So i understand we do protection bets/raises on earlier streets to deny equity/won't let villain realize his equity (free turn/river cards) when villain has a wide range of trashy hands that likely won't put in any more money later in the hand (such as villain will just x to the river).

Versus a narrower range that don't contain as many trashy hands that have good equity vs our vulnerable hands (like villain has K6s on T22r and we have 44) we don't need to be concerned about protection that much?

So protection bets/raises only work if villain is going to fold x% of the time in regards to our bet sizing similar to bluffing.

Ex:
Like if pot is 15, and villain bets 10 and we raise to 30 w/hand that wants protection, we risk 30/55 therefore villain has to fold 55% of his range and if he isn't folding 55% of his range it's just going to be a -EV raise. But say villain is folding 50% of his range then we can just raise to a smaller amount for protection like 25, so 25/50 which means our raise will at least be +EV.

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So my main question is when to have calling ranges/raising ranges on earlier streets, if we know how villain will deviate/play on later streets like have a high turn + river betting frequency in terms of over-bluffing etc.

Ex:
Say we are OTF and face a bet from villain, and know villain x back turn frequently and x back rivers a lot, we x-raise flop more often.

But now say villain will still x back turn frequently, but when xed to OTR villain will have a high river betting frequency, do we want to be calling more or raising more OTF for protection instead?

I haven't gone through the exact maths for the example you've given here but personally I don't usually deviate my strategy too drastically for protection like I do playing PLO. This may well be a leak so feel free to correct me.

My general opinion is that normally the EV you lose from deviating from your standard line will be less than the EV you gain from betting for protection. Yes reraising on certain flops (eg. T22) may be +EV but in these spots I find bluffcatching multiple streets plays out to a higher EV with the middle of my range (eg. small pocket pairs), even if it allows villain to realise equity. Two overcards on a flop only have what like 22-28% equity vs a pair anyway and denying that equity won't make up the EV lost from every time you're called by better or every time you fold out worse than can keep barreling. Also I think if you're called in that spot you can be put into really difficult situations where your hand is weirdly overrepped and you're then just looking to get to showdown with two more streets to come.

In terms of balance, I think I obviously value bet wider in spots where I'm going to have more bluffs (eg. on 8h6h3s from the BB vs UTG I think you can make the case for checkraising any pair for value/protection due to the you will have so many draws as bluffs to balance your range and you have the range vs range advantage). On less co-ordianted boards though like T22, I play fairly conventional.

Again no expert on the maths here though so would be interested to hear some other responses

This doesn't seem right to me depending on what equity level you are classifying as trashy. If villain has low enough equity he won't call bets I typically wouldn't bet in the hopes villain will bluff.

The way I like to think about it is betting to deny equity is like purchasing the equity. I want the price I pay (my bet) to be less than the equity I buy as much as possible. On the other end it doesn't make a whole lot of sense when we already own a significant amount of the pot to buy the small amount remaining with a bet larger than the equity we purchase but at that point we would just prefer villain put more money in the pot because of our equity advantage.

The purchasing equity idea obviously isn't a perfect abstraction about how to think about it because for one thing if we stand to showdown a high percentage of the time where we can "realize our equity" so to speak then we may prefer villain to call and we would win a portion of a larger pot as opposed to more frequently winning the rest of the pot. It's a balancing act between how often we can win the whole pot and how much equity we're folding out during those times villain folds and the proportion of the pot we win and the size of the pot
at showdown.

This to me illustrates the perfect example or where we WOULD want to bet to protect our equity. K6s has roughly 27% equity here and buying out that equity with something like 44 is great because 44 may be harder to take to showdown on a lot of runouts.

This is only valid for hands that have NO equity which is not the hands you are talking about in the OP.


This seems backwards to me. If I know villain is going to allow me to get to showdown it would make more sense to try to showdown than vs an opponent that makes things more difficult for me if I open betting.


Making streets easier to play can be alright if for example you're against competition that has an edge vs you on later streets but in general your goal is to make the most +EV decision given the information available to you and not just make decisions easy for yourself.