I'm struggling with the connection between fold equity, hand equity and betting frequency.
Example; given a preflop open-raise situation:

Our betting size is 3BB
We can win 1,5BB
=> Villain needs to fold 67% for our open-raise to show immediate profit.
We can thus conclude that, when villain folds 67% or more, it is profitable for us to open-raise 100% of our hands, right?

When villain folds less than 67%, and open-raising 100% doesn't show immediate profit, should we forget about fold-equity when constructing our ranges and only look at hand equity vs. his calling/3-betting range? Or should we construct a range based on hand equity vs villain's calling/3-betting range and then 'add a little' because of the extra fold equity we have?

Thanks,

Teski

Construct a range that plays well against the hands that call. It's not just raw equity that counts, but how a hand plays over multiple streets. (A term that is often used is a hand's ability to realize equity). For example, I don't open A2o on the button by default (it's literally impossible for villain to call with anything I dominate, unless he calls with K2s, Q2s), because it realizes equity badly (it rarely gets called by worse if I bet multiple streets for "value"), but I'll open 96s, 64s, 53s etc, since these can bet multiple streets when they flop a draw or 2pr+.
If you're relatively new, opening something like 35-40% on the button should be good. You can tighten or loosen your range once you get a better feel (or stats) for how the players in the blinds react. e.g. If they often 3-bet, then don't open trash like K5o or T5s. If they are nits, then more of your EV comes from pre-flop fold equity, so you can steal with some trash hands that you'll rarely even c-bet. (If a nit defends the BB, then his range will be stronger than an average player's, so the last thing you want to do is keep putting money in the pot with air. When a looser player calls, you'll often need to fire two barrels to get him off 2nd pair or a draw, so hands that flop straight/flush draws are ideal for that).

This is a test of the duplicate thread warning system .. This is only a test .... to see if we give the same answers as received in the other thread ...

https://forumserver.twoplustwo.com/3...stion-1700447/

Unfortunately the other thread only got 1 post as well ... GL

How much narrower does the BB range become when you are offering 2 to 4.5 odds? BB needs to feel like he has 31% equity going to the Flop. That's not a lot of Fold Equity there. FE is more commonly 'offered' when you (over)bet Turn or River giving bad odds to call against what you think is a weak range .. even if/when they think they are ahead.

Hand Equity is what Art is talking about IMO, you want to 'steal' with hands that play 'better' if you do get called.

You should be aware of your B opening frequency since it will open you up to a BB playing back at you with some weaker 3-Bets in the long run, IMO. GL

What size do you open? If your opening 3x or less I'm fairly certain that is a default mistake against most online environments.

edit: any online environment I've played in at least

First for fold equity: Villains must fold 67%, unless you are on SB there are more villains and chance they all fold is hard to guess.

Your profit always comes both from FE, equity of your hand and playability of your hand.

There are hands like 98s suited with lower FE and rather lower equity but their playability makes it UTG open.

There are hands like AJo with lower playability but FE + equity makes it UTG open.

There are hands like A2o with low playability, average equity, but FE makes it BTN open (edit: talking about blocker, you see how massively our A blocks their continuation range).

I usually open for 2.5x and I don't think I'm missing out on much/any EV by folding. A3o is likely also a GTO button fold (and A7o is probably -EV in the CO) even in low rake environments like 2000NL. (There's a video somewhere of Negreanu analysing some 2kNL hands with holecards face up and when one of the endbosses folded A3o on the button, Dnegs thought it was a misclick, but it's actually a standard fold in tough games.)

It's possible that the weak offsuit aces are profitable for you as CO/BTN opens if you check with filters in your tracker (I didn't even win with ATo/A9o on the button last year, that's probably just variance), but I've always found ragged aces to be breakeven at best. Exploitatively (against blinds that fold too often), they should be profitable stealing hands, but they don't belong in a balanced opening range. You've already got millions of Ax combos for board coverage on Axx.

I often treat A2o-A5o as 4bet bluffs, and originally got the idea from PokerSnowie after it ran a huge bluff vs me deep and OOP BvB like 300 or 400 bb's deep. At first I just thought it was just a huge whale when I snapped off its river bluff shove with the pure nuts, and it showed me A4o which it 4bet from the sb vs me, and then went all aggrofish with postflop. But the more I thought about it the more I liked its play using blockers, etc.

FWIW, I also think A3o is probably a GTO fold at 3x+ RFI, I think at 2.5x it's really close. I'm kind of coming from an in-practice perspective. I bought some datamined hands awhile ago and compiled the stats of the winningest regs at my stake at that time (although the datamined hands were on a different site) and it showed stealing on the BTN wide (compared to say Snowie) was very profitable. Similar to you, my db shows A6o losing, but A2o winning, but I just assume that's variance/sample size issues. I do agree that opening a hand like A2o isn't printing or anything, and also that a hand like 64s will realize equity better, but I still think most micro to lowstakes online environments call for opening this wide.

People in these pools just aren't fighting for pots hard enough to not justify opening these offsuit aces. Maybe they defend their SB/BB at the right frequency, but most people are x/r OOP at pathetically low levels compared to solver recommendations, probing too little with way too much merge value and wayyyyyy too few bluffs on a lot of textures, overfolding to turn barrels, and delay cbet. All this stuff just makes me think you overrealize pretty significantly.