theory questions i never bothered to ask
Posted by jc3235
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jc3235
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theory questions i never bothered to ask
2. range balancing - what does having a balanced range mean? does it mean i bluff at the exact same frequency of that where i actually have the hand? for example, i know i should bluff my missed flush draws X% of the time, but how do i determine what X is?
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Basically poker is a solvable game, it's just incredibly complex. But there is a solution or strategy such that if you play it, you cannot lose money. This is known as GTO, or being perfectly balanced. The best way to understand it is look at a simple game like rock paper scissors. The GTO solution to this game is pick rock 33.33%, paper 33.33%, and scissors 33.33%. If you do this it is impossible for you to lose (at least EV wise) no matter what your opponent does.
However, most of the people we play in poker are very unbalanced. To continue the analogy, a typical opponent will pick rock 45%, paper 30%, and scissors 25%. Therefore we can exploit them by playing unbalanced ourselves and picking rock paper 100% of the time to maximise our EV (assuming they don't catch on.)
The GTO solution to poker has not been found, but good players who play other good players on a regular basis will try and play as close to GTO as they can.
Just reread your question slightly and realised what I wrote above probably over simplified it a lot, but i'll leave it here anyway, hopefully someone will find it useful, and someone else can go into frequencies more.
(1) Range Polarization - The best way to describe it would be to say that situationally, it is often optimal. The idea is that in any form of poker, you want to get value out of your best hands, call them X. This means making a bet. But if you're always only betting strong hands (just X), you're easy to play against. Opponents will just fold when you're making bets. So what we strive to do is supplement your betting range of {X} to {X, Y} where Y represents bluffs. When choosing which hands to bluff from the rest of your range (after you've taken out X as bets for value), it makes the most sense to choose the WORST hands in your range because they are the LEAST likely to win if you get to showdown. Thus we have a polarized betting range consisting of {X, Y}, our best and worst hands.
Of course, this concept is easiest to apply in a one street game like the river. However on prior streets, hands like semi-bluffs with draws can muddle things up for us so that not everything is so clear cut. But the concept remains applicable in that in most situations, we want to remain unexploitable by betting a range that makes our opponent indifferent to proceeding with bluff-catchers (medium strength hands). And the way we construct our ranges are designed to appreciate that idea, when also embracing any possible exploitative opportunities that individual opponents create for us.
(2) Balance - It's a very loosely used term within the poker realm. Just recently there was a thread in 2p2 NVG regarding some comments by Matt Hawrilenko and it had a ton of awesome game theory content/discussion. Ike (Isaac Haxton) made a really insightful post about what he considers to be "balanced".
"It's often used in more complex situations, too.
For example, I might say, "I think this guy has a pretty balanced 3betting game plan." By saying this, I would mean that I think all of the following things (and probably a few more things, too):
The range is strong enough that I have to fold enough hands preflop and on the flop that I think the weakest hands in his range are doing better than they would by folding or calling.
The range is not so strong that I think he could add lots more hands he's currently folding and have the above statement still be true.
The composition of his 3bet range and the way he reacts to a 4bet is such that 4bet bluffing him is neither totally hopeless nor wildly profitable.
His postflop play is sufficiently reasonable that I don't think I get to do anything wildly exploitive postflop after calling his 3bets.
This isn't any sort of precise game theory claim but it's a meaningful statement in terms of how I'm going to approach playing against the guy's 3bets. Contrast it with some things I might say about an unbalanced 3betting game plan:
"This guy's 3bet range is way unbalanced toward bluffs and I can exploit him by 4bet bluffing a lot."
"This guy's 3bet range is way unbalanced toward value hands. I'm folding a lot and he could get away with adding a bunch more bluffs but he isn't doing it."
Since we're not anywhere close to knowing what optimal preflop play looks like in HUNL, I have to be content with being "balanced" in something like the above sense.
I should revise what I said earlier. The "giving them a tough decision with a lot of hands" heuristic only really applies in situations where a lot of their range is composed of interchangeable hands. It's not possible to give my opponent a tough decision with a lot of hands preflop since he has a wide range of hands with varying values. If it's a close decision whether or not he should call my open with 86o, it's not going to be a close decision whether or not he should call my open with k5o. Instead the heuristic is something like "it should be a close decision whether or not he gets to play loose enough to make the weakest hands in my range lose.""
http://forumserver.twoplustwo.com/showpost.php?p=35951603&postcount=806
If we bet 40 into 60 on the river, villain must call 40 to win 100 with his bluff-catchers, assuming his range is all bluff-catchers and we have {nuts, bluffs}. Note that this is a simplification and a strong assumption, and should be appreciated as such. But its often a very useful model.
Let X = optimal bluffing frequency. Look at EV of villain calling with a bluff-catcher:
X*(+100) + (1-X)*(-40) = 0
100x -40 +40x = 0
X = 28.6%
Thus, we want to have {29% bluffs, 71% nuts}. Our nut hands are a finite number of combos and thus we need to bluff with the appropriate amount of our potential bluffing hands to reach this ratio.
If we extrapolate things back a street to the turn, like your next question... yes you're right in that equities begin to be a big factor because ranges are not so clear-cut and begin to overlap. And yes you're absolutely correct that this complicates things greatly. However, we can still use the model to find more specific balance like making sure our turn betting range is strong enough to combat a raise enough of the time, or that we get to the river with enough bluffs to satisfy our desired river bluffing frequency, etc..
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