The Relationship Between Pre-Flop Pot Odds and Post-Flop Defending Frequency
Posted by AF3
Posted by
AF3
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Mid Stakes
The Relationship Between Pre-Flop Pot Odds and Post-Flop Defending Frequency
Has anybody thought about this, or could James expand on the idea?
I see the argument being something like:
1) When we call and flop big with any two cards, we should expect more bets to go in, or else our weak hands get to showdown much too often.
--If we're getting to showdown too often, meaning that Villain doesn't put bets in post-flop (at some non-zero rate), then Villain loses expectation, because we will often have to fold our weaker hands to avoid paying off Villain's value. Villain then has incentive to change their strategy, and so we should therefore not be getting to showdown with weak holdings much of the time that we have called with them pre-flop--
2) Because we should expect more bets to go in (see 1), we should have some non-zero implied odds with many hands.
3) When factoring in the discount we are getting pre-flop, combined with the "mandatory" implied odds
(see 2), then we can improve our expectation by calling instead of folding.
4) Since the pre-flop call should be immediately profitable, it does not matter if Villain is able to c-bet any two cards profitably on the flop.
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I was randomly thinking about this today........ I was walking to the shops thinking about how on Earth to get my defending flops up to 65% or whatever, but it suddenly crossed my mind that surely I have to defend less, the cheaper the preflop price gets.
To take an extreme, inexact example, say we somehow had a price of $0.50 to see a $10 flop, we could fold way more than 33% to a potsize bet and still make money. So, flatting minraises in the BB would have the same effect, and we probably only have to defend HU flops like 55% or something.
Hopefully this is what you were talking about.
it suddenly crossed my mind that surely I have to defend less, the cheaper the preflop price gets.
I think the example that you gave is a much better illustration of a concept that might be applicable than showing that it actually applies. I think the actual numbers are quite important.
For example, if you receive odds of over 100 to 1 pre-flop, then you can call with any two suited and technically you can fold whenever you don't hit a flush, but still "make money" overall. However, here's where I'm getting stuck (I'll bold the most relevant part):
If you open shove pre-flop, then I defend appropriately. If you min-raise pre-flop, then I defend appropriately. Either way, you should have the same overall expectation from sitting down to play against me, no matter which raise size you choose.
I don't see how Villain isn't increasing their overall expectation by
min-raising and then cbetting any two if you're folding the flop so
often (you're defending much less than 1-A).
It seems like a bit of a contradiction to have both concepts be applicable here, so I'm trying to figure out where the gap is.
This concept isn't nearly as difficult when you examine your line, "we don't need to defend as much" and ask the question 'defend as much' compared to what.
I guess the idea is that Villain doesn't win as much as I think they do, because the pot is also smaller than if they had raised larger and our range was narrower?
To be honest, I don't think the premise of your question is correct that you don't have to defend as much preflop. From a GTO standpoint you're just trying to find an equilibrium.
For example, if the Villain's range is static so that his equity doesn't increase on future streets and the bottom of his range is 0%, then you're going to need to defend pretty close to 1-A on both streets preflop regardless if you're getting better odds preflop. What happens if you're getting better preflop odds is that the Villain's range just gets tighter so that the EV of the bottom of your preflop defending range goes to 0.
However, if ranges are dynamic so that both players can outdraw each other on future streets, then you don't just defend at 1-A on both street. When you're getting better preflop odds, then your range is going to get much wider preflop. And the wider your range gets preflop, the more likely that your opponent's range will have decent equity postflop to the point that it would be incorrect for you to defend at 1-A because you wouldn't reach an equilibrium because his bluffs postflop will always be higher as a check if you're defending at 1-A.
You can solve this sort of question by setting up a 2 street game.
If villain is checking all of his bluffs on the flop because it is higher EV to do so, then wouldnt Hero defend less Vs cbets because villains range is so value heavy. Also leaving Villains turn range innately weak and prone to 'stabs' that he cannot defend against, due to having too many air hands in his range. Therefore all of villains bluffing hands on the flop that check back are no longer higher EV to check flop because villains range will have to fold extremely frequently on the turn Vs hero's turn stabs.
I feel like I understand you point, but also feel like I may be getting confused somewhere along the line.......???
To be honest, I don't think the premise of your question is correct that you don't have to defend as much preflop.
The premise of my question is about defending less than 1 - A. Defending at 1- A seems to be a necessary but not sufficient condition to keep Villain from making money.
increase on future streets and the bottom of his range is 0%, then
you're going to need to defend pretty close to 1-A on both streets
preflop regardless if you're getting better odds preflop. What happens
if you're getting better preflop odds is that the Villain's range just
gets tighter so that the EV of the bottom of your preflop defending
range goes to 0.
That's interesting. Theoretically, you would actually min-raise the button with a tighter range than you would to 3X it?
