Wednesday, February 21, 2007

Tournament Pot Odds: All-in or Fold?

Today I want to talk about tournament pot odds, specifically in allin-or-fold situations. This is actually a post I've been writing in my head for some time. In fact, I've sat down and tried to compose it on the pc on at least two separate occasions in the past several months, but it has quickly become more difficult than I thought to get my point across. In the end on those occasions I have ended up giving up the chore for another day.

Well today, that day is here.

Pot odds. To some people, in particular poker noobs, this concept is nebulous at best. For people who've read the popular poker books and have gotten a minimal understanding of the basics of the game, calculating pot odds is becoming easy enough to do. You just count your outs, figure out your percentage chances given that number of outs, and you compare that percentage to the percentage of the existing pot you will have to call in order to draw to those outs. To the better and more experienced players out there, these types of calculations aren't even formally done anymore, as instead it becomes fairly easy for this entire concept to just be done internally, instinctually, in such a way that you often don't even realilze you're doing a calculation at the poker table. Among our ghey little group of bloggers, I like to think that many of the group are within this last category, at least in the amount of experience and time we spend at the poker tables -- virtual or live.

And yet, despite all this, I seem to have a somewhat different view of pot odds in all-in decisions in poker tournaments than most of the rest of the group out there, and today I'm finally going to put into writing what I've been noticing over the past year or so. This is something I have seen said and thought-out incorrectly (in my view) in countless blogs, and in even more comments to other peoples' blogs, and I think today is the day I get my own point of view on the subject out there once and for all. Based on numerous commentary with about a hundred other bloggers and poker friends, I believe what I'm about to say here will be disagreed with by just about all of you. And I accept that there can be differing opinions in the subject. But I still think my point is valid. All I can really point to -- other than the logic of my argument itself, which I will try my best to make clear here -- is the fact that I have won a whole lot of poker tournaments in my day -- both small 1-tablers and huge multi-thousand field jobs -- and that my poker tournament success has been accomplished by following the general theory on tournament pot odds that I'm going to espouse in this post.

Now, I'm not in any way trying to suggest that just because I've won a lot of poker tournaments, that that means anything I say or believe is correct, or that you should automatically accept everything I say as true. I'm only mentioning this because I know mostly everyone has disagreed with this point as I've tried to make it in the past, and I am a big believer in trying to get people to be introspective and open-minded, about their game, about poker in general, etc., as I am myself, and thus I want to try to do whatever I can at the beginning of this post here to maybe get some of you to suspend disbelief for a bit, and open your minds to the possibility of what follows.

OK, so with that ghey introduction, the Hoyazo theory on tournament pot odds basically comes down to this one basic premise, which I will then try to explain:

Sometimes blindly following pot odds in allin decisions leads to the wrong conclusion in a poker tournament.

There. I said it. Fire up those flame throwers, people. But in my view, it's true. Sometimes if you blindly make allin calls based purely on pot odds in a poker tournament context, I believe you are making a big mistake. Allow me to explain, which I think is best done by starting with an example that has probably happened to all of us at some point in our poker lives.

So it's late-ish in a nlh tournament, call it a 1-table sitngo that pays the top two spots, for simplicity's sake. There are 5 players left, and blinds are at 500-1000. You are sitting on the button with 7000 chips, while your other four opponents have 4000 chips, 6000 chips, 10,000 chips and the chip leader has 12,000 chips. So you're in 3rd place of 5 remaining players (not that this really matters to this discussion), albeit not in a terrible spot, chip-wise. You have 7 big blinds left, which isn't huge, but the other players have 4, 6, 10 and 12 big blinds between them, so it's no big thing for mostly any of you just yet. So that's the setup.

Now, you're on the button as I mentioned, and you look down to find 63o. A veritably terrible hand. Yet, UTG and UTG+1 both fold and the action heads to you. Now, in most cases I would give serious thought to folding in this spot, since the 63o is just about the worst hand imaginable, but let's just say you have watched people stealing the blinds all night, you don't want to get too short and so you feel you need to take this one down without a fight and pocket the 1500 chips from the small and big blinds. So, you raise it up 4x from 1000 to 4000. You know your hand is terrible so you really want to take this thing down here.

The small blind insta-folds, but the big blind, on a larger stack than yours, thinks for a minute and then min-reraises you, bumping it up another 3000, making the total bet 7000 back to you, and requiring you to slide the rest of your stack into the middle in order to make the call.

What do you do? Think about it. What would you do here?

Let's look at the pot odds for a minute. There is already 1500 in the pot from the blinds, plus your 4000 that you bet from the button is 5500. Now your opponent has put another 7000 in the pot, representing the rest of your stack, so the pot is up to 8500, and you will need to call 3000 more chips into that pot of 8500 in order to make the call. So the pot odds in this situation are 2.83 to 1 (8500 / 3000), meaning that you would need at least a 35% chance (1 / 2.83) to win the hand in order to "justify" the pot odds you are being laid in this pot, following traditional pot odds rules.

