Ok I first read about Cepheus the so-called "unbeatable" poker bot back in January when it first came out. I was interested and thought it could be possible to GTO solve hu limit holdem..... maybe. But then I read about the way that these non poker playing computer scientists supposedly solved the game. They had the computer making random decisions and comparing and evaluating the different values of folding, check/calling, bet/raising against another computer making random decisions. The problem with this method that became readily apparent to me is that the computer is going to assign more value to betting raising and calling and less value to folding because the random computer its playing against is going to be folding the nuts sometimes randomly to bluffs.

Now I could see this was going to be flawed so I decided to sit back and wait for someone else to debunk it. Three months later and the only articles I can find online just take the creators claims as true. (If there is someone else whoes disproved it please let me know). I even read David Sklansky saying that even though he couldnt beat it, that it wouldnt extract as much money from a bad player as he would. Which would be true of a GTO solution, but why is everyone so accepting that Cepheus is unbeatable?? Deep blue beat Gary Kasparov. Who has Cepheus beat?

I played Cepheus last night for 200 hands to test my theory out. I won 64.5 big blinds in the first 100 hands and 27.5 big blinds in the second hundred. The program played very poorly in my estimation. The last hand I played basically sums up how bad Cepheus plays. I have A2o in the SB/button. I raise to 20 and Cepheus calls 10 from the bb. Flop A85. Cepheus checks I bet 10 Cepheus calls. Turn 7 Cepheus checks I bet 20 Cepheus calls. River 6 Cepheus checks I bet 20 Cepheus calls with J5 and loses. I bet every street and Cepheus called down every street with bottom pair jack kicker. Horrendous. This is GTO play? A four card straight and ace on board and this program calls on the river with bottom pair??

I plan to play a session of at least 200 hands later and record and upload the video to debunk this bot. I understand that winning 92 big blinds over 200 hands doesnt mean I've debunked it yet, but after how many hands would it be undeniable? I feel confident that I'm right and I'd even be willing to bet 80% of my bankroll I could beat Cepheus long term. I'd be interested to hear what other people think and I'd really like to hear results of your match with the bot. Keeping in mind I think it overvalues betting and calling and undervalues folding so dont bluff and bet middle pair and bottom pair for value all streets.

Also looking at the bots preflop play. How is it GTO preflop play to call 100% of the time after raising from the sb and being reraised by the big blind. With the top of your range I think its pretty obvious the GTO play is to raise back again not just call 100%. At least some calls and raises but to just call in position when you could put another bet in preflop with Aces is just wrong.

KICK THIS BOTS ASS!!!

jack high call down is a bit loose but not as horrendous as u think.

You are correct to be skeptical. Extraordinary claims require extraordinary proof, etc.

However, your description of how Cepheus developed its purported GTO strategy is not correct. The whole idea is to play against one's own nemesis which will lead to a Nash equilibrium (it did not simply play randomly against an opponent making random plays) given enough time, resources, and improving algorithms.

The Alberta boys have been on this trail for many years and have access to innovative algorithms and nearly unlimited computer power and memory. So it was not a bolt out of the blue when they made their most recent announcement.

A GTO strategy will (does) employ non-deterministic plays, meaning mixed strategies. A certain pct raise, a certain pct call, a certain pct fold. So if you see a "strange" play, it may well be attributable to a low-likelihood mixed strategy occurrence and is likely not cause to dismiss Cepheus's claims.

Also, I think most people believe that there are multiple Nash equilibria in heads-up limit holdem, meaning that different local strategies may not be shared across all of the equilibria strategies. So I would not necessarily read too much into any one aspect of the currently available Cepheus's strategy.

Of course, continue to play against Cepheus, keep track of your results and hand histories, and keep us informed of your battles against the purported GTO Cepheus.

Variance!

Yeah you got this buddy.

200 hands is a bit low to decide if you have an edge though.

Get a real sample like 500 hands and then we can tell for sure.

Gl

Ok I played 200 hands. The first 100 I did well and won 42.5 big blinds the second hundred I played poorly and lost 53 big blinds for a net loss of 10.5 big blinds. The second half I was tired and playing bad so I played poorly but whatever I lost. I'll try again tomorrow when I'm not tired and we shall see what happens.

