Saturday, December 6, 2008

Should Kings be Folded Preflop?

Given the action of one of the final hands of WNP’s action, the debate rages on about whether or not it is correct to ever fold Kings pre-flop. Ryan’s Kings vs. Martin’s Aces played out I believe as follows:

Mike limps, Woody limps, I limp, Martin limps from the late position, Ryan raises to 15, blinds fold, Mike calls, Woody calls, I call, Martin goes all in for about 700 +, Ryan calls for about 560 chips, everyone else folds.

Although there was some dead money in the pot, Martin’s bet size and Ryan’s decision on whether or not to call was close to a 1:1 decision, i.e. the pot was laying Ryan only sufficient odds to call if Ryan was convinced that he was in a coin flip or better decision. If Ryan believed he was in a better than a coin flip situation he should call, otherwise he should fold.

Though we have to use some assumptions and logic in this decision, mathematically, we can determine if Ryan’s decision was the correct decision in this situation, and if we change the player’s name from Martin to another player we can simply alter the likelihood of the nearly 3x buyin shove with a different distribution of the ranges of hands that the player might hold.

With nearly a 3x buyin shove, we can narrow the range down pretty tightly. Martin’s range, or for that matter any player’s range, is as follows:

Air: Martin may be on tilt, spaced out, needs to go home, or just feels like gambling. Martin has to my knowledge never demonstrated this type of behavior on a shove of this magnitude, but let’s say it is possible and extend the probability of an air hand at 2%. Let’s also at least narrow down “air” to a suited connector or 1 gapper, and say that true air has a near zero percent probability.

JJ or QQ Very unlikely at a nearly 700+ chip shove especially as I am in the hand (potentially) and I have Martin covered. Martin also has a history of set mining with big pair hands. Let’s extend the probability of Martin holding this type of hand at 4%, which I think is an overestimate but let’s go with it.

AK Again, very unlikely given the reason’s stated above. Let’s give AK a 4% likelihood.

KK Extremely unlikely, given that Ryan has 2 Kings in his hand. Let’s extend this possibility as statistically insignificant.

AA The only other logical hand. Let’s extend this possibility at 90% given that Martin is the player and given the set of circumstances surrounding this hand.

Ryan’s probability of winning this hand by calling Martin’s shove is as follows:

75% win rate against air hands @ 2% probability = .015
80% win rate against QQ and JJ hands @4% probability = .032
70% win rate against AK hands @ 4% probability = .028
20% win rate against AA hands @90% probability = .180


If the forecasted probabilities of the given hand ranges are accurate,
Ryan will win the hand approximately 25.5% of the time.

The tipping point as to whether to call or fold an all in shove with KK in a deep stacked hand (assuming one big shove vs. a raise re-raise situation) is determined by the likelihood of the villain holding a hand other than AA. Leaving air at 2% and assigning an equal probability to either having an underpair or AK, the decision will be a break even proposition at the following probabilities:

75% win rate against air hands @ 2% probability = .015
80% win rate against QQ and JJ hands @24% probability = .192
70% win rate against AK hands @ 24% probability = .192
20% win rate against AA hands @50% probability = .100

Win rate = .499

Replacing Martin with another villain, and assuming the pot is only laying you effectively 1:1 odds to call, the decision as to whether or not to call with KK is simply based upon the likelihood of the villain holding AA being greater than or less than 50%. If you believe that the villain’s likelihood of holding AA is greater than 50%, you should fold, if you believe it is less than 50% you should call.

To be fair to Ryan, he did point out that he had been raising a number or pots and that it was very unlikely that Martin put him on KK. At the time, I believed Ryan’s decision was a tough one that could have gone either way. With the benefit of a couple day’s rest and some analysis, I would be very surprised if anyone would say that the likelihood of Martin holding a hand other than AA was greater than 50%. Thus, the correct decision in this given set of circumstances was a fold with extra heroics if Ryan had been able to fold the KK hand face up for the table to see.

12 comments:

royalbacon said...

Interesting Jason-land reasoning, Jason. I wouldn’t expect anything less!

Now, I haven’t been at WNP in a while, so I may be a little rusty, but I would say – for me – there’s not ever going to be a situation where I fold kings pre-flop at WNP. There’s simply too many winning situations to too few losing situations. The “glory” factor of folding my kings to Martin’s apparent aces is so miniscule, cocentrating on that will only cause you to second-guess your own kings too often, and cause you to lose much more than you could win.

Please refer back to the hand where you folded your kings to my aggressively-bet 7s. You folded on the flop, or the turn, so that was a bit different. But I think the self-defeating logic still applies.

Are there other times where you’ve folded kings only to find out later that you’d made a mistake? I would tally up that total loss compared to what you would have won had you stayed in the hand. You’ll most likely find that it’s a losing proposition to fold kings pre-flop (or to convince yourself that you should have and then fold on the flop or turn).

jason said...

