Hand Ranges

I'm just going to take this hand and tried to explain some theories behind hand ranges and possible optimal plays. Also, I want to explain how to make good profitable decisions based on hand ranges. Understanding the Bayes' theorem of probability is pretty important to make good profitable decisions.

This hand history is borrowed from a buddy of mine. I actually don't know the details of the hand, so I'll make some assumptions and I'll try to branch off thoughts as it comes up. We'll see how this goes.


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I'm going to split this hand into 2 scenarios: A and B

Scenario A:
Hero and Villain are completely unknown to each other. No history, no table dynamics, no read.

Scenario B:
Hero is very loose on the table, he's been caught a couple bluffs and playing very aggressive. Villain is similar to Scenario B. Villain might be tilted or fed up with Hero.

PokerStars No-Limit Hold'em, $2 BB (6 handed) Poker Stars Converter Tool from http://www.flopturnriver.comFlopTurnRiver.com (Format: Plain Text)

SB ($87.60)
BB ($355.80)
UTG ($54.40)
MP ($414.25)
Hero ($369.40)
Button ($232.30)

Preflop: Hero is CO with 3s, As.
UTG calls $2, MP calls $2, Hero raises to $11, Button raises to $20, 2 folds, UTG folds, MP folds, Hero calls $9.

A:
Since there are a lot of unknowns, we need to work around them and make some assumptions. Hero does not know villain so he has to respect Button's min3bet but it's unlikely hero will fold to a min3bet. As hero, you have respect villain's range as probably AK, QQ+. This range can be tighter or looser, but I'm just making a pretty "safe" estimate.


Hands Breakdowns:
AK - 12 possible combinations of hands(AcKc, AcKh, AcKs, AcKd, AhKc, AhKs, AhKd, AhKh, AdKc, AdKh, AdKs, AdKd[there are no AsKx because you hold As])
QQ - 6 hands
KK - 6 hands
AA - 3 hands(again you hold one ace)

So far, Hero is basically ~30% equity against 24 hands and ~15% equity against 3 hands. We can safely assume without doing any further calculations that we are most likely a little less than 30% equity. The probability that you run into AA is much lower than you run into those other hands.


B:
Hero's image is terrible. Villain's minraise could mean a huge range. Let's try to break it down a little. Villain's min3bet range is close to the following: AJs+, AQo+, TT+, KQs. I believe this is pretty fair, it could definitely be even looser than this but let's work with this estimation for now.


Hands Breakdown:
AJs - 3 hands(only 4 suited AJ in the deck, you hold one ace)
AQ - 12 hands
AK - 12 hands
KQs - 4 hands
TT to KK - 24 hands
AA - 3 hands

Again, not much change in equity pf as compared to scenario A. Almost all hands have similar equity against Hero's hand with exception to AA. We have 30% chance of holding the best hand at showdown against that range of hands.

Flop: ($47) 4s, 9d, Ah (2 players)
Hero checks, Button bets $32, Hero calls $32.

A:
The flop is seemingly good for Hero. We don't know anything about villain, villain could do one of two things: 1.) selectively check behind or bet based on his individual holdings. 2.) cbet with his whole range.

Since we don't know villain at all, we can just c/f against his range or c/c once and play poker. Let's look at the decision based on the pf ranges:

Hands that we are way behind(~15% equity):
AK - 8 hands(since the flop has an ace, we take away some combos of hands)
AA - 1 hands
total: 9 hands

Hands that we are way ahead(~90% equity):
QQ - 6 hands
KK - 6 hands
total: 12 hands

So if we have information to believe that villain will cbet his whole range. We are looking at a little over 50% of villain's range that we are ahead and a little under ~50% we are behind to. Since both equities are pretty much equal(9:1 vs 1.5:8.5), we can expect that we have roughly 50% pot equity. Again, this is with the assumption that villain cbets with his ENTIRE range. It would pretty much be correct to at least give the flop a call.

If villain only cbets with hands that beats us(occasionally he'll slow play his strongest), without doing more calculations, we can assume that calling the flop would be a big mistake. But keep in mind that it is very possible that villain will check behind all his "hit" hands and cbet all the vulnerable hands. In that case, it would be again a huge mistake to just fold the flop. So Hero's line is indecisive due to his lack of information. Notice how our decision changes based on information we know about villain.


B:
Since hero is such a loose player, and villain is probably fed up with hero, villain is probably going to cbet almost his whole range. Villain can definitely decide to slow play his strongest hands but let's not factor that in for simplicity sake.


Hands that we are behind:
AJs - 2 hands
AQ - 8 hands
AK - 8 hands
AA - 1 hands
total: 19 hands

Hands that we are ahead:
KQs - 4 hands
TT to KK - 24 hands
total: 28 hands

We can see that Hero beats more hands than lose to if villain cbets his whole range. If our past assumption is correct, then at least calling would be pretty favorable. Raising is a possibility but villain might possibly fold the hands we are ahead of. It might not be a bad play based on our image, but the board is probably too dry to represent any type of draw to get called by worse.

Turn: ($111) 9h (2 players)
Hero checks, Button bets $90, Hero raises to $317.4, Button calls $90.30 (All-In).

A:
Turn gets interesting. The assumption is that villain probably stop bluffing his QQ-KK hands because they have showdown value. So the assumption here is that villain's betting range is almost always a complete bluff or a hand that beats hero.

