This post is a continuation of my previous post, based on some of the info I have gathered on constructing balanced ranges. I recommend everyone check out spadez01 thread called "Value to Bluff Ratio," which has some extremely valuable info regarding this topic.

https://forumserver.twoplustwo.com/1...ratio-1713833/

This question is based on ArtyMcFlys posts in this thread and my previous thread:

QUOTE

"As I said in an earlier post (and many other posts in this forum), I'm not a great believer in using ratios and frequencies on the early streets. If you pick a "balanced" range of hands that will have solid equity on most runouts, you'll be able to barrel at a decent frequency (whatever "decent" means, there really isn't a precise number) and won't end up having to check the turn and then fold the river too often. i.e. Some people c-bet way too often on boards where they shouldn't be c-betting a lot, and then their turn/river range is in bad shape vs the range that called on the flop.

Literally every flop and board runout has a different solution, so even if the terms "value" and "bluff" were clear, it would be wrong to say anything like "have a ratio of 1:2 on the flop and 1:1 on the turn". Some of your strong hands become weak on the turn, and some of your unmade hands on the flop become the nuts on the turn. A 'good' c-betting range is one in which you've always got "enough" combos of the nuts on every possible runout, and every action sequence. It's why it's appropriate to bet some/most of your draws, but also check back with some. (e.g. you want to be able to turn a monster even if you check back the flop). I can't give you a precise number, because it's different in every spot. Sometimes your range does best by betting loads of unmade hands, including hands that have no draw at all, and sometimes it does best by hardly bluffing at all. You can only get to grips with it all by studying/analysing hundreds of spots. You'll find some trends/similarities between some textures, but you won't find strict ratios or frequencies.

P.S. As an example of what I mean, that is somewhat relevant to your other questions, imagine that you check-raise (in the BB vs BTN) on something like 8h 6h 5c. If the turn comes a heart (completing the flush), your flush draws are now "nuts", but your sets and 2 pairs nosedived in value, and your straight draws could be drawing dead. The strategy for what to do on the turn will be radically different if it's a heart, an ace, a nine, a card that pairs the board, or an offsuit deuce. You just want to build a "good" flop check-raising range so that you'll be able to keep barreling "fairly often" (whatever that means) on all possible turns. Sometimes the turn will just be a terrible card for your range. In that case, you might have to check-fold at an annoyingly high frequency, but the correct strategy for the flop will be the one that maximises EV on average. You can't use a strict ratio/frequency, because you don't know what the turn card will actually be!"

QUOTE 2

"By the time the river comes, ranges will be narrower (you'll have folded your air, and villain will give up with some of his bluffs, for example) and at that point, the continuance frequencies will usually be much closer to the MDF numbers*. That said, sometimes the river card is so "ugly" for one player's range that he still has to check back or check-fold at a very high frequency."

END QUOTE

This will be a redundant question but I want to make sure I understand.

My question is this: on the flop/turn should range construction be primarily based on board texture, position-texture implications, possible run-outs (as mentioned above), and then on the river tailored to be mathematically balanced?

For example hero is OOP and goes heads up to the flop, the flop connects favorably with his range, hero picks some made-hands, drawing-hands, and a few blocking-hands to continue with, the turn completes many draws, on the river hero decides to make a pot sized shove, so he chooses to continue with a value-bluff ratio of 66% - 33%. Hero did not decide to factor in the math until the last street, is he correct in doing so?

There's always maths underlying every decision, but it's EV maths, not MDF maths. When you continue past the flop and turn, it's because you have a hand that should be +EV against the perceived range, given the probability of each possible runout.
When you get to the river, some of your hands will maximise their EV by betting for value, and some will maximise their EV by bluffing. Often it will happen almost by accident that your max EV pot-betting river range will be balanced 2:1, but more commonly you'll actually pick a smaller size, or (less frequently) an overbet jam, and your ratios will be somewhat different. Sometimes the river card is so bad for the range you were betting with that you have to check-fold at a high frequency. There really isn't a strict rule for how many v-bets or bluffs you have on each street, but you want to aim to have "enough" value hands on the river, so that you can either bet for value (and get away with bluffing at a "decent" frequency), or so you can call with a bluffcatcher and make money that way.
I'll repeat what I've said in a couple of other threads. The aim of the game is not to be balanced on the river. The aim of the game is to maximise your profit. Sometimes this means you bluff at lot early on and win the pot without a showdown, sometimes it means you make a lot of small bets for thin value, hoping villain calls, sometimes you want to build a big pot planning to jam the river with total air (if you expect villain to fold quite often). Every pot/runout is an individual occurrence. Each one has its own solution.

