Another interesting concept in equities

FIXED limit holdem here. Example taken from Small Stakes Hold'em by Miller/Sklansky/Malmuth.

Assume everyone in the hand is very loose (%50vpip+), and somewhat aggressive.

Action goes:
Limp
Limp
Limp
Limp
Hero raises with A♦A♣
SB folds
BB calls
All limpers call

Flop comes 9♣7♣3♠ (pot is now 12.5 small bets)

Big blind bets
First limper raises
and all but one of the remaining limpers call.
Hero ...

Now how does this change if we have 10♦10♥ for example?

This is a pretty interesting concept, and is one I don't really know how to apply very well myself yet.

You should be more a little more aggressive with AA here than with 10 10, but I don't think it really makes too much of a difference. Say someone has K 4 suited in clubs. Against 10 10 they have 12 outs but against AA they only have 9 outs.

How about this:

What are our equities on the flop vs typical loose-peeling, draw-chasing opponents with AA and TT respectively?

How do they change on the turn depending on what cards come?

BIG difference.
The "ace of trump" makes it less likely there is a flush draw in the first place, and gives us a re-draw as well...
Also there are no overcards to our aces, unlike w TT, where we are not actually "ahead" of KQc as far as equity in the pot.

But say someone has K9 or Q9. Just one pair. If he has this it doesn't matter if we have the AA or 10 10, if he makes trips or two pair on the turn he'll be beating us. Same with an open ended straight draw, doesn't really matter if we have 10 10 or AA. And if we are already beaten by, say a set or two pair, then we still have the same number of outs (two) with both hands. And a King high flush draw or a Q high flush draw are still possible. But there are a few situations where it matters, like if there's a lot of preflop raising and you suspect someone may have JJ QQ or KK, then we can feel a lot more comfortable with AA. But in this case it looks like no one has KK QQ or JJ.

I see what you mean ben where aa is protected vs overcards, but pock tens reduce the odds of a straight draw being hit, so the question is, it it more likely calls that flop with a draw or overs.

According to Pokerstove we're about 45% to win with AA and 28% to win with 1010 here. I don't really understand where you are going with this one Chuck. Care to enlighten us?

The 10s are much more vulnerable to turn cards, so they should be raised for protection. This is not (so much) the case with the aces.

Edit: they could be raised, is what I meant. Which line works best (raising now or on the turn) with the respective hands depends a bit on the tendencies of the other players. If we can get anyone to fold by raising on the flop, doing so with the tens is much more important than with the aces. If no one will fold the flop, ever, raising the flop with the aces is OK.

Basically, with tens, we want to get rid of people, with the aces we want to pump it for value. If they will fold the flop to a 3-bet, do it with the tens. If they will just call anyway, do it with the aces.

The concept is alluding to larger and smaller equities, and how we should be betting much more aggressively when we have a clearly bigger edge than if we have a smaller edge.

For this example say we have %40 equity with the aces. 5-way we only need %20 equity to break even, so anything significantly above that calls for bets and raises since we want to build the pot.

Now with the tens, we apparently only have around %25 equity here, so we should wait until the turn to raise - when our equity could jump tremendously in either direction depending on the card.

The concept is basically that building the pot when you have a small equity edge isn't nearly as important as when you have a big one.

Thoughts?

The concept makes sense but how does it balance against a raise to protect a potentially vulnerable holding. For instance in the example of 10's or Q's when one raises a lot to push out over cards that could possibly draw out on us. In that case the pot isn't being raised for the same reason as when one is holding A's and we want as much in the middle as possible due.

Not exactly sure what you mean, Steve. That's why we're raising - to both build the pot because we have an equity edge, and also to protect that edge.

You are saying for us to wait to raise in the turn when the equity increases, but due to the vulnerability of 10's a common play is to make a raise right now on the flop to prevent ever having to get to the turn card or to make the other player make a pot odds mistake to call correct.

I am saying that the two plays seem to be contradicting themselves.

Here are my thoughts on this. First of all limit vs. no limit is a very important difference, but the concepts still stay the same. In NL we would be making differently sized bets here but if we have positive equity (basically if our equity is at greater than or equal to our share of the bets ie 5-handed we need >= 20%) we should bet. The big problem with TT here though is not knowing where we stand. When a J comes on the turn, how do we know if we're beat here? Although equity is a big part of this problem another is knowing if we're ahead. Even if on average here we have a certain equity, that means nothing if we don't know when that over card hits our opponent and when it doesn't.

Now if it's 5-handed as in the example, we probably have positive expectation with TT for an overcard not to come. Of course now we have to worry about being behind due to sets, 2-pairs, etc. I haven't played much limit at all and really don't understand the strategies of when to bet/raise/fold, but that's my 2 cents fwiw.

If by raising you can get everyone else to fold, then raising the flop is definitely the way to go.

I made my post a complete mess, misread the original hand, and didn't really make myself very clear, either, so let me take a stab at it again:

We have two different objectives in this hand:

1. Build the pot.
2. Win the hand.

We win the hand most often by pushing others out of the pot. We build the largest pot by keeping the most people in.

With aces, we don't care much about what comes on the turn. Sure, there's a risk that someone hits two-pair or picks up a strong draw, but our plan for the rest of the hand isn't going to change much.

With tens, however, we're pretty nervous about the turn. A paint card is going to look very ugly for us, and an ace especially. If we can eliminate a few of the players by raising the flop, we're much safer going to the turn. If no one will fold - and I believe SSHE presumes that no one will - then raising the flop is little more than tossing even money into the pot.

This is what I misread in the original hand; I thought the action had made it possible for us to 3-bet and face a large portion of the field with a raise and a reraise. Apparently it's just one more for everyone to call. At that point, raising with tens is mostly pointless.