip kings with queen and nine Q9o
uhbw wins 160, bringing their balance to 80

a few other hands for fun:

Hand #5 of 100 dealt by Cepheus, Cepheus pays SB (5), uhbw pays BB (10)
Cepheus calls and raises (#1 of 3) with A9o
uhbw calls (10) with QJo
K♠4♦Q♦ are revealed.
uhbw checks
Cepheus bets
uhbw calls and raises (#2 of 4)
Cepheus calls (10)
9♠ is revealed.
uhbw bets
Cepheus calls (20)
A♦ is revealed.
uhbw checks
Cepheus bets
uhbw calls (20)
uhbw shows pair of queens with ace, king, and jack
Cepheus shows aces and nines with king kicker
Cepheus wins 160, bringing their balance to 5

Hand #11 of 100 dealt by Cepheus, Cepheus pays SB (5), uhbw pays BB (10)
Cepheus calls and raises (#1 of 3) with j6o
uhbw calls (10) with 73s
8♦4♣7♣ are revealed.
uhbw checks
Cepheus bets
uhbw calls and raises (#2 of 4)
Cepheus calls (10)
J♣ is revealed.
uhbw bets
Cepheus calls (20)
7♦ is revealed.
uhbw checks wanted to mix it up here as there's quite a few busted draws i could see it betting for value but folding if i bet again
Cepheus bets
uhbw calls and raises (#2 of 4)
Cepheus calls (20)
uhbw shows trip sevens with jack and eight
Cepheus shows jacks and sevens with eight kicker
uhbw wins 200, bringing their balance to 215

GOOD ONE. i wanted to test it to see if it folds to river k/r's on this kinda scare card:
Hand #17 of 100 dealt by Cepheus, Cepheus pays SB (5), uhbw pays BB (10)
Cepheus calls and raises (#1 of 3)
uhbw calls and raises (#2 of 3) with A5o
Cepheus calls (10)
10♥4♦8♥ are revealed.
uhbw bets
Cepheus calls and raises (#2 of 4)
uhbw calls (10)
5♠ is revealed.
uhbw checks
Cepheus bets
uhbw calls (20)
K♥ is revealed.
uhbw checks
Cepheus bets
uhbw calls and raises (#2 of 4)
Cepheus folds
uhbw wins 200, bringing their balance to 500

super interesting play w/ KJo:

Hand #30 of 100 dealt by uhbw, uhbw pays SB (5), Cepheus pays BB (10)
uhbw calls and raises (#1 of 3) with 96hh
Cepheus calls (10) with KJo
7♥8♠7♦ are revealed.
Cepheus checks
uhbw bets
Cepheus calls and raises (#2 of 4)
uhbw calls (10)
Q♦ is revealed.
Cepheus checks interesting donk check here
uhbw bets i thought the k was giving up more than getting to showdown
Cepheus calls (20)
2♣ is revealed.
Cepheus checks
uhbw bets
Cepheus calls (20)
uhbw shows pair of sevens with queen, nine, and eight
Cepheus shows pair of sevens with king, queen, and jack
Cepheus wins 160, bringing their balance to -315

NOTE: i'm up 25ish bets on cepheus so far over a few hundred hands. wondering when i'm gunna start getting crushed

I'm going to chime in again here because I'm confident that this logic is incorrect and I think that it's an important point for the community.

This is basically the same argument that I was making in the recent "40 80 hand" thread and it seemed like most posters there were not getting what I was trying to say, so I'll try again here.

There is just no such thing as adding more value bets in order to balance our large number of bluffs. A value bet, by definition, makes money against our opponent's continuing range. The key factor to consider here is our opponent's range -- not our own range, not whether or not the board favors us, and not whether or not we "want" to have a lot of bluffs in a given spot. How our hand is doing against our opponent's continuing range will determine if we can bet for value. That's it.

Therefore, the logic should be -- which hands in my range can I bet for value? Given that, how many bluffs do I need for balance and which hands should I choose as bluffs?

Now I will speculate about the hand in the OP and with everything that follows I have less confidence in my analysis than I do about what I've written above . . . Cepheus probably assumes that you are 3betting preflop with a very large number of your ace hi combos and maybe some of your stronger king hi combos. It probably also assumes that you fold very few hands preflop. With the given pot size and action in huhu, you have to show down at least 50% of your preflop range to prevent from being run over (FLHE, page 75). You will also have post flop raising ranges along the way, so the worst hand that you'll need to show down with this line will end up being even worse.