Stack size is the relevant factor here. I doubt you or anyone else is raising preflop with pocket 7's with 3x your buyin in front of you, all in after a limp, and someone having you covered with a history of limp reraising. Your raise with the 7's was to about 60 I believe.

The day I see Royal limping in with 7's and then raising to 700 with me in the hand and Ryan showing aggression to 15, is the day I may have to find another game where I have better intuition and hand reading abilities.

Your raise with 7's at the time was a very good one and my lay down was a poor one. But this situtation should be a laydown every time, unless you put someone on another possible non AA hand with a greater than 50% chance. This is possible because to some it will be "just 700 chips" but almost no one in the WNP crowd will be shoving in 3 buyins preflop with a non AA hand.

jason said...

My apology for leaving out one relevant fact. I had limped and I had a stack size of over 1000 chips having Martin well covered.

Sushi Cowboy said...

"...but almost no one in the WNP crowd will be shoving in 3 buyins preflop with a non AA hand."

I would even say that is unlikely that anyone else is shoving in 700 pre-flop to a raise of 15 with or without AA.

Sushi Cowboy said...

OK, here's the play by play from my chair. It is late in the session and I pick up Aces. I thought that I was an EP limper but Jason said that I was late and after he said that I vaguely recollect considering the risk of entering a pot with a bunch of limpers. But I was prepared to go in set mining with Aces and be ready to dump them to action. I felt that a standard raise would only collect a bunch of callers with the "-itis" in full effect at that hour. After seeing the waterfall after Ryan's raise I think that ended up being an accurate assessment. So once Ryan opens the door and gets that many callers I am ready to snap off all action with a shove. I am of course open to a caller as well since I am getting my money in good against all hands and even more so against the most likely hands to call me. Frankly toward the end of the night I get lazy and I don't want to have to make any hard decisions. I know that overvaluing AA is a hole in my game and I'm fine with winning a small pot instead of losing a big one. Yeah I know that I am giving up a lot of potential value by playing them as fast as I did but I'm fine with that under those circumstances.

Other factor #1 to consider, the week before I did the exact same maneuver with Aces. I collected a call from AJ which rivered trip Jacks to crack my Aces. But the setup was the same, an overbet re-raise with me going to 400. After the hands were tabled there was a comment to the effect that "he is ONLY doing that with Aces or Kings" which I corrected by saying that I'm doing that with Aces only.

Other factor #2, shortly before that hand I was in a big hand with Ryan. On a K8x flop with two diamonds I check raised him from 40 to 100. Ryan flat calls. Turn is a blank and I check to him, he bets 120 and I shove. Ryan asks for a card and I show him the 8d. He reluctantly folds his JK and I am pretty sure that he feels that he may have been bluffed.

Now for the analysis, I would say that players will always tend to their core style and even though I was Farha-ing it up that night, my range there is going to be extremely tight. Would I shove with JJ or QQ in that situation? I would say no, regardless of how I was playing earlier that night. I recall one time when I just took a bad beat and tried to make a steam looking raise with either KK or AA and Ryan didn't bite. He even commented at how I fade bad beats. I have also only half-jokingly said that Queens and lower are for set mining. I also play a very trapping style of offense which would favor the idea of limp/raising with AA more than trying to out-aggress other players. How often do I take down pots pre-flop, especially compared to Marsh?

But for the sake of argument, let's say that I wanted to try to steal the 60 in the pot by trying to elicit folds by everyone. I would say that a bet of 200 would do the same job as a bet of 700. But for giggles, let's say that I am out of my mind and want to steal the 60 in the pot with a shove. My range for a steal is going to be quite narrow, namely a middle suited connector because I see the most likely hand to call a shove is going to be a premium pair and I want to have the best odds to crack whatever hand is calling me. So *if* I am on a shove steal a caller is about 70% at best to win. Chances of me doing that with absolute air are vanishingly small.

How about AK? I think Jason underestimates the chances of me limp shoving with big slick. AKs would get somewhat more play than AKos and I would shove with both of them before I would shove with JJ or QQ.

And Cowboys? Possibly, but in this case since Ryan had KK it is pretty safe to assume that I don't hold KK also since that would be a roughly 1 in 7000 occurrence.

If I knew Ryan was as strong as KK then I think it would have been more effective to raise to something like 160 to make it look like I'm trying to steal the 60 in the pot. And since Ryan thought that I thought he was being overly aggressive I think he would have either shoved there since there is already >220 in the pot or raised me to 350 or something. If I re-raised him all in then I think he would have to call of the rest of his stack even if he thought I probably had Aces based on my shoving range and being roughly priced in to hit a set.