As an example of how the river can "break" your strategy, imagine you are betting overpairs for value on 9xxx and you think villain is calling down mostly with a 9. If the river is a 9, then suddenly his "bluffcatchers" become monsters, and your overpairs no longer have as much value. It's really hard to bet with a 2:1 v:b ratio if you have hardly anything on the (horrible) river that can get called by worse. A similar "bad event" happens when the board makes loads of straights and flushes, and villain's range contained a lot more draws than yours. Your overall strategy has to take into account these rare "bad events", but since they are quite rare, the strategy for the majority of boards can still be sound, even though it sometimes breaks. In short, don't go looking for a perfect/optimal mathematical strat that works for every spot, because there isn't one. Just try and build strategies that work most of the time and win most of the money. Poker is hard.

This is excellent, thank you for explaining this in detail.

All variables stated above will have influence on our strategy. Some variables will have more influence than others.

I believe that ArtyMcFlys quote is basically not exact. But it right at the same time, it is just not phrased properly.

First, let me say that the 'minimum defense of the pot' is what the game is about. That's because you need to defend the pot that poker exists in the first place. If there is no pot to defend, you just play As.

Now how does that work. For every street including preflop, before the cards are dealt, you can compute mathematically what your frequency must be exclusively by taking into account the number of players still in the hand. The key is before the cards are dealt.

So preflop, before you are given any card, you can determine that you need to defend x% of the time. Now the card are dealt and they dictate your action on that street.

Let's jump to the turn now. On the turn, before the turn card is dealt and that's the confusing part because before the card is dealt it feels like the flop but it isnt, you need to know your frequencies and ratios, and once the turn card is dealt, it dictates your action.

Let's take an example. Say the flop comes 8d5h3h. Now on the turn, before the turn card is dealt, you can calculate that you need to defend 50% of the time for example. And so what you do is that you determine the turn cards which you will defend and the turn card you will not defend given your range here (your range preflop is always 100% if you follow me because it's before the cards are dealt. Before the preflop is dealt, you show up with a range of 100%).
Since you need to defend 50% of your range on the turn on the given example, you can for example determine that if it's Ah through Th, you don't defend, any other heart you defend.

What that says basically is that on a board like 8d5h3hAhKh, you will maybe have 1% of your hands left on the showdown and that's ok, you still have defended 60%/60%/60% on flop, turn and river. It doesn't matter that you fold most of your range on a river Kh here because that's the point: you would do that only on a Kh.

The percentage of your range you must defend is determined on a particular street before the cards are dealt and the cards dealt now determine your action. So just as a conclusion, I'll resume every streets. Preflop, you start with a range of 100% and you know you need to continue with say 20% of them. Your preflop cards are dealt. You continue 20% of the time. Before the flop is dealt, you show up with a range of 20%. You know that you need to defend 60% of that 20%. So you determine the flops you continue with, and the flops you dont continue with. On the turn, you show up with a range of 20%*60% and you need to defend 60% of the time. So given the turn card, you can determine if you continue or not. Same on the river, you know you need to defend 60% of your river and you show up with 20%*60%*60%, and then according to the river card you continue or not. Showdown.

That's what ArtyMcFlys basically said but phrased correctly I believe.

Let me clarify something here. If someone raised, of course the pot is different and then you can compute what your new MDP frequency must be.

Sorry I've messed up this part. Your frequency should be determined by the pot odds.

Funny that the number of players reminding in the hand should affect your frequency but I can't remember having read anything about that.

Anyway, the whole point being, you don't "should be able to continue x% of the time whatever is the turn card". Instead, you determine what are the x% turn cards that you continue with.