Edit: Patch has correctly pointed out that my math is effed up here. Oh well. I went to fix it and decided I'm just not going to bother. Just humor me instead, and play along with the pot odds on the assumption that I have them correct. So assume the pot is laying you roughly 2.83 to 1 odds to make an allin call when your chances of winning are roughly 35%. I've already got what I think is an even better example of what I'm talking about, which I plan to post on Thursday, but for now if you can just try to accept my [incorrect] calculations as true and think about your likely play here.

Now, you have 63o. Let's assume that, since your opponent has reraised you allin, he does not have any cards 6 or lower in his hand (pretty much a guarantee to be correct). This means that in all likelihood, unless your opponent holds a very unlikely pair, he has just two overcards to your two undercards. This means that your odds of winning the pot are somewhere around 35-40%. It could be a little more or a little less (considering the suits, connectedness, and the possibility of a pocket pair in your opponent's two cards), but the point is, you're basically right there at the 35% chance you need in order to "justify" making this call here according to the price the pot is laying you.

So do you make this call in this spot? You're getting the "right" odds, yes?

The fact is that most of the bloggers I see out there routinely choose Yes here, and make the allin call, often times even typing things like "well I'm getting more than 2 to 1, I have to call here" or some such commentary. But me, I say no to this call. No way.

In a cash game, when you can go back to your pocket for more chips as many times as you see fit, there is I think a certain logic to this kind of blind devotion to pot odds. If you're getting 35-40% to call where the pot is laying you 2.83 to 1 odds, you can basically make that call and know that, over time, you're going to win slightly more money than you're going to lose, based purely on the mathematics behind the odds of the situation. But in a tournament, I base my play on the understanding that there are other factors at play that dictate sometimes straying from results that are determined stricly by pot odds. Namely, the fact that you need to put the rest of your stack in on this call, and if you get eliminated in this spot, you're done from the tournament. Finito. No more chance to win the cash for finishing in one of the top two spots in the tournament.

See, this is the part that I find a significant number of the people I run into on a regular basis in my online poker play don't seem to get. I can't count how many times I've seen someone call off the rest of their chips in a tournament -- blogger tourney or otherwise -- saying or thinking things like "well, I'm getting 2 to 1 here, so I gotta make the call and hope I hit something." And in some cases, I'm all about pushing in the rest of your chips when you're truly pot committed. But, in my example above, even though you've put 4000 of your 7000 chips into this pot, you've still got 3000 chips left, and that still gives you a chance to make a move in this tournament, in a far better spot than when you know you've got two undercards to two overcards. With that 63o, why take a chance with a 2/3 likelihood of resulting in your complete elimination from the tournament, when you can instead fold it and wait for a better spot to put your tournament life on the line?

So my point in this post is that sometimes in a tournament where once your stack reaches zero you are eliminated, I find that making allin calls based strictly on having the pot odds, when the call you're contemplating has you at a significant disadvantage to win the hand, is not good tournament poker. In a cash game, different story if you truly don't mind getting stacked and truly can go back into your pocket for more chips. But, the price of elimination is something that IMO needs to be weighed in every decision where pot odds are dictating making a "crying call" in a tournament context.

So, in summary, pot odds, while a very useful and even crucial tool in making allin call or fold decisions, is in my view not at all the end-all-be-all determinant in such decisions. If it is used as such, I believe people are led to making decisions that give negative tournament equity overall to their play. Yes, even where you are technically getting the "proper" pot odds to draw at a 1-in-3 shot of doubling up, and 2-in-3 shot of going home. I believe instead in using a more balanced approach, one that takes into account the likelihood of elimination from a tournament in making an allin call or fold decision, and only dictates a call where I am truly pot committed, or where there is a significant pot odds advantage to calling instead of folding. Using this method of determining whether to call allin or fold when I am surely behind to an opponent has worked very well for me over time poker-wise, and I firmly believe that others would see better tournament results as a whole if they would not make themselves slaves to pot odds and pot odds alone when faced with such decisions.

I have much more to write on this subject, but this is the general idea I wanted to get out there, so have at it. Gentlemen, start your flaming!



Blogger bayne_s said...

Playing pure pot odds is reasonable play in a tournament when you not only can't go broke and you are leaving yourself enough chips to reasonably play. As long as I am left with 10+ BB behind play is pure pot odds regardless of hands. 5-10 BB depends on stage of tournament.

If you raise a hand like 6 3 off and are going to call a re-raise then you should have pushed to eliminate play back.

