No Limit Holdem GTO Theory Q
Posted by Alex W.
Posted by
Alex W.
posted in
High Stakes
No Limit Holdem GTO Theory Q
This is a game theory question that came up when I was reading some discussion between Sauce and Galfond on the site a while back. After talking it over with some people I still have it gotten a clear answer so I figured I'd post it here:
Lets say I'm playing someone HU. In one hand I check raise a flop, bet the turn and get called. In another hand I lead the flop, get raised, call, lead the turn, and get called. That's two different ways that 3 bets (two bets and a raise) have gone in on two streets. If the board is the same in both spots, and we are both playing GTO, are our ranges equally strong in both situations?
Basically the question is whether or not HOW the bets goes in matters in a GTO strategy.
Side note: Really hoping Sauce or Sean Lefort make an appearance in this thread--I have a huge amount of respect for your guys' understanding of game theory and would love to see your thoughts.
Thanks!
Loading 5 Comments...
1. A multistreet game with similarities to poker.
2. The GTO strategy pairs, with the BB both having a bet/call and a check/raise range and a donklead turn range after bet/calling the flop.
3. The exact ranges of the BB in both situations.
However my general prediction: on the flop the BB can only lead under certain conditions, generally being that the range of SB is not much stronger/clairvoyant. Barring card removal effects, the leading range should contain the weakest hands for a bluff and medium strong hands for value. Whilst the checkraising range should be more polarized, with the strongest hands for value.
Now in a multistreet game with draws this gets much more complicated. First off, the BB should contain some of his strongest hands in his lead(call) range, in order to punish the SB for both bluffraising and valueraising thin on multiple streets. Moreover both his checkraise and his bet(call) range should contain draws to have an uncapped range on various runouts.
Now on the turn it gets even more complicated. In general the betcall range should contain more bluffcatchers relative to the raising range of the SB.
Lets consider two possible turns, a blank and a card that brings a major draw:
On a blank, leading into the raiser is uncommon. The BB should mostly be in checkcall mode if the SB was totally polarized/clairvoyant. Hence, that leading into the raiser is part of a GTO strategy implies that both the BB and the SB have mixed ranges. For instance when the raising range of the SB is very draw heavy, the betcall range of the BB could be become stronger, if this range is moreover uncapped, leading can become optimal. In a more static game leading becomes dominated since the strongest hands of the BB gain more value by protecting his range against bluff and thin valueraises. Lastly, it is clear that the leading range should also contain bluffs, for instance his missed (backdoor) draws.
On a card that brings a draw, again leading into the raising should only happen when both ranges are mixed and the BB has an uncapped range. Mostly this leading range should contain the medium strong and/or strongest hands that have improved on this turn, together with bluff and/or hands that can redraw on the river.
Now the checkraise range. Clearly this range should contain strong hands on both a blank turn and on turns that complete a draw. Since in general his range is stronger and less capped, he can bet wider for value and as a bluff on both types. The exception for this could be rare draws that neither the BB or the SB do have in their range.
My conclusion would be that:
a. If the BB leads into the SB on a blank turn after betcalling the flop, this implies that the SB does not have a very strong/polarized range, so it must contain relatively more draws. In contrast to the case that the BB checkraised the flop, where the SB should have more bluffcatchers.
b. On a turn that brings a (major) draw, if the BB betcalled the flop, his leading range should contain relatively more made draws and bluffs, and the SB should contain more bluffcatchers. If the BB checkraised the flop, his betting range should still contain his strongest hands on the flop, combined with various (made) draws. And the SB should contain relatively more bluffcatchers.
But still this is extremely tough to say, since the structure of the game could change this tremendously. The above prediction is based on general properties of NL, such as that topset if often ahead on the turn, even if one draw comes in. In 6-card omaha these conclusions might easily become invalid.
What is your own opinion on this subject, Alex?
I think the line makes a huge difference. C/Ring and betting, then getting called can be completely different that leading/getting raised/calling, then leading and getting called again.
