Live Poker Hand -- What are the Odds?

So here's an interesting poker problem I ran into recently when I was playing a no-limit holdem tournament at a live casino. The guy to my left had been raising and betting pretty actively early on, including in a couple of hands where I felt fairly sure that he had nothing more than a drawing hand. Contributing to my image of him as a reckless, super-active player, I won't lie that his face definitely had the look of a euro, and, well, if you play at all during the day on the major online sites then you can imagine what my generalization is as to the euros out there. Anyways, suffice it to say that I had this guy pegged as a loose, maniac style of player, and I could not wait to get involved in a pot with him.

I got my chance maybe an hour in to the tournament, with blinds of 100-200 and average stacks of around 14k (10k to start), when I open-raised to 750 from middle position with Q9 suited, and Mr. Euro quickly called my preflop raise to my left. The flop came down a juicy-looking TJQ rainbow, giving me top pair plus the bottom end of the open ended straight draw, and moreover I figured I was likely ahead of whatever my opponent had since he had quickly called my preflop raise. AK of course was a scary possibility with this board, but in the end he had called quite fast preflop, and AK is not a hand that I find many people act quickly with before the flop when it has already been raised up ahead of their action. So I figured my top pair might not be good, but my draw together with top pair likely was. And, since my opponent had called a preflop raise, I figured there was a good chance he hit this board in some way as well with a high card or two.

Figuring therefore that my opponent was likely fairly strong but that I was ahead with two cards to come, I led out on the flop for 1200 into the 1800 chips already in the pot, and Mr. Euro did his usual move of a very quick smallish raise, only up to 2700 total, just barely more than the minimum allowable raise. I had around 8k left in my stack at the time, and I pretty quickly pushed allin, figuring that this guy was making another Euromove and was probably himself either bluffing or drawing, given what I'd seen him do so far in this tournament. My opponent sat for a while, clearly struggling with what to do, which made me really want him to fold since I figured he probably had a King (for the higher oesd than mine) plus one of the other cards on the board. But alas, eventually he called. The Euro tabled JTo for flopped 2nd and 3rd pairs, and he happily yelled "come on, HOLD!" as the dealer burned and turned a rag, and then burned a turned the river, the 9 of diamonds to give me the hand with a higher two pairs.

When that 9 hit the river, you would not believe the ruckus that this guy made at the table. He slammed his hand down hard on the felt, so hard that everyone's chips jumped a little bit, and he kind of screamed out "I cannot believe that suckout!!" As he had had me outchipped by a little bit, he was then forced to sit there and continue muttering about his luck and how he could lose that hand after flopping the two pairs for the next 20-30 minutes until he was finally eliminated from contention. As he left he made some kind of nasty comment under his breath to how I got my money in as "an 80% underdog", which did not sound right to me given where I thought I was in the hand.

So the question is, off the top of your head (of course any monkey could look this up on a holdem odds calculator, like I did after I returned from the casino), what does your gut tell you his and my equity were in the hand in question? Again, I held Q9 and he held JT on a QJT rainbow board. I knew for certain that his estimate that he had 80% equity in the pot was a gross overstatement, but my instincts were telling me at the table that this was about a 60-40 shot. I actually guessed out loud to the guy who was on the other side of Mr. Euro that I was maybe a 42-58 dog in the hand, whereas he was estimating that I was maybe a 38-62 dog, but we both figured this hand to be somewhere around 60-40 given all the outs I felt I had.

So, again with no cheating by looking this up, what does your gut tell you in terms of my and my opponent's equity in the hand in question?

Utility Odds

As promised, today I want to talk about the concept of "utility odds", as described by Arnold Snyder in his excellent poker book sequel The Poker Tournament Formula II. In a nutshell, Snyder argues that it is utility odds, and not just normal pot odds or implied odds, that are the most important mathematical determinant in making call-or-fold decisions in poker tournaments. I mention this point because, frankly, I think Snyder is clearly quite on-point with his whole discussion of chip utility and his focus on this concept throughout his writings, but I find this particular concept of utility odds to be the hardest to quantify of the various aspects of the ramifications of chip utility that he explores.

Snyder's basic point regarding utility odds can be summed up well with an example he uses in the book. Snyder gives an example of a well-known poker pro who called allin with just a naked flush draw during the first hour of one of the smaller World Series of Poker events a year or two ago. I don't remember who it was and obviously it doesn't really matter, but all you need to know is that the guy was an accomplished tournament poker professional, he was at about 80% of the starting stack in the event somewhere during the very first blind level, and there he went calling an allin raise on the flop with just a flush draw, in a situation where he was only getting close to even money to make such a call. Snyder explains that many spectators were in disbelief that a pro would make such a call, and yet Snyder explains that he too would have made the call in a heartbeat.