Sadly if hungry or tired I am still likely to call all in late in tournament as you described.

11:37 PM  
Blogger Hammer Player a.k.a Hoyazo said...

Bayne, note in my post I don't disagree with what you've said there. I'm talking only about situations where elimination is at stake for you in a poker tournament and you can either call at long odds (even "correct" ones) or fold and live to fight another day.

And of course we all make these kinds of calls on occasion. Man, when I'm tilting like last night I will call with just about anything. It's good for me sometimes to get in touch with my inner tilt-donkey.

11:55 PM  
Blogger jjok said...

Posted the same type of situation regarding the Big Game on Sunday.....except that it was on the flop.

I'm agreeing with you a point.

12:08 AM  
Blogger Hammer Player a.k.a Hoyazo said...

Yes jj I read your post today and it reminded me of what I had just written about. I do like your laydown there against Fuel, and yes I've been the guy just dumping off the rest of my chips more times than I can count. Doesn't make it right though....

12:32 AM  
Blogger Haley said...

B+... with a couple of situational incompletes. One biggee here concerns how long it is until the blinds jump again. If they can be expected to jump in the next four hands, per your example, then it's an auto-call, sorry. You're committed, babes.

Of course, you should have jammed, like Bayne says, so it's a bit of an artificial construct to illustrate your point. Frankly, the whole point of the post seems to be about the ability to get away from a hand, and in this case, and given the fact that everyone has small M's, a wiser play might be to dump the 6-3 and wait another hand or two. I know, I can hear the Strasser types talking about jamming with any two in that spot, but realistically, you might get looked up by any two, too.

The second point has to do not only with how and -where- those other chip stacks are located, but how much of a chance there is that a couple of these stacks will mix it up in the very near future, leaving you a chance to sneak in to the third-place money. Because if you give it up, the likelihood is that you're going to have to win two straight showdowns to cash.

1:15 AM  
Blogger Alceste said...

With respect to your specific example, if one is categorically never going to call a re-raise in this situation, then why would one ever try the steal-raise in the first place given the relative size of the stacks to the blinds (where pot odds should be more strongly guiding your decisions)? Here, you've effectively crippled your stack to 3 big blinds by raising/folding and will almost certainly have to play a random hand from the big blind for 2:1 odds at the end of the orbit). It also seems like you're providing your opponents with an opening that they can exploit in the future in short stack situations.

It's where the stacks are larger (effective M's between 5 and 10) that I think your point is stronger. Why do folks call off chips from the big blind or re-raise a similarly short stack (who has to call you) with overcards or the "easily dominated" hands you hate so much? The odds are frequently there (and at least in the calling situation, writers like Sklansky say it's the correct play in tourneys), but it does seem to introduce a lot of unnecessary variance into situations where the edges are small and losing means elimination.

1:23 AM  
Blogger SirFWALGMan said...

I totally agree with you on the MTT front. I think in cash game you need to ask yourself about implied odds.. the cash game guy is not going to re-raise you all in and if he does you have invested maybe 3BB and its an easy fold.. if he re-raises you another 3BB, you have pot odds, if you hit hard you know this guys going to pay you off so you have implied odds so you make the call and play some poker possibly..

LHE is all about Pot Odds exclusively.

1:57 AM  
Blogger Michael Albert said...

All right, time for the "math guy" to weigh in. Close to the bubble it's incorrect to use raw pot odds. There's no absolutely perfect model (because of issues of rising blinds and the asymmetry of position) but the independent chip model (ICM) is generally accepted as the best approximation.

In a standard 1 table SNG with payouts in the ratios 5:3:2, the situation Hoy described would leave you (under ICM) with a cash equity of $1 if you fold, and just a shade over $3 if you call and win. All figures are approximate, but given the limitations of the model, that's not really an issue.

Put another way, the ICM odds are 2:1, as opposed to pot odds of 2.8 to 1. You're only just getting 2:1 against a calling range as wide as "any ace, king, broadway, or pair" so laying it down is not hugely wrong.

Now Hoy specified a two person payout, which I'm not familiar with in a SNG. Randomly deciding on a 7:3 distribution makes the money odds significantly better (about $3.4 if you call and win, only $0.9 if you fold.) The point is that this tournament is farther from the bubble than the standard payout SNG, and there are less opportunities to scrape up some cash.

Do you need to learn ICM now? No. I think even the SNG specialists who worship at its altar, and who would have been appalled at my blatant acceptance of approximate numbers above, tend to just internalize the ICM decisions to a set of rules concerning when to push and when to call pushes in the late stages of a SNG. But the example above already illustrates the key general principle:

The closer you are to the bubble, the more valuable the chips you have in your stack become, as compared to those that you might add to your stack.

