Pluribus Poker Preflop Defense Detailed part 1 of 2

We’re going to focus on poker preflop defense frequencies and hand ranges played by Pluribus. In order to look properly at defense strategy, we need to consider both the position of hero in defense and the position of villain who opened RFI. That’s where we wished Pluribus had played 1M hands and not just 10K hands.

Indeed when we get to this level of detail, we’re down to about 300+ hands in each scenario and this does not allow to look seriously at ranges. It is good to stat the frequencies though. So we’re going to look at all these frequencies first, and then look at ranges but withour consideration for villain position. These ranges are just pointers to help us see what hands Pluribus calls with, or 3 bets with… and mixes up, using our own judgement to infer what hands are played against what villain opening position.

We’ll have a quick view on average 3bet sizings, but will keep detailed analysis for another post.

Detailed frequencies of preflop defense

poker preflop defense frequencies
3bet size is multiples of rfi and average for the given positions

So we show the number of hands the data is based on. Obviously can’t do hand ranges for these, but frequencies should be pretty good. In theory, we’d need to also compare that to opening size, but again this will make the data sets way too small.

I split the ranges in only 3 categories: IP (in position), SB, and BB. They are a bit confusing to study but combined with the above frequencies, we should have decent ideas.

Legend for reading the charts:

Defense hand range in position

poker defense
 hands range in position

Defense range from SB

Defense hand range from BB

Key learnings for poker preflop defense

By combining detailed frequencies and overall hands played, we can infer a better view of the “probable” detailed poker ranges from Pluribus. And we see a lot more variation in call, 3bet and fold than what most players do. IE a wider range for a fairly low frequency.

HJ vs LJ preflop defense

So we have 3.3% calls and 5.4% 3bet. That is 44 tuples for calls and 72 for 3bets, so a total of 116 tuples .

Hands actually played:

so 106 tuples more or less played. Counting KQo as only 6 as obviously mixed +- 50%

So we need a total of 116 tuples. AA-77 are obviously played even if many pairs not seen here. Probably most suited Aces (A6s and A2s folded) , QJs, K9s and lower is folded. So are Q9s and lower, J9s and lower, T9s, 98s, 87s, AJo and lower etc.

So we have a total of 116 + KK, JJ, TT, 99, 88, 4 more suited Aces so 162 tuples. A good chunk of them have to mix with folds to get to 116 tuples.

So the overall range would be:

  • 77+ with a combination of 3bets and calls. Note that QQ is a call, and 77 is a 3bet in the hands played
  • A2s+ with a mix of call, 3bet, and fold .
  • KTs+, QTs+, JTs mixing 3bet and call
  • AKo, AQo mixing 3b and call, KQo probably 3bet and fold
  • 76s and 65s mixing 3bet and call

CO vs LJ preflop defense

With 8.7% tuples, we still need 116 tuples. Here are the hands actually played

So we have more or less the same range as for HJ vs LJ. Maybe 54s and 66 added. We also get confirmation that pairs are sometimes a call sometimes a 3bet, look at 88 and JJ. Also confirmation that low suited connectors are a mix including fold sometimes, same for suited Aces below ATs or A9s…

CO vs HJ preflop defense

So we gradually increase the range, now we need 179 tuples.

Cut  Off vs HighJack preflop defense strategy

So now the range adds lower pairs and K9s as a 3bet. We keep seeing pairs mixed between call and 3bet (like 55 here) and some folds for 44. Everything else much the same, we just get more tuples by having less folds on the range, but always with the same hands, ie KQ0 , bad Axs and lowest pairs and connectors.

Button vs LJ preflop defense

So we now need close to 200 tuples with twice as many calls as 3bets. In other words significantly less 3bets than from earlier position.

Button vs Lowjack preflop defense strategy

Again we see pairs 3bet or called, and the lower pairs sometimes folded. Below 55, probably fold, Pluribus didn’t get 44, but did fold 33.