However, if ranges are dynamic so that both players can outdraw each
other on future streets, then you don't just defend at 1-A on both
street. When you're getting better preflop odds, then your range is
going to get much wider preflop. And the wider your range gets preflop,
the more likely that your opponent's range will have decent equity
postflop to the point that it would be incorrect for you to defend at
1-A because you wouldn't reach an equilibrium because his bluffs
postflop will always be higher as a check if you're defending at 1-A.
So I guess the mistake I made was assuming that Villain being able to cbet any two profitably should mean that they should cbet any two (instead of checking lots of hands)?
@Rugularblue
You're thinking in terms of exploitative play, whereas my analysis was talking about GTO play which is about finding an equilifrium.
@ AF3
"The premise of my question is about defending less than 1 - A. Defending at 1- A seems to be a necessary but not sufficient condition to keep Villain from making money."
Defending at 1-A is a necessary condition to keep the opponent from "making money" assuming that the Villain shouldn't be able to "open" any two cards profitably. However, if you defend more than 1-A preflop than you can fold more than 1-A postflop without the Villain being able to open any two cards profitably. But it's important to remember that our goal isn't to defend enough that the opponent can't open any two cards profitably, but to defend exactly enough that we reach an equilibrium.
That's interesting. Theoretically, you would actually min-raise the button with a tighter range than you would to 3X it?
No. Because when you open the button ranges aren't static and you also have position and the blinds already have money invested. A better example, would be to set up a two street example where you're oop and the button is the only person that needs to defend and then a counter example where the button has already invested money like a straddle. It's important to isolate concepts and not construe or mix things.
"So I guess the mistake I made was assuming that Villain being able to cbet any two profitably should mean that they should cbet any two (instead of checking lots of hands)?"
yes. this is a basic concept of EV. EV works backward to the previous streets. just because the Villain can bet any two cards on the flop, doesn't mean he can open any two cards preflop. And ultimately equilibrium needs to work back to preflop.
But it's important to remember that our goal isn't to defend enough that
the opponent can't open any two cards profitably, but to defend exactly
enough that we reach an equilibrium.
I see what you're saying about certain parts of the game tree being inherently favorable towards a certain player over the other (and having a positive value for the favored player), but I don't see how reaching equilibrium pre-flop is any different than neutralizing the worst hand in an opening range. I say this because:
If we reach equilibrium, then by definition, there should be a hand (or range of hands) which Villain is indifferent to opening or folding pre-flop. For any position except the Small Blind, this would imply that Villain is not able to profitably open these hands, since folding is 0EV.
yes. this is a basic concept of EV. EV works backward to the previous
streets. just because the Villain can bet any two cards on the flop,
doesn't mean he can open any two cards preflop. And ultimately
equilibrium needs to work back to preflop.
I certainly agree with this, I'm just trying to understand why we're able to defend less than we "should" without ceding extra BB's to the Villain. I think I just figured it out, though.
I think its good you started this thread because it will probably bring forth some good discussion, but fwiw a lot of this was already talked about quite a bit here...
http://www.runitonce.com/nlhe/theory-question-in-three-bet-pots/
"If you open shove pre-flop, then I defend appropriately. If you
min-raise pre-flop, then I defend appropriately. Either way, you should
have the same overall expectation from sitting down to play against me,
no matter which raise size you choose. "
no...and not close.
So you're saying the first part of the statement is true but the second part is false, right?
"For example, if you receive odds of over 100 to 1 pre-flop, then you can
call with any two suited and technically you can fold whenever you
don't hit a flush, but still "make money" overall. "
yes, so you can conclude that calling > folding in this spot even if you only flush-mine. In particular EV(call and flush mine) > EV(fold)
"I don't see how Villain isn't increasing their overall expectation by
min-raising and then cbetting any two if you're folding the flop so
often (you're defending much less than 1-A). "
In your above example, villain's overall expectation decreases when we move from "fold" to "call and flush mine". But it would (almost certainly) further decrease if we moved from "call and flush mine" to "call and two pair+ mine" or "call and top pair+ mine" or etc. The price we're getting preflop has some effect on this minimum threshold of flops we need to be able to profitably defend before EV(call and defend less than 1-A) > EV(fold). e.g. if we're getting 2:1 preflop then call and flush mine will not be a better strategy than fold pf.
The price we're getting preflop has some effect on this minimum
threshold of flops we need to be able to profitably defend before
EV(call and defend less than 1-A) > EV(fold). e.g. if we're getting
2:1 preflop then call and flush mine will not be a better strategy than
fold pf.
Right. On a related note, I'm also trying to figure this out (how much we can pin down the exact relationship).
Getting great odds pf allows to call with more speculative hands that can also completely whiff the flop without even high card value. Therefore we are not required to have a minimum defense frequency really right. I think we give villain the benefit of the doubt and don't try to defend a very weak hand op with no equity
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