Anyways has anyone else played it and want to post results? What do you guys think about it's preflop play, specifically never 4 betting only calling a 3bet preflop? That can't be GTO.

http://youtu.be/F-jNn6UGNlo

The authors of the paper included the exploitability numbers for Cepheus so yes very truly Cepheus is not unbeatable.

However the exploitability numbers were for the perfect counter strategy to Cepheus' play and the number was something like .05bb/100 I believe. It could be smaller as most of their results are usually reported in millibets or something like that and I don't remember if the exploitability numbers were reported as such.

There is no way for a human to play the perfect counter strategy without computer assistance either so the likelihood you beat Cepheus long term is slim.

I believe the authors also commented on the number of hands it would take for you to play Cepheus and have significant confidence that your winrate wasn't simply due to chance and it was a ridiculous amount of hands.

Yes by all means let's settle this matter once and for all via the most scientific/mathematical of means, an internet poll. Kudos!

If you could actually beat it by more than the precision to which the game was solved it only means there was a bug in the programming. The methodology is sound.

It was J5, so a pair of 5s and I'm fairly certain OP is clueless

I don't play limit HE, so I don't really know what ranges look like. But I assume OPs ranges on the river should be quite polarized, so it shouldn't really make a difference whether bot is calling with A2 or 52 on the river. He probably chose J5 as calling hand because of good blockers and pot odds.

Lets simply look at the preflop play. How is never 4 betting preflop GTO? Cepheus calls 100% of my 3-bets preflop, never raises. It defies logic.

I was hoping some more people would play Cepheus and post their results here instead of just doing what everyone else did, accept their conclusion without evidence. And I don't appreciate being ridiculed or called clueless. I believe that sort of attitude is frowned upon on 2p2. Fyi I am quite literally, a genius. Especially concerning matters of recursive programming.

When I heard about how Cepheus learned I did a quick run in my head. Initially Cepheus was doing random **** and learning which random action had a more profitable result. Correct so far? Then he would do that action with a higher frequency until it reached an equilibrium where profit is maxed. The problem with that approach is that the regret value that Cepheus initially learned for betting/raising/calling is not regretful enough simply because it will add value for times when it bet itself off a hand that shouldn't fold. Now of course it's going to learn to regret folding the nuts also, I understand that. So it might take away the erroneous added value for raising and getting the nuts to fold. I don't think it's getting it right

Another thing to consider, in a spot on the river with a board of A5678 it will call like a bet on the river with a hand like T5 40% of the time and Q5 51% of the time etc. Well wouldnt it be more GTO to call with Q5 91% and T5 0%. You'd have the same frequencies to pick off bluffs except youve simply strengthened your range on the end. Of course you'd need to randomize those hand on earlier streets for deception, but on the end when theres only 1 more bet to call I think Cepheus would be better off calling with the same overall frequency but with the higher end of cards. Seems obvious.

Also since Cepheus never 4 bets preflop what does it think of my 4 bets?? Is it just laughing to himself going "you're going to regret that idiot"? How can it play against that never doing it itself? Maybe the regretful 4 bets are still there in memory somewhere. Which is another important thing. Why does it never 4 bet? Again I'm thinking it should 4 bet with mostly the top end and some of its lower end, and just call 3bet mostly with the lower end and occasionally with the top end. Please try to explain how never 4 betting preflop is GTO. Should be funny.

The J5 hand is utterly standard.

If you ever play the hand differently you are burning money.

In regards to 4betting preflop I've anecdotally heard limit players at mid/high stakes and tough games had already been doing that for awhile and I believe the authors commented it had been a confirmed suspicion with this solution.

I believe the common explanation is that the fraction of a small bet you miss in 4betting can easily be recouped in later betting rounds and 4betting makes other strategic options untenable in later rounds.

Not sure why you think their algorithm is somehow flawed though. Could you elaborate more specifically why you think CFRM or the author's implementation of it is poor?

You can't just isolate pieces of the strategy or take a limited set of results and expect them to stand on their own as evidence.

Well according to Cepheus it would randomly play the hand differently at spots so don't be such a know-it-all. The standard play is to fold as it was only 45% to call on the river and 53% to fold and 2% raise. And it might have raised on an earlier street randomly according to the program. Btw I have never played heads up limit hold'em before this. I play full ring NLHE.