The key to how a skilled tournament player can call off his stack at around even money pot odds with just a 35% chance flush draw lies in the relative value -- the chip utility -- that the skilled player can obtain by amassing the stack he would get if he manages to double up on this hand. At 80% of the starting stack, and this being one of the smaller (faster) WSOP events, this player was already sitting with only somewhere between decent and competitive chip utility, and a good half of the 100 big blinds level that Snyder considers full utility. So the thinking is, this guy is already in pretty bad shape, and he needs to get himself back to full utility as quickly as possible, or he knows he is more or less hopeless to make any real noise in this tournament. And, he also knows that if he can get up to full utility and get himself a larger chip stack than most of the players at his table in the process early on in the tournament, then he will be able to make great use of those chips to get himself more and more chips as he can open up his arsenal of poker weapons to include all the types of moves I discussed in my posts from late last week. So to this player, being that he is skilled compared to most other entrants in this event, the value to him of getting back from his weak chip position up to full utility early here, and the relative value of him doing that as opposed to one of the other weak-tigher players doing so, gives him the ability to make a call at less than the "required" pot odds. This is because if he wins, it significantly enhances his ability to grow his chip stack, and eventually to cash and score big in the tournament. In other words, the truly skilled tournament player can call allin with a flush draw early getting only close to even money, because if he loses the hand, he was already in a fairly desperate situation anyways and he hasn't really lost much, and if he wins that hand, he will suddenly be at full chip utility and in a situation where he can really do some damage in the tournament. It is all that extra damage the professional player will be able to if he is able to win that pot and get himself up to full utility do that enables him to take the worst of it from a pure pot odds perspective early in a large mtt.

That, in a nutshell, is the concept of utility odds. As far as my reaction to this idea, in general I have to say once again that Snyder is on to something. I mean, I ask you again to think about the times you might have sat on the rail and watched one of the better mtt players playing in a poker tournament. I know personally I have done this many times and have remarked to myself how these better mtt players do not mind taking chances early to either double up or get busted. Look at the Lindgren's and the Gus Hansen's of the world -- they play their tournaments the same way. This is because they know it is worth taking some chances, maybe even taking on a race very early in a tournament under the right circumstances, to either try to get themselves up to full (or better) chip utility, or to bust out early trying. That's what it comes down to in the end -- especially in the world of online tournaments which are basically all faster than their live counterparts -- you just have to double up early and it's ok to bust out early and move on to something else if that's what it takes. I know there is definitely an element of that to the way I play in mtts, and I have personally witnessed the same strategy from most of the other tournaments I have watched from players whose mtt skills I respect as well. I might easily call an allin preflop very early in, say, the nightly 28k guaranteed on full tilt, with my AK, even when it is obvious from the action that my opponent is holding a pocket pair of some kind, making me a slight dog in a situation where I still have a fair number of big blinds in the tournament to fold and wait for a better spot if I so choose. Although again, I've never thought of this in terms of "utility odds" per se, the idea here is definitely that I want to take a shot at getting a big stack early, or go home trying, because I know with that big stack early I can significantly increase my chances of growing an even bigger stack and eventually cashing and making a final table run. This is exactly what Snyder is getting at when he talks about using utility odds instead of pure pot odds in tournament decisions.

The one complaint I have about this whole thing is how hard it is to quantify something like utility odds. I mean, fine I accept that a truly skilled mtt player and someone who knows how to use a big stack like a weapon to crush the other players at his table has the freedom to make some calls that might not be exactly right from a pure pot odds perspective just because of the added value he gets if he does in fact win the hand and get himself that big stack. But surely this idea does not mean that a skilled player can call off his stack drawing at just an inside straight draw with one card to come, just because if he does manage to hit his 11-to-1 shot on the river he will then achieve full utility. So the question that Snyder does not really address -- and I can't really complain because I'm quite sure there is no good bright-line answer to this -- is a way to accurately quantify utility odds. In the end I suppose this calculation, if one can even be accurately devised for such a number -- is going to depend on exactly how close to full utility one's stack is before the hand in question, just how many big blinds one will be left with if he wins the hand in question, and most of all, just how much his chances of a big score in that tournament will increase if he is able to obtain such full utility early on in the tournament like this. All of these variables will need to be taken into account, in combination of course with the actual pot odds involved in the hand in question, in order to come up with some sort of actual calculation of utility odds in any given situation. And those numbers will be really different for every individual player (depending on their current mindset, how well they play a big stack, etc.) and in every different tournament situation, but from my perspective at least those are the types of things that I will try to consider as I face such decisions at key points in poker tournaments going forward. I also think Snyder's approach fails to consider the likelihood of a strong player being able to wait for a better spot to double up to full utility with better pure math chances of doing so, something which I'm sure Snyder would not deny, but that doesn't change the fact that utility odds are a useful way of looking at poker decisions in tournaments that simply do not exist at all in a cash game or a "pure poker" context.

