Do we know who Linus is in the sample?

the one human who didn't play like trash

it only uses set sizes like half pot and pot because that is all that there is in its base strategy (whereas something like libratus had a ton of sizes for the earlier betting rounds)

it didn't discover those sizes on it's own, the betting abstraction was chosen for its blueprint

then it resolves the game with subgame solving using the closest ev's from its blueprint to get a more accurate solution in realtime

so if a player uses a size that isnt in its betting abstraction then it can add the size when it resolves the subgame (though i think they said they just translate it to the nearest size instead of adding a new size if it is really close)

So basically pluribus trims down computational requirements by making certain assumptions (primarily wrt preflop choices) from previous experience to reduce the complexity of the trees each time the hand is played.

It seems like a trivial issue to integrate these features into other solvers.

I would be shocked if people weren't already doing this (for years now).

yeah I did cuz it confused me and sometimes I know pio makes some very light calldowns after it's raising river but it wasn't a thing here

PokerStars Hand #112118: Hold'em No Limit (50/100) - 2019/07/12 07:08:38 ET
Table 'Pluribus Session 112' 6-max (Play Money) Seat #6 is the button
Seat 1: MrBlue (10000 in chips)
Seat 2: Pluribus (10000 in chips)
Seat 3: Eddie (10000 in chips)
Seat 4: MrPink (10000 in chips)
Seat 5: MrOrange (10000 in chips)
Seat 6: MrBrown (10000 in chips)
MrBlue: posts small blind 50
Pluribus: posts big blind 100
*** HOLE CARDS ***
Dealt to MrBlue [9c 8d]
Dealt to Pluribus [Kc 8h]
Dealt to Eddie [Qs Jd]
Dealt to MrPink [Jh 4d]
Dealt to MrOrange [7d 7h]
Dealt to MrBrown [Qc 6c]
Eddie: folds
MrPink: folds
MrOrange: raises 110 to 210
MrBrown: folds
MrBlue: folds
Pluribus: calls 110
*** FLOP *** [Qd 3h Jc]
Pluribus: checks
MrOrange: checks
*** TURN *** [Qd 3h Jc] [2d]
Pluribus: checks
MrOrange: checks
*** RIVER *** [Qd 3h Jc] [2d] [5h]
Pluribus: bets 940
MrOrange: folds
Uncalled bet (940) returned to Pluribus
Pluribus collected 470.0 from pot
*** SUMMARY ***
Total pot 470 | Rake 0
Board [Qd 3h Jc 2d 5h]
PokerStars Hand #112119: Hold'em No Limit (50/100) - 2019/07/12 07:08:39 ET


Thoughts on this hand? Pretty unusual bet... Pluribus does block hands like AK which it wants MrOrange to have but then it also blocks hands like KJ as well. I think it probably works really well if MrOrange folds all low pairs and maybe even some weak Js.

Are there vids or HHs that show all this donk betting the AI uses that I keep hearing about?

Yeah, I guess the runout favors BB range, raiser is likely on weak capped range, so 2x bet has enough success to be the play.

PokerStars Hand #94064: Hold'em No Limit (50/100) - 2019/07/12 02:07:44 ET
Table 'Pluribus Session 94' 6-max (Play Money) Seat #6 is the button
Seat 1: Eddie (10000 in chips)
Seat 2: Pluribus (10000 in chips)
Seat 3: Bill (10000 in chips)
Seat 4: MrOrange (10000 in chips)
Seat 5: MrBlue (10000 in chips)
Seat 6: MrPink (10000 in chips)
Eddie: posts small blind 50
Pluribus: posts big blind 100
*** HOLE CARDS ***
Dealt to Eddie [2s Kc]
Dealt to Pluribus [Ts Js]
Dealt to Bill [4h 9d]
Dealt to MrOrange [4c 9h]
Dealt to MrBlue [Jh 8d]
Dealt to MrPink [Kd Kh]
Bill: folds
MrOrange: folds
MrBlue: folds
MrPink: raises 150 to 250
Eddie: folds
Pluribus: raises 1100 to 1350
MrPink: raises 1450 to 2800
Pluribus: calls 1450
*** FLOP *** [Ac As 2c]
Pluribus: bets 1412
MrPink: calls 1412
*** TURN *** [Ac As 2c] [8s]
Pluribus: checks
MrPink: checks
*** RIVER *** [Ac As 2c] [8s] [Th]
Pluribus: checks
MrPink: checks
*** SHOWDOWN ***
MrPink: shows [Kd Kh]
MrPink collected 8474.0 from pot
*** SUMMARY ***
Total pot 8474 | Rake 0
Board [Ac As 2c 8s Th]