We add to the range:

  • K7s+ with the lower ones 3bet
  • Q9s as a call
  • J9s mixing call and fold
  • T8s+
  • ATo+ with here AT as a 3bet and AJ as a call
  • We get to 200 tuples by not folding much in the mix strategy except lower pairs and the newly added tuples (J9s, ATo etc .)
  • Important we call twice as much as we 3bet, I assume because of the position and less players behind

Button vs HJ preflop defense

This is the same range as Button vs LJ. It confirms 44 is played. It confirms we fold some bad Axs, and lowish pairs.

Button vs highjack preflop defense strategy

Button vs Cut-off preflop defense

We are now looking for 241 tuples, with a slighly more balanced call vs 3bet, still with more calls.

Button vs Cut Off preflop defense strategy
  • Much less folds in the mix, here only JTo
  • All pairs (don’t know for sure on 22 as not dealt)
  • QJo and JTo added
  • K6s+
  • The rest is much the same
  • Note again the variety of 3bets: 66, 99, ATo, JTs, QJo etc.
  • And the real mix in 3bet/Call like K9s 3bet, K6s call, JJ or JTs both call and 3bet. QQ call. I get the feeling only AA and AKs, perhaps KK are 100% 3bet…

5 thoughts on “Pluribus Poker Preflop Defense Detailed part 1 of 2”

  1. Love what you’re doing! I think we can learn a tremendous amount about poker from Pluribus.
    That said, I caution everyone to be a little wary bc I don’t believe Pluribus won in any meaningful sense:
    1. At a fundamental level it followed strategies with an astronomical variance (compared to any decent human player) for several reasons: to ekk out small average advantages over huge numbers of hands, prevent itself from being exploited by esoteric strategies no human would ever consciously use, create deception, and allow it to have a very wide range of possible holdings on most boards. Then the programmers used statistical techniques to filter out all that variance and effectively deny that it exists.
    Some examples from your own charts: folding Ako against a raise from the big blind once (while doing things like calling with A3o and raising with A2o); folding TT, 99, and 88 in position against a raise while calling with K6s and K8s, and 5 or 6 betting all-in w A5s and getting called by QQs. You can make game theoretical arguments for these plays bc of your range, but each and everyone is a money loser each time you actually do it. Then their “statistical methods” get to erase away all these loses effectively bc it can count both that A5s might have drawn out against QQ and that it usually would been the favorite in that situation with AA or KK. I want to point out five or six betting all-in against a human who will call you with not only only with AA but also Kk, QQ, Aks, and often AKo is an astronomically negative play. I figured out it’s the right game theory play, at least sometimes, in 2005 using my own Nash calculations. But I’ve never done it against a human being bc I have yet to find one who folds KK when they should, and most don’t fold Ak or QQ enough. But of course it “won” by the rules of this competition making this terrible play against humans bc it forced what would have been a bad call if it actually had AA. I am reminded of Doyle Brunson: “Only an idiot tries to bluff someone who is always going to call you.” But the arbitrators of this game score this play as crushing the game bc it gets to count itself as having 6 times for every four times it has A5s. Winning!
    No. Actually loosing.

    1. I agree that Pluribus doesn’t give a *** about variance which means in real high stakes, the bankroll needed to win is astronomical. IE Pluribus going to Macau or Triton will go bankrupt more than likely. Would be interesting to do the maths on this 🙂 (if we knew actual variance and defined a “reasonable” bankroll).

      A more interesting learning algorithm would add requirements on limiting bankroll requirements or more precisely on reducing bankrupcy risk.

      An example of solid player variance reduction behaviour is folding the river more than theoretically called for, or using behavioural tells more than just bet sequences and ranges to decide on calling or folding the river. Like always fold to fish on river except…. when he hasn’t been in a hand for ages, 2 hearts on the flop, he calls big bet on flop, big bet on turn after tanking a bit, and goes all in on river in less than a second, with no hearts coming. Usually with something else big, he’s raised before river. Remains only stuff like he had top pair bad kicker on flop, and hit second pair on river, but he might even check/ check back, call that as well, worried we have trips or better.