There is so much more to be said about Arnold Snyder's thoughts when it comes to poker tournaments, and you can see more about that here later this week as I continue to read deeper into his second book and continue to think in new ways about my own poker experience.

For now, just revel in the Eagles' 38-3 domination of the Rams, easily the worst defense in football, to start off the 2008 season the same way almost every season starts off lately for everyone's favorite Philadelphia sports team, and maybe I'll run into you this week at the tables.

Tournament Pot Odds Redux

Man I have so much to write about in the world of poker these days, my biggest struggle is narrowing it down to just one or a few topics to write about every day. That reminds me FWIW, I've seen Jordan, TripJax, DNasty and a few others comment several times on their own blogs over the past few months about the "pressure" to post every day. I have got to say, for me personally, I don't feel any pressure to write about poker every day. Instead, I have a desire to write every day, almost a need to write every day. So for the time being, nobody needs to worry about me disappearing into the weeds and this blog going stale. I've got so many effing ideas stored up for poker posts in my head that Bill Frist could order full tilt and pokerstars to shut down effective immediately, and I'd probably still have enough content to post for another 6 months or so as if I've been playing every night. So that's a great thing for me about this blog. I know I haven't been doing it for nearly as long as some of those other guys I mentioned above, and I may eventually face the same fate as they as far as feeling pressure to write when I don't really have any particular ideas to write about, but for now I am still going stronger than ever in that department.

So, last night was a banner night of sorts for me (not really). For the first time ever, I managed to win a seat into the nightly 30k guaranteed tournament in the 8:15pm ET satellite:



and the 8:45pm ET satellite:



Of course I've won that 8:45 satellite seat many, many times, as that is the $14 flavor of satellite, and with an average crowd steady at around 100 players or so since Neteller effed us, it typically ends up paying out somewhere around 13 seats or so. As I've mentioned here several times in the recent past, these multi-table, multi-seat satellites are far and away my best, most profitable tournament structure these days, something which I credit a large part of to Smokkee since he really is the guy who turned me on to these things in the first place a long time ago. It was probably last spring or so, when I was already an avid reader of Smokkee's blog, when he started playing more and more satellite tournaments on line, mostly on full tilt for the WSOP and on pokerstars for the WCOOP.

I remember realizing after reading about a particular satellite tournament win on Smokkee's blog that those tournaments really are where it's at, and also that the bigger the buyin, and thus the larger the ratio of winning seats to number of players in the satellites to begin with, the better the satellite is. That's why the 8:45 30k sat is so juicy, because you basically only have to finish in the top seventh of total entrants to win your seat. But the 8:15 satellite, which sports just a $6 buyin, is much, much more difficult to win one's seat with, since it also typically has around 100 players, but only awards seats to an average of 5 of those entrants. And let me tell you, finishing in the top 5 out of 100 in the fonkeyfest that is this $6 turbo 6-max nlh satellite is no small feat. I've only managed to win that satellite a small handful of times, and never on the same night as I've won the later $14 sat as well, so yesterday was a special night in that regard for me.

In case you're wondering, I doubled up early on a great play in the 30k itself, and then got recockusucked by duping a guy with Q5s into getting allin on the flop with me with just his flush draw against my overpair pocket Jacks. Well, he didn't hit his draw, but the river cruelly brought the 3-outer queen, and I never managed to recover from this blow. I made it to the first break still slightly below the 3000 chip starting stack, shortly after online "retiree" Chad joined my table, but then the next thing I knew, I woke up an hour later, just 2 minutes before the second break. Not sure what happened there as I wasn't even tired at the time (that I thought). Needless to say, when I awoke I was in 87th place of 87 remaining players (only top 36 paid out), and I quickly busted on the next hand when my KJ failed to hold up against a smaller pocket pair and IGH. But hey, I did find an effective way to outlast Chad, who had just gone out in I think 91st place overall. Dam I'm good like that.

