peelnutsjamtime

good catch, no cheating here haha
I gave OOP a river bet of 33%, 100% and shove on the river and IP no longer bets turn at 100% but instead uses the small size 80% of the time(Ac is pure small bet)
OOP splits defense by both calling and raising. The river result is the same in the call line.

In my original sim when I solved it down more, IP stopped betting when checked to. So I gave OOP's drawing hands more equity on the turn.

IP bets 100% but does not use shove. OOP pure calls vs the smaller bet and shoves on 2c. AA makes the call 13.46% of the time. OOP's turn call with 87s without flush draw is indeed 0.

https://imgur.com/a/CuJOlta
IP Range: AA
OOP Range: 87s, 10% 66

I find it interesting that IP chooses the smaller size and this forces OOP to not have a raising range.

IP ends up calling the bet less than its single street MDF but can just fold 100% in a river sub-tree.

This is a no limit example where OOP has some nuts to discourage IP from shoving.

I'm a chess player myself, though only at the amateur level. The key difference between the two games from a game theory perspective is that chess is a game of perfect and complete information where as poker is a game of imperfect, and incomplete information(hole cards hidden, future runouts uncertain). This makes chess the same as Tic-Tac-Toe, albeit with a much larger game space. Another difference is that exploitation is important in poker where as it is not a thing in chess. You want to maximize your chip amount in poker where as in chess you just want to check mate. How many pieces you have at the end doesn't really matter. These factors make poker a really interesting and complex game.

MoP made it pretty clear that a multi-street game is conceptually different from a series of single street games chained together and I don't think that result changes whether it's NLHE or LHE. We are always trying to maximize our EV at the root in either case so the point of indifference is always at the root. (kind of explains why most flop strategies are mixed).
If I remember correctly, AA undercalls the river in that situation compared to its naked river MDF on its own because the opponent doesn't get an opportunity to bluff every river. The way his calling range is constructed only allows him to have bluffs on flush run outs, which only occurs a fraction of the time. This discounts his river bluff EV on flush runouts so AA doesn't have to call as often to make his call on the turn indifferent.

Interesting thoughts at the end regarding the way we approach the game by separating preflop and postflop. I think this is more of a necessity rather than an assumption. There's simply no better way to solve these spots given today's technology and resource constraints. I think of it as a nodelock, as long as our opponent isn't allowed to change the part of his strategy that is locked (preflop range) then our sim result is GTO(still only with respect to the postflop abstractions we give to both players). Like if we cap a player's flop strategy, the solver will still find an optimal way to play the turn and river, but the real adjustment should be made on the flop. In the same way that if our preflop ranges aren't close enough compared to the real game then adjustments could be made preflop rather than postflop. Though I don't think this is something we need to worry about in practice.

Like in the dark

Also do you think the disparity between BT's betting frequency vs PFR's betting frequency is mainly a function of the sizing rather than the ranges/positions involved? If we gave BT a larger betsize we'd see the betting frequency go down like MPs and vice versa?

Excellent video as usual. Haven't done any multi-way solving but agree with all your heuristics.

On boards that give callers a lot of sets/2p as well as those that are dynamic, I think a range check is the only way for the PFR to proceed. But on more static boards that favour the PFR's range(say A72, K83 etc), do you think a high frequency small bet is better than the large bet/check strategy the sim is using?

Hey, really nice video. I took a break from poker and and you're still one of my favorite coaches despite being an elite member before.

Regarding the theoretical question at the end. Optimally it is not possible to increase EV by not playing +EV hands as villain has no incentive to change strategy in this case and we just lose out by not playing a hand that has positive expectation while the rest of our range retains the same EV. On the other hand, it is also impossible to gain EV by playing a -EV hand though we do gain EV by playing 0 EV hand. This is quite easy to illustrate, imagine if we only played AA, opponent would over fold. This means any hand we add to our range at this point is going to be +EV given our opponent's current strategy, so say we add hand X. Then villain would have incentive to start putting more money into the pot making hand X 0 EV while increasing the EV of our AA. Note that villain's new strategy cannot make X -EV because we can simply remove this hand and gain EV, which violates the assumption that he was playing optimally vs (AA+ X).