I in no way think that my play was optimal overall though I would also add that I don't think Ryan is stacking off in that hand if I follow many other lines. If I raise then he re-raises and the pot is too small for him to get all of his chips in since we were so deep. If we see a flop which I am pretty sure had a Q in it then he isn't beating anything that I raised pre-flop and still betting the flop with.

So should KK be folded pre-flop? In general I would say no. But if there ever was an occasion to fold them I think that this is one of them. At the very very least it is a high variance hand with 3 buy ins at risk. As Jason points out the pre-shove chips are relatively insignificant in regards to pot odds so it boils down to the range that someone puts me on. *I* know that I'm only doing that with Aces but it doesn't hurt me for other people to have my range considerably larger than that.

Marshall said...

Good stuff guys. After careful consideration I also came to the conclusion that a fold is right here basically every time.

When Ryan called I was all for the call, but after actually dissecting the play, it's a fold, and it's not really close IMO.

I don't think that for that much risk Martin is ever shoving non AA. I just don't see it. He has like 4(?) people behind him, including Ryan who had raised, and also including Jason, one of 2 people that have Marty's very considerable stack covered. These stacks were very deep, and Martin just won't put that much at risk with QQ and have someone get stubborn with AK or show up with KK.

Now I have seen Marty make some big ass snap-off type raises with big pairs like QQ-KK, and also AK. But this was not just a big snap-off bet, that's the difference. If Marty makes it 100, well then I can open his range up at least a bit to QQ-AA,AKs. I would still generally give him credit for AA, but I may have to call with KK, or just ship myself.

There was one other meta element, and that was that Ryan had recently lost a biggish pot to Marty as mentioned, and was blasting away preflop (with real hands mind you, but it looked like he was just steam-rolling). When he raises pre with KK, *he* is thinking that it looks like the 5th preflop raise in a row from a steamer. Which it sorta did. But one key thing to consider here, is that from Ryan's seat, that is not a big factor because it's Martin who is betting. If it were Jason or Jeh or whoever, they might have picked up on Ryan's constant betting and just decided to snap him off, but Martin will not take that kind of risk very often. Like he said, his style is to notice that you are steam-rolling, and instead wait on a hand and trap you.

royalbacon said...

I love all these comments, mainly because it shows that we’ve been playing together for so long, we can nail down with 99% certainty what somebody has when they're doing something like this.

What I can’t wait for, and will be sad to miss if I’m not there, is the next time Martin goes all-in pf with a huge stack in front of him. The conversation leading up to whoever his opponent is making a call, raising, or folding will be quite good.

Miss all you guys, in case you couldn’t tell. Looking forward to coming back to the game in February ’09. What is the state of the game? With Ryan moving on, and the state of Surreal itself in question, will the weekly game live on?

Marshall said...

We miss you too bro. Fo real.

The game will go on. As always, it is up to the people who play in it to carry it, meaning if people keep coming out then the game lives.

As it stands now, Ryan was the main one committing to stay to the end each time while at Surreal. As far as I know, Chuck, Joe or Brant would have to fill that role on any given week. Otherwise there are a few other things in the works, but in reality Surreal is a really good place to play and I hope we can keep playing there.

I have offered my place for the occasional WNP, but it's not all that well suited to bigger games. I feel confident that the game will soldier on, and I certainly hope it does as I look forward to it week after week.

Sushi Cowboy said...

Thanks to everyone for reinforcing the idea that I'm only doing this with Aces. I can't wait to see Jason lay down Kings when I overshove with 72os. Priceless.

Marshall said...

I was thinking about a situation like that Marty. I know you are half joking, but it's sort of a built in mechanic of poker that you *won't* do that exact move, because you can't do it profitably.

You are simply taking on too much risk to put that many chips in play preflop with a non-awesome hand. The one time it works you make 40 chips, but you have to do that like 17 times successfully before you can lose it one time just to break even. Jason will have AA one of those times or just call you with AKs or QQ-KK.

It's always fascinated me that poker has a sort of built in checks and balances system against plays like this. Of course Marty could get away with it a few times, and even show the 72 for the pride value, but he just can't ever make that play profitably with a weak hand.

Although I do encourage him to try.

royalbacon said...

But haven’t we established that it simply makes no sense to call with QQ-KK in this situation? So if we all played the “smart” way, wouldn’t Martin win every time, regardless of whether he’s bluffing or not? The only time he would NOT win would be when he does that and somebody else at the table has AA. And that would NEVER happen.

Before you respond, please note the sarcasm.

Ryan said...

All I have to say is that Jason is, bar none, clearly the best pre-flop KK-folder the world has ever seen. I mean, in our discussions he's come up with *multiple* scenarios where it's obviously the correct play.

I can't wait to see him actually do it someday.