OK so on to what I really wanted to talk about today. Yesterday's post about tournament pot odds in all-in situations made my general point, but there were two issues with it that make me want to redux this topic again today as well. #1 as many of you pointed out, the example I gave was not a good one for a number of reasons, and #2 in the end my post focused on all-in calling situations, which is not really where I wanted that discussion to go when I started it. Today I plan to rectify both of these problems with a further discussion and a new example on tournament pot odds. I will credit Iakaris with unwittingly providing me the basis of the example I will use today, as it is closely (but not exactly) derived from a question he asked on his blog a week or two ago about a run he had in the 18k guaranteed tournament on full tilt.

So, say youre playing in a large mtt. Youre down to 25 players left from a field that originally started at 500. You are currently in 3rd place out of 25 remaining players, with a stack of 30,000 chips. Blinds are 500-1000. The action folds to you on the button, and you raise it up as a pure steal to 3000 with 63o. Small blind folds, and the big blind pushes his last 6500 more chips into the middle.

This puts 11,000 chips in the pot, and you have to call 3500 to see the big blind's allin bet and take a flop. Pot odds are 11,000 / 3500 or 3.14 to 1. Thus, you need just a 32% (1 / 3.14) chance of winning this pot in order to take the action here on a purely pot odds basis. You figure, you've got 63o, and assuming the big blind must have two cards above a 6, you estimate your chances of winning the pot to be right around 35%. Do you make this call?

I do not. Even though I am giving up a 1/3 chance of winning a pot with 11,000 chips in it, my cards dictate that I will lose this showdown around 2 out of 3 times I play it when my opponent has two overs, as he is fairly sure to have. And what's more, on the times when my opponent flips up any pocket pair above 5s, I am going to lose here more like 4 out of 5 times I play the hand. Why donate another 3500 chips out of my stack (which has already lost 10% of it into this pot as it is)? Why put 20% of my chips at risk from my 3rd place stack with a hand like 63o? Given the choice of losing 10% of my stack that I've already put into the pot here on my steal attempt, or a 2/3 chance of losing 20% of my stack with this cripehand, for me this is the easiest decision in the world. No go, take the pot, have at it thank you very little.

And this gets me to my overall point about tournament pot odds, even in a non-allin context. I think people sometimes "trick" themselves into thinking they have the right odds to make a call, but I say "trick" because the only reason they have the right odds is that they've already made a poorly-timed decision to put chips into the pot with a bad hand to begin with. For example, in the situation above, would you, as the player with the 3rd place stack and 30,000 chips, ever call from the BB if, say, the button had open-pushed his last 6500 chips into the pot before the action got to you? Of course not. Why take a hand with a likely 1/3 chance of winning, and put up 6500 chips into a pot already containing 8000 chips with it? You'd have to win far more often than 63o is going to win in order to justify this play. So, since you happened to act before the big blind in this case, and happened to decide to kick it up to 3000 on a 4x steal before seeing the big blind push in his last 6500 chips, now in a sense you are allowing yourself to be "tricked" into calling another 3500 chips based on the 3-to-1 pot odds you're now receiving on the hand because of your earlier steal attempt with truly terrible cards. But, the only reason you're getting those 3-to-1 odds instead of the 1.23-to-1 odds with your crappy 63o is that you acted before the big blind and you made an ill-timed decision to dump a lot of chips in with a horrible hand.

Now, I've never been one to fight the math, and I'm not trying to do that here either. I understand that, from a purely mathematical perspective, once you've bet those 3000 chips into the pot, the strict math of the situation dictates that you have the pot odds to call an additional 3500 chips into the 11,000-chip pot because you can expect to win roughly 1 in 3 times with your 63o. But, just because you are getting close to the "right" pot odds, does that mean that you have to make this call? Again I come back to the point I made in yesterday's post. In a cash game, I think you should be basically fine making a call where you are getting 3 to 1 from the pot on a 1 in 3 shot to win. I believe that is true more or less by definition. But, in a tournament setting, where not going bust is itself of some value, I don't like to just automatically make calls for any significant part of my stack, where I'm getting no fold equity at all, and where I know I have low odds of winning the pot (even if the pot is laying me good odds to chase that low-odds hand). Maybe it's just me.