The reason why I really like your videos is because you don't get lost in the technicalities of game theory and simply uses it to improve real play. No one can be perfectly clairvoyant and execute perfect GTO strategies even if they are, so exploitatively it's possible to gain EV in both scenarios. I think nowadays exploitation is more about making our opponents play the wrong game tree and taking advantage of their wrong assumptions rather than relying on them making mistakes against standard ranges/lines.

A video looking at turn play would be great!

Interesting topic and the heuristics make a lot of sense. Curious to what BB's general turn strategy is after XR so aggressively on the flop. I guess it would continue with a high frequency small bet on low/medium connecting cards again and mix overbets on high cards?

One thing that I noticed is that the percentages for BB response vs p33 doesn't add up to 100% on the excel spreadsheet at the beginning (6:00). So something isn't right on the aggregate report.

Hi, nice results and great content plan. I like your live play videos and the way you explain your thought process. The idea of an intro, main body and conclusion can organize it even better!

KK vs 99 hand around 44 mins. You expect to mostly lose when getting called and said it's fine because we can have some bluffs that want to shove here. Shouldn't we be building our range around value hands, rather than bluffs? If we expect to "mostly lose when called' then KK is clearly not strong enough to value bet for this sizing, and if that's due to our opponent over folding then the correct exploitative adjustment should simply to over bluff without changing our value threshold?

I do agree that a block is better for this region of hand strength especially given your read of his range.
Would you be implementing 2 sizes on this river or choose one of the following:
1. Shove with say sets+ for value and bluffs like KQ and Axs as you mentioned and check with hands like KK which might face a tough decision on the river.
2. Block bet with a wider range that includes hands like KK for value and our bluffs.
I think we don't lose value with our nuts if we only block and still get folds from his missed draws and draws with weak pair. He may still hero fold a J sometimes too.
Would love to hear your thoughts on the above.

Very nice video and interesting format. Cool to see some tough hands and complex equilibrium. Much better than some elite videos of standard live play.

You exploit a GTO player by GTFO

Please no live hands on a RIO Elite video... I believe most Elite subscribers are online players who may or may not mix in some live play.

Live poker is exploitative and it has to be due to the pace of the game and lack of hud/database as well as generally weaker players.Content specifically catered towards live players will only be applicable to said live players. But good content(theory, analysis) based on online play will always apply to live games.

The analogy is kind of like studying solvers to get a baseline understanding of equilibrium strategy to which you can adjust based on reads to exploit deviations from opponents. Live players should use the theory/practice they learn from studying/playing online and adjust to the specific game conditions they are in.
For example, nobody can give you a perfect RFI range/size for a FR live game. It all depends on game conditions. Do you get 3b too much from maniacs? Then stop opening hands that you have to fold vs the 3b. Do you get 6 callers when you have AA? Then size up!

Educational AND fun to watch. Welcome and thank you!

Did they really restrict bet sizes to at least half pot?Pretty sure I've seen 1/3 bets on the flop/

Great video! Surprised how much value it has even to a 6max only player.
On the topic of turn aggression on paired boards, I think IP tends to skew passive here as well in analogous 6max situations like BT vs BB. Not going as thin for value and not bluffing enough with air type hands. However, I also think that the OOP does not XR as much on the flop and tends to overfold outright. Given that the OOP player's turn range contains more strong hands and less air type of hands on the turn, IP's passive strategy here has a lot of merits as an exploitative adjustment in my opinion.
What are your thoughts on this?

I think SB vs BB edition would be an interesting value add to this series. Playing OOP with wide ranges is even harder.

Excellent video, great work Mark!

no live poker hands please...

Nice video, really like the PIO examples to supplement the theory concepts.

Nice videos, keep up the good work up.

Nash's Existence Theorem guarantees that as long as the strategies are finite and there are a finite number of players, at least one Nash equilibrium exists (possibly involving mixed strategies). Poker fits the above conditions and a Nash Equilibrium is what solvers try to approximate.
1. It's possible that there are multiple Nash Equilibria in the subgame and you happened to find a different pair each time?
2. It might also have something to do with the underlying algorithm and accuracy settings. If the solver works by minimizing an objective function, it's possible that it might get stuck in a local minima. Since you didn't solve it to completion you might have gotten 'stuck' in a different local minima each time. Maybe letting it converge to a smaller Nash distance might help on getting a unique solution.

Just some educated guesses, maybe someone more familiar with the actual algorithm that PIO uses can help shed some light haha

Curious to how big the discrepancy is, are they actually different strategies?