HugePoker

Caution: This post will probably only be of interest to poker nerds – maybe math nerds might have fun with it, or anyone who has ever studied game theory. Or if you just want to roll your eyes at what poker nerds get all excited about, you might enjoy a couple of pages of it in that context. You’ve been warned.

In his comment to my last boastful post about my Step 6 tournament win, Pete brings up a good question about the three final hands in which the chip leader had a total catastrophe and busted out on the bubble. His comment was:

Congrats! So, were the last 3 hands a complete meltdown on Octavian’s part, or was that just terrible luck? (both!) He went from chip leader to bubble-boy in just 3 hands! It seemed like he was in ”I’m chip leader, I’m all in every hand” mode, and didn’t put on the brakes once his stack had a big bite taken out of it. Sucks to be him.

It certainly was striking to watch the one guy at the table who seemed to have a lock on winning one of the three prizes fall apart in three consecutive hands. A couple of months ago I would have thought the same thing, ie that he threw away a near lock on victory, but now that I’m trying to be a student of this Nash Equilibrium & ICM stuff I’m not so sure. I’ve wanted to go back over all the bubble hands in that tournament to see if I can find mistakes I might have made, and tendencies in some of the opponents I’m likely to run into again, and just to make myself more familiar with the different kinds of situations that can come up on the bubble, so I’ll do that (publicly) here. If you’re going to follow along for this, you’ll need to bring up the hand replayer by CLICKING HERE and skipping to hand number 95 (actually if you do a Shift-Click it should open the replayer in a new window so you can have both on your screen). [It's possible that these hand histories only get stored for a limited time. If you click on this link and get an image of a poker table but you can't actually play any hands, let me know and I'll reload it] I’m also going to be linking to the “ICM Nash Calculator” at holdemresources.net which I use to calculate shoving and calling ranges for situations in a single table tournament. If you click on each hand number I list, you’ll see the analysis for that particular hand/situation. If you’re just interested in seeing Pete’s question addressed, just read the preamble here and go through the first hand, and then skip to hand 122, but I’m going through every hand on the bubble from the time we got down to 5 players until bubble-boy was eliminated in fourth. I’m going to get a donut and settle in – you might want to do the same…

The 6th place player was knocked out on hand 94, so the 5-handed bubble starts on hand 95. At this point we all have $1200 locked up and we’re playing for $5300 that will be awarded to the final three players standing. In effect the five of us are playing for three $4100 prizes.

Octavian_C 9335
woltas 5735
strike1 (hero) 5535
Dirty4b 3305
DDBeast 3090

At the start of the bubble my stack is healthy but I’m in a tough spot position-wise. With Octavian_C on my left, any stabs I take at the pot are going to have to go through the chip leader, who can try to bust me without risking his tournament life – in fact if he calls me and loses he will just be knocked down to third.

If I go to the entry page of the Nash calculator and enter all the stack sizes and blinds, I end up with THIS PAGE.

I’ll explain what some of the numbers on that page mean:

Players are listed in order of their preflop action. I’m the first player on the list (UTG or under the gun) with 5535 chips. I should go all-in with the best 18.3% (my Push%) of possible hands, and my tournament seat is worth about $2657 (remember we’ve already discounted the $1200 we have locked up, so it’s really worth $3857, but for the purposes of calculating this stuff it’s simpler to remove the 5 $1200’s that are already in the bank). The next player (CO = “cutoff”) is Octavian_C with 9335 chips and $3372 in equity. Next is dirty4b on the button (BU) with 3305 chips and $1828 in equity. Then there’s woltas in the small blind (SB) with 5735 chips, just slightly more than me, with corresponding equity (EQPre) of $2712 (EQPre means equity prior to posting the blinds). Finally in the big blind (BB) is DDBeast with the shortest stack of 3090 and the lowest equity of $1729. Note that even though the chip leader has over three times as many chips as the short stack, he doesn’t even have double the short stack’s equity – that reflects the fact that poker tournament chips have declining value – ie your first 1000 chips is worth x, and your next 1000 is worth y and your next 1000 is worth z, where x is greater than y is greater than z. This is in contrast to a regular old cash game (or a tournament that only awards one prize) where every chip has the same value.