To me, I liken this situation to carrying a credit card balance in a way. In the past I have often thought that it's ok to carry a small credit card balance, if doing so means I can have the money I need to live my life (within reason) more or less without worrying about money. No I can't go buying midieval castles and 100-foot yachts on the Mediterranean. But, in the past I have found that by carrying a small credit card balance I can have a "better" life overall. Most of the people I know think this is insane, because it is a fact that I am paying interest on that balance while I carry it. They explain that it is actually costing me money to hold that balance, and that if I can find any way to pay that balance down instead, I should. This is fact which I, of course, cannot and do not argue with. My point, however, is that, to me, it is actually worth the small money loss (interest) in order to have the financial freedom that that credit card balance buys me. Again, I am not arguing that there is no financial cost to holding a small credit card balance -- I pay x dollars in interest every year by keeping such a balance and I acknowledge that and in fact openly embrace it. What I am arguing, though, is that there is a benefit to me (financial freedom) that actually outweighs that cost (interest), and so in the past I have lived this way at certain times of my life.

In my perspective, I view tournament pot odds in situations like the example above in very much the same way. I understand that by folding my 63o for just another 3500 chips into an 11,000-chip pot, thereby sacrificing a roughly 1/3 chance to win the 11,000 chips, I may be incurring a certain cost to do so (I am giving up the pot odds expectation and the 1/3 chance of winning those 11,000 chips). But, not having to lose 20% of my 30,000-chip stack in a pot that I am quite likely to lose is itself a benefit that, to me, is worth me paying that cost of losing my 1/3 chance of winning those 11,000 chips by folding. So, even though I acknowledge that by folding in this spot I am costing myself a 1/3 shot at 11,000 chips, I also know that the benefit I get from being able to retain those last 3500 chips rather than call them off into a pot I am likely to lose has a real value to me. In a tournament, having chips is itself a real value, in a way that is just not present in a cash game when you can always go back to your pocket for more chips.

Now, make no mistake, this theory I have of being willing to give up some pot odds in order to save some chips in a tournament when I have a good-sized stack is not something I take too far. In other words, if I am being laid 5 to 1 odds by the pot in order to draw to a 50-50 shot, of course I'm going to make that call without hesitation. But, my theory in tournaments is, if I'm dealing with a close situation where the pot is basically offering me roughly the same odds as my chances of winning the hand, and it is a longshot for me to win the hand, I am far more apt to fold it in a tournament and preserve my precious chips rather than to make that call. This is only exacerbated by the possibility that I will have to call another bet after the next card in order to stay in the hand to see the river. That is yet another reason why I hesitate to draw on or before the flop when I think I've got a longshot, even at decent odds -- because in all likelihood I am going to face another bet on the flop which I will not be able to call with the proper odds.

Please understand that I'm not even trying to suggest that my way is the only right way to play these sorts of situations. Just like with my credit card example above, I fully respect and understand that everyone gets to place their own value on the benefit of "having chips" in a tournament, just like everyone gets to decide for himself or herself how important being debt-free is, or how much it's worth to them to have a little bit of extra cash laying around, even at the cost of x dollars of interest paid over a year. I will simply say that I have had quite a lot of success in poker tournaments over my career by approaching decisions with longshots where I think I'm getting close to the "right" odds to draw in this way.

That concludes my post today on tournament pot odds. Again let me apologize for using what really was not a great example yesterday, though I still think it got across the point I was trying to make. Hopefully today's illustrates a little better where I'm coming from in these decisions, and why in the example I give above, I would happily release the pot, save those extra 3500 chips and retain 90% of my stack before that hand, rather than have a 2/3 chance of only being left with 80% of that stack after the hand. In tournaments, chips are king, and having them, or having a lot of them relative to my peers, is itself a desirable end, and something that really has intrinsic value in the way I approach poker tournaments.

Now before I go, everybody should not forget tonight is the latest Riverchasers event, hosted by Big Al himself:

Tournament: 13185806
Name: Riverchasers.com Tour Event #4
When: Thursday, February 22nd 9pm ET
Game: NLHE
Buyin: $10+1
password: riverchasers4

Note the password change for this event please! As with the other Riverchasers tournaments this one will take place on full tilt tonight, and I will just say that Al's tournament has quickly become one of my favorite private events of the week, as it has a large field, replete with many of my favorite bloggers, and it also has a bunch of cool guys to chat with week in and week out. And, many of them don't seem to have the focus on or understanding of the nuances of poker like many of our blogging brethren do, so that always makes it fun as well. Flop top two against one of these guys early in the tournament, and you're probably going to get TPTK or even TP2nd or 3rd K to call you for all their chips early. Yummy. I will definitely be there tonight, and I plan to do what I can to personally dethrone Gary from his perch atop the Riverchasers standings so far through I think 3 events this year, in which Gary has dominated all of them. Not tonight my friend, not tonight.

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!