On this flop texture (rainbow, paired board) you will "miss" most of the time. Further, hands that you might be expected to fold right away on the flop include 5-hi, 4-hi and 3-hi. So, as the board runs out in this manner you are very unlikely to have a pair. So, at showdown, I believe Cepheus expects you to show up with a ton of King hi and maybe even some Queen hi (and not a whole lot of Ace hi because of preflop) and therefore it is betting for value because of how it's hand is doing against your assumed continuing range on the river.

As a side note, I think it's important to mentally realize how different our ranges will look in spots like this in huhu than even in the next widest possible range spot -- Blind vs. Blind in a game with 3+ players, where A7 hi might not be a value bet on the river.

good post up.

and yea i messed up the logic there. obv can't go against FTOP so have to simply adjust strategy to match. it's not the give-and-take thing that i outlined.

I’d c/r the flop fir value

~half the time i was doing just that.

Trying to flesh it out from Cepheus POV:

Flop: Cepheus has a standard value / continuation bet as it can get value from K hi's, Q hi's, draws, and fold out bad hands that still have 6 outs like 43s. It likely expects 9x and 8x to xr the flop at some frequency.

Turn: This card is much better for Cepheus, as it has many more random 3x than we do (we really only have A3, K3, and maybe some other 3x w/ BDFD). Since this really almost never improves you to a hand that can xr the turn, it bets again.

River: The river is actually pretty neutral; I think you both could have the flush (slightly more likely for Cepheus), but besides random flushes and 76s, you really don't have much better than like A3 here too often. So he can pretty much value bet any Ace that beats your Ace hi distribution, as you should be selecting your folds from your straight draws (and therefore calling a fair bit with K hi type hands that arrived here).

I don't mind Cepheus's river bet overall. If our general 3! range preflop consists say of ATo+ and A5s+ then it seems that although Cepheus is not getting much value vs. our Ace Hi hands on river (as it only beats A2, A4, and A6 and chops with A7o), it is getting value from some of our K highs which may make crying calls here ~20-25% of the time and get to the river in most cases as well.

I'm obviously not going to argue against Cepheus's decision to bet turn in this hand, but I would say that I check back this flop, at least in 3+hande BTN v BB situations, probably 50% of the time vs thinking opponents who are capable of xR turn at good freqs. Versus standard ABCplayers/fish/nits/etc (e.g. IMO make up most live 40-80 players) who aren't that balanced and never check raise bluff turn, I will exploit and fire turn almost 100% and just fold if check raised. Overall, I would be somewhat surprised if Cepheus is betting most of his Ace highs on turn here because he is almost forced to showdown once xR. Hero can exploit his opponent's high turn cbet frequency with a well balanced xR monster hands/monster draws.

I have not read the thread where this was argued; however, it is my understanding that Cepheus may be betting river here (or even betting lighter) not as a complete value bet, but as a bet that will create a more balanced bluff-to-value betting frequency. When Cepheus bets A7o on river, although it may be giving up small immediate equity in this particular hand, it will improve its odds of bluffing in future hands, and therefore it's overall equity in a large sample.

See this is exactly what I believe it is NOT doing, particularly on the river, and the reason why I keep bringing this up is that this seems to be a community-wide misconception about how GTO play works and I think it's important for people reading these forums and learning about this stuff to think about it correctly.

To put it more bluntly, there's another term for some of the bets that follow the thought process you've described -- spew. Spew means that some money is unnecessarily lost through aggressive action on average, meaning that the more passive action would have been more profitable. A simple example is when we arrive on the river in a heads up pot and our opponent checks to us . . . if we bet "too thinly" such that when our opponent calls with a correct frequency he wins 2/3rds of the time but the bet also does not function efficiently as a bluff (it should not be included in our bluffing range) because better hands are never folding . . . that bet would be spew because we would make more money on average by checking behind. If we are making that bet simply because we want to have more bluffs in that spot then our overall strategy is suboptimal -- instead, we should value bet less often and bluff less often and check behind more often. This might mean that we need to be careful that we are giving up with some hands that we'd normally want to bluff with and/or perhaps we arrived on this street incorrectly and should look to correct decisions on previous streets so that we are not tempted to be so bluff heavy on the river. But the solution is NOT to add spew bets to balance more bluffs.

Obviously Cepheus cannot be analyzed except holistically, but nothing really looks out of the ordinary on those hands. A few close decisions but it looks like the bot plays good.