LOL preflop play by human

PokerStars Hand #53047: Hold'em No Limit (50/100) - 2019/07/11 14:44:07 ET
Table 'Pluribus Session 53' 6-max (Play Money) Seat #6 is the button
Seat 1: Pluribus (10000 in chips)
Seat 2: MrOrange (10000 in chips)
Seat 3: MrWhite (10000 in chips)
Seat 4: MrBlonde (10000 in chips)
Seat 5: Eddie (10000 in chips)
Seat 6: Bill (10000 in chips)
Pluribus: posts small blind 50
MrOrange: posts big blind 100
*** HOLE CARDS ***
Dealt to Pluribus [Td Qd]
Dealt to MrOrange [Qh 9s]
Dealt to MrWhite [3s 5h]
Dealt to MrBlonde [Ad 8h]
Dealt to Eddie [5d 4s]
Dealt to Bill [9h Jd]
MrWhite: folds
MrBlonde: folds
Eddie: folds
Bill: raises 187 to 287
Pluribus: raises 1011 to 1298
MrOrange: calls 1198
Bill: folds
*** FLOP *** [6s 8c Th]
Pluribus: bets 1441
MrOrange: calls 1441
*** TURN *** [6s 8c Th] [3c]
Pluribus: checks
MrOrange: bets 1755
Pluribus: calls 1755
*** RIVER *** [6s 8c Th] [3c] [Qs]
Pluribus: bets 5506
MrOrange: calls 5506
*** SHOWDOWN ***
Pluribus: shows [Td Qd]
Pluribus collected 20287.0 from pot
*** SUMMARY ***
Total pot 20287 | Rake 0
Board [6s 8c Th 3c Qs]

Wow that Q9 by human. Bot really had some tough competition

lol so you have to be the best player in the world or you play like trash? good logic.

Q9 gotta be a misclick, ive seen a few of those where it's obv they aren't just bad plays by the weaker regs.

agreed it's gotta be a misclick, I looked at the stats of all the players pluribus played against and apart from MrOrange who seemed to be a giant nit (chris ferguson?) the other player's stats pre flop at least seemed fairly standard

All these poker bots have made it clear researching is a total joke, apparently no matter what you do you have to make **** up and claim victory.

It made some news out there so it worked.

I didnt study the variance reduction technique details, but its quite simple to understand the basline idea. The bot plays a fixed strategy, so for every hand that happend during the experiment, they know which hands would play the same line and with what frequency. So they can calculate the winrate of the whole strategy instead of accounting only for the specific holding the bot had. Thats also why they cant do this for the human players - they dont know their complete strategies and frequencies.

Why don't they just play more hands? Instead of trying to simulate variance?

Ah that's interesting. Surely how likely Pluribus is to have certain hands depends on the ranges of the other players though? Like depending on what the ranges of the other players are and how weighted they are to particular cards, this will block some of Pluribus' hands at varying frequencies and change the weighted range of the bot...

It seems to me that they’re not particularly close on this. If they really had it dialed in, I expect it would waffle crush a game with 5 Linus clones. Like 30-40 bb/100. It would look like Jon Jones fighting the terminator in an MMA match. I imagine Linus (or whoever else is the best 6 max NLHE player) 2 years from now, would beat present-day Linus for more than this bot did. When you consider that a bot like this could potentially get hundreds or thousands of years of playing experience practically in the blink of an eye and have perfect recall, I’m not super impressed with it’s results.

Maybe it’s just because they did it on the cheap with the hardware?
Or because 10k hands isn’t anywhere near enough to start going deep into all the exploits?

Even if they played more hands, they would apply that variance reduction technique anyways, its just a free way to get more info out of the sample.

Yes and they have this info. This technique is used in the 5AI+1H game, you are interested in the hands human VPIPed so you take his hand fixed and you know strategies of all the 5AIs, so you can work with bots ranges and account for the blocker/bunching effects from the other bots.

According to same of the papers, the sample of 5k is relevant as a 200k sample would be, after using this AIVAT method.

In a general sense, you really only lose to a perfectly balanced player when you choose an action that is meant to be played at 0% frequency. In a game like poker it is possible for ai's to keep improving while not beating top players for much.

Someone has uploaded the hand history video to you tube. Search for "Pluribus AI vs Poker Pros".

Leave it to a wizard to not share the link itself

Part 1



Part 2



seems to be more on the way

Mr Blue has like 33% VPIP, very low 3bet% and 45% WWSF too. I'd consider a couple of them to be very weak regs even by small stakes standards.

Most of them have at least a few obvious sizeable leaks too - don't imagine any of them (other than Linus) would hold a 1kNL table without it filling up, tbh.

I'm guessing LLinus is eddie?

and yeah Lucas you're right I guess MrBlue, MrWhite and Hattori are a bit on the weaker side

it's wrong to say very weak by small stakes standard though because if they'd be sitting at a small stake table with the same exact style of play, their stats wouldn't look like that