      1. Thank you!
        I think I’m just about as big a game theory player as there is. But there is more to game theory than Nash Equilibria and perfectly unexploitable strategies. And even more to game theory than minimizing variance and return on investment/return on bankroll.

        Against imperfect opponents, there is value to giving them opportunities to make big mistakes. In fact, that is exactly how Pluribus “won.”

        There are also flexible strategies that are highly profitable against a wide range of opposing strategies versus brittle strategies that have most of their value against opponents who play close to perfectly themselves.

        Pluribus used a number of strategies that, although profitable and unexploitable, appear to be both high variance and brittle!

        As an example, versus the LJ, from the HJ and CO, Pluribus called 6 of 7 times with AQo and AQs, and repeatedly with 99. Conversely, it went wild reraising most of the time with KQs-KTs, QJs-QTs, and ATs-A5s, as well as sometimes with 88-66. In addition to making it’s reraise range harder to read on boards, against a very disciplined opponent who mainly plays something like AA-99 and AK-AQ against a 3-bet, these suited hands all do better if called than say AJo and almost as well AQo and 99. But they have less value as calling hands bc AQo and 99 are ahead as calling hands while all the suited hands are behind.

        However, if your opponent even somewhat regularly starts calling 3-bets with AJ-AT, KQ, and 77-55, suddenly QJs, KTs, and 66 get a lot worse versus AQ and 99. Now instead of being ahead in big reraised pots and dominating your opponent you are in the opposite situation! Pluribus appears to have never called against a RR with AJo or ATo, and not from the LJ with KQ. But these happens all the time in real play by, for example, LAGs, stuck players, players who are drinking, readers who think they have a tell you are making a play, game theory players who call the top 50% of their range against a RR, game theory players who place a high premium on randomizing the hands they call reraises with, and great but stubborn players like Patrick Antonius.

        AQo and 99 actually have a special quality versus the LJ that none of these other hands have: Assume for simplicity you get four bet and have to fold versus AA-QQ and AKo, but we put an opponent on a slightly wide but reasonable calling range versus a three bet like JJ-77, AQ-AJ, ATs, A5s, KQs, JTs, and 65s. Now we are favorite against a call with AQo and 99 in a big pot. But except for KQs, we are 45% with the smaller pairs, and even worse with suited boadways and Axs. Moreover, AQ and 99 usually have a better sense of where they are with top pair or a scattered board than hands like QJ and 66.

        So Pluribus strategy both increases variance and probably does worse against a lot of human players than a satandard TAG strategy of protecting the best hand (and getting info) by raising with AQo and 99, while calling with ATs, KQs, and 77 in position with nice drawing, multiway hands.

        1. Let me say I do really like a lot of it’s strategies and insights!

          I appreciate its’s very careful to construct it’s cold-calling range so that it can call-call or call-push w about 1/3 of its hands against squeeze plays behind as well as the bottom half of SB and BB reraises for value.

          This, I take it, is the main reason why it likes to coldcall QQ versus the LJ, as well as AQs and sometimes JJ or TT and rarely AKo. It can then potentially push all-in with QQ and AQs if raised behind (pricing AKo out of a profitable call), while calling in position with AKo and JJ-TT when it has them. From the cutoff it can also call 99-88, sometimes AQo, and probably 76s since it has a much wider calling range.

          QQ is also a nice trap when this doesn’t happen in that it goes up a lot in value if no A or K comes on the flop but it’s super concealed bc you cold-called.

          Human players will cold-call with AA, KK, AKs to trap squeezers, but you give up a ton of value and protection as well as exposing 3 bets to aggressive 4-betting if you trap with these. Likewise, if you only call and recall with TT, you are way behind players who like to 3-bet for value from the blinds.

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