We don't believe that villain would turn his QQ-KK into complete bluffs, so hero's pot equity is very close to drawing dead. The best choice is to just fold. Also, we do not know what villain's bluffing frequency is. Villain could be bluffing here all the time or none of the time. But logically the best choice is to fold here based on the lack of reads. Keep in mind that villain's range had changed once he made a further action on the turn. This resulted in allowing hero to make a better decision.

B:
For this scenario, this actually gets a little tricky. Villain could be tilted based on hero's past crazy plays. Villain could easily be not looking to fold any of his middle pairs, therefore he wants to keep betting. Villain only had 90 behind after betting 90. If villain is still betting with that same range on the turn as with the flop. It is correct to get the rest of the money in because hero has over 50% pot equity. The optimal decision for hero is based on villain's turn bet range. If villain's range consists of more hands that dominates hero, then hero's play should be to fold. Let's evaluate this thought with actual hand ranges.

Let's assume that villain's betting range on the turn only consists of QQ+, AJs, AQ+. Villain decided that he didn't like TT-JJ that much, and only get his money in with a tighter range.

Hands that hero is ahead:
QQ - 6 hands
KK - 6 hands
total: 12 hands

Hands that hero is behind:
AJs - 2 hands
AQ - 8 hands
AK - 8 hands
AA - 1 hand
total: 19 hands

Our equity are very similar when hero is ahead and villain is ahead, and there are more hands that beat hero's holding. It is actually a close decision to put $180 to win a pot of 291. Basically we can assess that villain leaving 90 behind after betting 90 is essentially an overshove of 180 into a pot of 111. Hero would need to be correct ~40% of the time, which is very close to his equity on the pot against that range. So getting this hand in on the turn is very close to neutral ev.

If we change the range back to the original range. Villain is terrible and tilted. He decided that he's not folding ANY of his hands to hero(same range as pf).

Hands that hero is behind:
AJs - 2 hands
AQ - 8 hands
AK - 8 hands
AA - 1 hands
total: 19 hands

Hands that hero is ahead:
KQs - 4 hands
TT to KK - 24 hands
total: 28 hands

Now it is obvious in this case that we will be correct over 50% of the time, if we have an infinite stack size, we should stick it in as long as villain is willing to call it off.

River: ($471.60) Td (2 players, 1 all-in)

Final Pot: $471.60

Results below:
Hero has 3s As (two pair, aces and nines).
Button has Kd Ks (two pair, kings and nines).
Outcome: Hero wins $608.70.

I don't know if Hero played this hand correctly or not due to lack of information given. I hope I tried to explain that hand ranges can drastically change what would be the optimal line. Brian Townsend had explain once in his article. While facing a PSB on a particular street, if your equity is 33%-49%, you should be calling. If your equity is >50%, you should be raising. And if <33%, you should be folding.

If people like these, I might do another one with bluffing frequencies and with a villain with a much wider range. I hope this was informative.

I'm a big Wussie!

As a poker player, it is imperative that you make your decisions based on "logic" and not by "feel". Some people will say that their "gut" feeling always serves them well, what am I talking about? Well, surely, feelings are created to protect you. It's built from your past events and are re-enforced as there are more samples of favorable results.

Actually there is a famous 2+2 post written about development as a poker player. (I'll post it if someone can find it.) Basically it's about the development of a successful poker player. He talked about players being more of a "feel" player or a "logical" player. I personally think someone would have to be extremely lucky to build the perfect "feel" and still be correct in most spots. Most winning players are definitely logical players like myself. But by nature, I'm a very emotional person. I rely on feelings more than a lot of other guys. Actually in the past, someone who I respected greatly told me that I should become an artist because that would maximize the type of person that I am. Well that point is unimportant, but I'm naturally a very passive and non-confrontational person. Jman described in his well post about his personality and it is very similar to myself. The reason I rarely tilt is probably because I usually don't let little things bother me, and I tend to see the brighter side of things. So it's ironic that I am required to be aggressive to be successful in the game.

Constantly during a session, my feelings definitely kick in. For most part, I'm not as conscious about it as much as I would like to be. Maybe I got 3bet from an overaggressive player and I "feel" that he could have a better hand that time. So I prefer to let go of my decent hand and wait for another spot. In the state of the 2/4 games and with the good aggro regulars, you almost cannot completely just avoid them. You are giving them way too much long term edge. I find myself needing to go against my feelings very often. Sure, logic can be wrong and feelings can be right. But if I can logically understand why I'm doing this and it has good sound reasonings behind it, I need to go against those feelings. They can definitely become a distraction.

Frequently, it is way too easy to see a profitable spot and go "oh he might have a huge hand here this time, maybe next time.." or "oh I can't fire a barrel here, he might just call me down with ace high". In those scenarios, I should really assess like the following: "CO opener is a LAG and button's 3bet by an aggro TAG. If I 4bet here, I should get a lot of respect and I think both players cannot think I'm bluffing here very often" or in the second scenario, "I haven't been out of line against this villain. He's kind of tight. I've been giving up a lot of turns and he should respect my barrel on this scare card, his range is also not going to hit this very often". In the end, this is just all about getting away from standard ABC and think about each situation as a unique sample. It is important to fight certain feelings and make the most profitable plays.