Sorry I eat humble pie as I didn't appreciate the x5678 board, I would imagine if the river had been say another 7 or a 2, the calling % would be very high.

I'd be surprised if it never raises. How do you know it never raises.

Their methodologies has been mathematically proven. The only possible question is whether there is any mistake in implementation.

Then you need to read up on their methods. Your comments below seem to show you don't really understand them well.

Not really. It starts with a default strategy for each player of doing each possible action in a given situation with equal probability. It then looks at which actions would perform better in a given situation and "regrets" not doing those actions more, and increases the relative frequency of those actions while decreasing the frequency of actions the perform worse. So it's not trying actions at random as you suggest. This process continues and is guaranteed to converge to a nash equilibrium.

While it's doing these iterations, it is also computing the maximally exploitative response to the current strategy and it stops when that exploitation is below the desired tolerance.

If there is no bug in this step (even if there were a bug in the convergence algorithm) then it's impossible to beat the bot by more than a small amount in the long run.

The initial default strategy will include folding the nuts. But it will always regret doing that and yes it will learn to undo that.

No, it wouldn't be "more GTO" because the hands where that matters are never betting.

This shows you don't really understand how the algorithm works. Just because Cepheus never does action X in situation Y doesn't mean it never considered the consequences of doing that. In fact, it considers the effect of every action in every situation on every iteration.

If (big IF) it never 4-bets then either the GTO frequency of doing that is zero or there is a bug.

Sarcasm/ridicule from the mod. Im sure the nature of your post violates the forum rules. You are not adding anything to the discussion in fact you are just being negative. Let me point out to you that the poll question is "Do you think Cepheus is BEATABLE?", not "Is Cepheus beatable?". I just wanted to know people's opinions. Thanks.

You can simply look up the preflop strategy on the Cepheus website. It will only call a 3bet never 4 bet. Also I played 400 hands and I can confirm it never 4 bet one of them.

The preflop tables are shown below. Bet, raise is the table showing what the bot does in the face of a 3bet. It calls 99.9%. Thats a GTO distribution? 4 bet 0.1% of the time and never with AA.
http://poker.srv.ualberta.ca/preflop

Yes, I saw those after my post. That really surprises me too, but it wouldn't be the first time I would be surprised by a correct Poker play.

Like I said, the algorithms work, for sure. So either that play is near-GTO or it's a bug in the implementation.

Since you have doubts... What exactly do you doubt? The existence of a GTO solution to heads-up poker? The ability to find it using their algorithms? Or their particular implementation?

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Admittedly, I don't have any experience in the testing or training methods for GTO but the idea of testing it against a single nemesis always seemed wrong.

A GTO strategy must be unexploitable to any strategy including extreme strategies without adapting it's play.

At the least it seems like it should be tested against an extremely wide variety of strategies coordinated together to create the most difficult set of ranges on all streets for GTO to deal with.

Dividing ranges into 3 distinct ranges instead of 4 and keeping your last calling range uncapped makes you far less exploitable post flop.

Remember the GTO goal is to not be exploitable so it tends to favor minimizing losses over maximizing wins.

Once you have a GTO strategy X it's very easy to find a best-response strategy against X which takes into account all streets. There is no reason to try any other strategy.

Calculating a best-response to X is like calculating 3+3. You get 6. You don't test 3+3 against all possible answers to make sure 6 is the best answer.

The only difference is that there is are typically an infinite number of best-responses to a GTO because multiple actions will have equal ev's in many situations. But that doesn't change the fact that you don't search for a best-response to a GTO, you simply calculate it.

But it could keep all ranges uncapped anyway by raising AA sometimes but not always. That's what I would expect it to do.

This isn't true. Against GTO, one obvious best response would be to adapt an identical strategy.

However testing a strategy against itself doesn't prove it was GTO because it would just have the same result as any other fixed strategy played against itself which would be break even.

You may try to optimize or train a strategy by applying adaptive versions of itself against the previous iteration in order to keep making minor improvements until no further improvements could be found.

However, it doesn't prove GTO since you may end up finding a local maxima for a particular strategy or one that could be defeated by training a fundamentally different approach against it or design an extreme exploitative strategy that was divergent enough from the norm to be able to exploit the non-adaptive GTO style.