I don't play omaha, so I'll weigh in from a NLHE standpoint here.
I think our opponents tendencies make a giant difference here. We need to know the type of style that like to play. We really need to think about how our opponent perceives our leads on different board textures. Secondly, we need to think about how our opponent perceives our C/Rs and how often they float our C/Rs with hands that have very little to no part of the flop (gutshots or less).
If we lead on a 9s6h3c (rainbow) flop and call the raise, then lead a 7s turn, its very possible our opponent raised us with either K9+ for value or smth, or now has 8X that air-raised the flop, or picked up spades with help, something like T4ss, not to mention the prominent draws, 57, 87 and 54 that got there now... Secondly, once we lead the turn, K9 is not so thrilled about raising again, especially since we are close to the end (one card to come).
Conversely, T4ss here might simply fold to the C/R, and TT might reraise the flop looking to get it in, so the ranges can easily change based on the line that we took. I feel that its easier for our opponent to show up with backdoor draws in our lead scenario than in our C/R one, albeit both being longshots.
The bottom line is that the way the bets go in have a direct consequence on players' ranges from what I can see. And lead/raise/call, bet/call does not yield the same ranges as C/R/call, bet/call.
"If the board is the same in both spots, and we are both playing GTO, are our ranges equally strong in both situations?"
From my understanding, GTO is aiming for "perfectly balanced", but please correct me if that's not accurate, or if it's oversimplifying.
I can't see how it would be possible for the two ranges you've mentioned to have the exact same strength unless they were exactly the same (which seems unbalanced), so it would be more a question of how they're different than if they're different.
Lets consider two holdem like toy games:
1. Spade Turn Holdem. Spade Turn Holdem is the same as normal Holdem, except when there are two spades on the flop, the dealer will pick the remaining deck, sort out the first 9 spades, put them on top of the deck and then pick the top 12 cards of the deck apart, shuffle them and deal the turn from this part of the deck and the river from the remaining part of the deck.
Consequently, flushdraws have 75% chance of hitting on the turn, making them favorites over topset.
Now consider two GTO STH HU players, the flop is JsTs3h. The BB bets and gets raised by the SB and calls. The leading range of the BB will consist of flush draws, two pairs, sets, straight draws. And the raising range of the SB will mostly consist of nutflush draws and nutflush blockers.
Now the river is the 5d, since the SB range is very nutflushdraw and nutflush blocker heavy, the BB is expected to have a stronger range here. Hence he can lead his sets and missed straight draws against the SB.
If the BB check raises the flop and bets a blank turn, he is mostly repping the made hands he had in his checking range
Now if the turn was the 6s, the SB has check raised the flop and his turnbet got called. Now the BB has a more polarized range, mostly nutflushes and nutflush blockers, and the SB mostly has strong bluffcatchers.
Donk leading a 6s turn after bet calling the flop is likely a dominated strategy, if anything the SB should do this with nutflushes and nutflush blockers.
2. 2N card Holdem. Players each receive one card numbered 1,2,3,..,N from a black deck, a flop containing 3 cards numbered 1,2,3,..,N from a red deck is dealt, a round of betting follows. A turn and river are dealt from the red deck, after each follows a round of betting. There are only pairs and high card hands, pairs beat all high card hands, the highest numbered pairs and high card hands win at showdown.
Say that N=1000 and the flop is: 34h 257h 719h
The BB bets and get raised and calls. Say the valuerange of the SB is {950-100,34,257,719}. If now the turn is the 888h and the BB leads out, he should be repping 888s. But for his range this play makes no sense at all, since he is way better off by checking and letting the bluffs 1-100!34 from the SB continue to bluff. If he wanted to bluff, he would've been better off reraising on the flop, not giving a free card to the SB.
When the BB check raises the flop and bets the turn, he has a polarized range and the SB has a merged bluffcatching range, potentially uncapped. But it is dominated to call lower cards more than higher cards, since drawing to a pair gives very bad odds. Only at very deep stacks this should be done at low frequencies.
Be the first to add a comment