This same principle probably means, as others have noted, that the steal attempt with 63 off was misguided on a purely odds based basis -- it may have been absolutely correct on a situational basis.

2:20 AM  
Blogger Hammer Player a.k.a Hoyazo said...

Michael, some good points there. And make no mistake, I specifically made this example a 2-person payout structure with 5 players left, because I did not want this to turn into a bubble strategy concept. Bubble strategy might also very smartly dictate a fold here, but that's not what I'm talking about. In this post I am just trying to get at the point that just because one has "pot odds" in the strictest sense does not mean in a tournament that they should automatically call off the rest of their chips.

2:31 AM  
Blogger Patch said...

Is it just me, or is the math on this messed up? There's 1500 from the blinds. You raise it to 4000, making the pot 5500. The BB makes it 7000 to go, adding another 6000 to the pot. That puts 11,500 in the pot. You're calling 3000 to get 11,500 which means the pot is laying you almost 4-to-1.

I also have some quibbles with the range you've put your opponent on.

Given the odds in this situation and the very meager stack you'd have left, yeah, I'd make the call. The likelihood of getting something playable before you blind out is not good and you're getting a huge overlay from the pot here. You've gotten yourself into a mess, but the best action given the situation is to make the call and hope to get lucky.

I do think your larger point, if I understand it, is quite valid and suffers from a less than robust example. Pot odds are not the only consideration in tournament poker. If that's what you're trying to say, I agree completely.

I gave up on using only pot odds long ago when I read an opponent as donkey-pushing on the very first hand of a tournament and called with my two big cards. My read was correct, but he caught a card, I didn't, and I went home after one hand. It's clear to me now that I should have let him steal the blinds with his 86o and lived to bust him out on another hand.

2:48 AM  
Blogger bayne_s said...


I agree with your premise that pot odds alone should not dictate your play when it is for all your chips in a tournament. Hate your specific example as test case.

You were sitting in a solid 3rd position before you raised by betting 4/7 of stack and being raised you have left yourself in a position where if you fold you are SS hold 3 BBs with 2 hands until BB and have surrendered 4000 chips to one of 2 big stacks and only top 2 pay.

I probably still fold here and kick the dog for not pushing pre-flop or folding as I will almost certainly see a better hand in next 2.

That being said I have been BB with only 1 BB behind (thanks to an AJ beating my QQ previous hand) where I picked up 2s4s, UTG min raised 4 callers than big stack re-raised, getting 9+:1 and knowing I would have to be all in next hand I insta-called because it was 2 live and suited.

I think that was good decision as we were close to money but I was not making it without picking up chips. Rivered straight flush to crack AA on that one so results were good enough to reinforce decision good or bad.

4:32 AM  
Blogger Hammer Player a.k.a Hoyazo said...

Bayne, all things equal I think I would probably have called in your situation as well. 42s is 2 live cards as you mention, plus it is suited and has straight possibilities. With only 1 BB left in your stack, the best part about this hand is that it has the opportunity to be a very multiway pot, and the possibility of tripling or even more than that on the hand is to me too much to ignore.

I know my example sucked today. I've got a better one coming tomorrow in a slightly different scenario.

5:14 AM  
Blogger Iakaris aka I.A.K. said...

Very interesting post Hoy, and timely too for me in particular. FWIW I just want to reiterate a position I am experimenting with:

1. If you have a reasonable expectation of a race (50/50)early to give you a chance to exploit inherent weakness at your table (and you understand how to do so)you will create a profitable situation to do so. I know you aren't a fan of this style of early play, but that's strange because given your game you are the kind of player who'd maximize the benefit of such a stack (notorious restealer).

2. If you have a stack big enough to afford the hit while leaving you with a playable stack, it is reasonable to get your chips in behind if you are priced in by the pot.

My weirdo hand at MATH (which I know you hated) involving my AQs is an example of this. I am raised by UTG a standard 3x. I reraise him 3x to a thousand. He pushes on me and I have to call another 1200 to win the 4k in the pot...I have him covered by a mile (leaving me 4k in chips, and in fourth place overall - down from third, if I am wrong)...I am getting much better than 3:1 on an Ace that has a very good chance of being free and clear (I know the tendency is to focus AK and QQ, but realistically people will push on me with lesser holdings counting on my willingness to lay down and look for a better spot). Thus I call, and am right sort of...The ace is live but I'm looking at kings. From a Sklansky FTOP POV, I think this is the right move...but am still learning on this point and am open to pointers.

So that's that....but I like what you're saying too, and have used this style - learned from you - to very acceptable tourney results..

No one right way to play I guess.

12:41 PM  
Blogger cracknaces said...

Iakris, you have to call an all in with any two cards there getting 3/1 :)

5:06 PM  
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7:25 PM  

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