If we are betting to balance in a non-bluff spot where opponent wins 2/3 of the time, it is spew. If we are betting our 46-54% 1-1 equity hands where it is sometimes close, then yes, we should be betting. This particular hand is generally a way ahead or way behind spot for Cepheus. Improving our ability bluff and often getting about 5:1 on our money in these situations is always a good thing. If we are checking A7o, then BB can fold more of his King highs knowing we will check back a lot of Ace highs and are valuing better with much lower frequencies. A lower frequency bet polarizes our hand too much.

If you want study cepheus, look at its entire range v range instead of a particular hand.

I agree.

suggested reading imo:

https://forumserver.twoplustwo.com/1...08/?highlight=

Agreed. I played a few hundred hands with it and I feel it plays absolutely solid poker. It’s difficult and tiring to play against bc I have to be so thoughtful in trying to come up with first what gto strat is for cepheus in spots and then what my play should be.

I’ve experimented a bit w adding more donk bets too and obv I can’t quantitative conclude anything here, but it seems that’s definitely necessary. If you never force it to make 5:1 decisions otf and only give it 7:1 decisions (facing a kr), you’ll lose too much value from his check back range or you give him a shot to catch when he’s > 5:1 against and should fold. So the donk bets are definitely necessary in a nonexploitable strategy.

It’s also def a good study tool for decision making at the table.

Up, yea I got it now. It’s simpler than some make it out to be. Set value bets based on the minimum hand you bet to get called and win ~50% and from there build out checking and bluffing ranges based on pot size and your hand range at that point. It shouldn’t ever be doing -EV things.

Some of what you wrote here is not clear to me what you mean, but generally I disagree with this. Again, particularly on the river when checked to heads up, we should not be betting marginal hands "for balance", we should be betting them for value or checking behind. My understanding of way ahead / way behind concepts is that it does not apply to heads up river play. On the river, our hands no longer have any drawing equity. They either have value or they don't. To your last point, having a polarized betting range on the river (particularly when checked to heads up) is not a bad thing. In fact, being polarized on the river is almost always correct. We bet for value or we bluff. The stuff between those becomes our checking range and therefore our bets are (correctly) polarized.

Yes uphillbothways, I agree with this. The 50% figure would be exactly correct if your opponent could only call or fold, and we prevent him from folding all of those hands that we beat by THEN adding the appropriate amount of bluffs to our betting range. Once factoring in that your opponent could also raise, and if there's any chance that when he does that he could be bluffing, then we probably need our worst value bet to beat a bit more than 50% of his continuing range (we only want to bet/fold a small sliver of our value bets), but this is the idea anyway. The key is to determine our value range first by comparing each of our candidate hands against his continuing range and THEN we add in the appropriate number of bluffs -- not the other way around.

I would not first analyze the bot from the perspective of a human or from game theory perspective, but first and foremost from a machine learning perspective. The other perspectives might help explain why what it is doing works, but even that is just a guess.

In this case maybe his river bet is a bet that gathers value from both players who fold too much and players who call too much, but against a good player it's slightly losing. The bot is probably always adjusting to an opponents play, but maybe this spot is close all around? Close to a bluff, close to a value bet, close to a check.

No, I’ve read the paper (I’m a statistician by trade and am an amateur math lover). It’s built off of what they call CFR+ which stands for something lol but basically it minimizes post hoc regret. Regret=wishing it would have done something different using hindsight. Turns out, that’s an easier way to train a machine learning bot (makes it learn basically as fast as possible).

The result of this, they prove in their paper, is nearly identical to the Nash equilibrium. So the least regret possible = as close to a gto strategy as possible. So Cepheus by definition should be able to be analyzed using game theoretic concepts. If it does what you’re implying then that’s an externality if its programming.

Playing on my cell so no hh

I’m bu/sb w 22 no diamond

I raise, C 3b, I call (I’m capping about 1/4 the time w any pair <7s, 3/4 for 7s and up)

Flop was Qd9d4x. C bets I call.

Turn Ad. C checks. I’ve found this is polarizing. Either he has a killer draw, a super strong hand, or he’s in k/c mode (much of which I beat). Since I have no d and an easy fold to a raise, and some value to get, I bet. C calls

River was an off suit 5. C checks. I??

why? I mean, why half the time and not 25% or 65% or 52.8743%?

Interesting, where can I find the paper?

I’m not a computer. I haven’t solved my ranges. I know I should be doing a some of the time and b some of the time. So it’s just an easy way to do it.

Half=Black
Quarter=Spades

Super easy to implement.