In the next box on the page are everyone’s pushing, calling, and overcalling percentages and ranges. I should shove the best 18.3% of my hands: this range is expressed as 22+ A2s+ A9o+ K7s+ KJo+ Q8s+ QJo J8s+ JTo T8s+ 98s, meaning I can shove any pair, any suited Ace, any unsuited Ace with at least a Nine kicker, and so on. If I decide to shove, then the cutoff can call with 1.4% (meaning QQ, KK or AA) and if HE calls, then any of the remaining players can only “overcall” if they have exactly Aces. If the cutoff folds, then the button can call with 2.6% (pairs Tens or higher or AKs), and so on down the line.

OK let’s start looking at the hands:

As you read through this post, every time I list a hand number you can click on it (again, I recommend shift-clicking) to see the calculated ranges for that hand.

Hand 95:

According to the Nash calculator, I should be shoving all-in with the top 18.3% of my hands. Some of the weakest looking hands I could theoretically shove would be J8s, JTo, K7s, all pretty mediocre looking, but still above average hands. My pathetic little 86o comes nowhere near this list, so I have a clear fold.

Octavian_C can theoretically push all-in with the top 44.2%, meaning hands as bad as K2s, 54s, Q9o etc. He diverges from our little theoretical ivory tower by min-raising. This is something I’ve been trying to think about lately – when is it effective to just raise a normal amount instead of pushing all your chips in? Obviously if you can get away with it and people are almost as likely to fold, it’s great because it risks fewer chips, but if an opponent sees that raise as just more money they can steal by pushing all-in themselves then you end up kicking yourself for flushing those chips down the toilet. But this time it works for him, everyone folds and he picks up the blinds.

Hand 96:

With the big stack under the gun, he should be shoving a lot of hands, 46% according to Mr Nash, but he doesn’t. We don’t know his cards so we can’t judge him yet, but if he keeps folding in spots where he should be raising half the time, I’ll start to think that his pushing range is tighter than it should be, and I’ll tighten my calling range against him to exploit that. The next three players should be pushing 29%, 52% and 69%. The first two fold and DDBeast shoves, which is probably correct unless his hand was super-duper-stinky. Because I expect that he should be shoving a wide range, I can call with a somewhat wide range (29%), meaning I could call with K6s, 44, QTo or better hands. I would have a hard time calling that wide, so perhaps it’s just as well that I have 7-5-offsuit, and have no difficult decision to ponder.

Hand 97:

It’s folded to DDBeast on the button and he shoves again. This time he should be shoving 36% of the time, so there’s no reason to doubt that he has that good of a hand, but I’ll keep an eye on him to make sure he’s not shoving too much. In my shoes, with the chip leader to act after me, I would have to have a serious hand, top 7.1%, to think about calling, a pair of 8’s or better, AJ or better, etc, and again I have a hand I don’t even have to think about. Note that if DDBeast had folded, then I *would* have had to think about pushing with my 4-2: Nash says I should push 86.2% of my hands, and 42o doesn’t make the cut, but JUST BARELY … 42s is good enough to shove with.

Hand 98:

It’s folded to me on the button, I have crap, and I fold. The Nash calculator says Octavian should push any 2 cards, and he does, which doesn’t really give us any info. The short stack in the big blind would need a pretty good hand, top 16%, to call, so it’s no surprise that he folds.

Hand 99 (blinds are up to 200-400 with a 25 ante):

With the blinds up and antes added, everyone has to loosen their pushing (and calling) ranges a little, because there’s more in the middle to fight for and more danger in just sitting around letting the blinds and antes eat you up. I have crap again. It’s folded to dirty4b in the small blind, who just calls. That’s pretty weak. Nash says he should be pushing 74% of the time, so with hands as weak as 85o. If his hand is worse than that he shouldn’t even put in the extra 200 chips, and if it’s better than that he should shove and put pressure on the BB instead of allowing the BB to pressure him. He gets punished for his weakness and has to fold. “woltas” in the BB is the most accomplished player in this bunch and understands what an opportunity he’s just been presented with – he could be making this move with any two cards. Mental note not to ever try limping or standard-raising with him unless I’m trying to trap him, which I’m rarely going to be doing on a satellite bubble.

Hand 100:

I don’t think I really considered shoving with J8o, but it’s not that far off. Nash says 26.4% for me, so if my J8 were suited I could shove, and if I had JT or QT offsuit I could shove. It’s folded around to woltas who shoves. The suggested shoving range for him is kind of funny: 99.1%, 22+ 4x+ 32s, meaning any pair, any hand with a 4 or higher in it, or 32s. So there’s exactly one hand he should fold, 32o. DDBeast needs a decent hand to call, and he doesn’t.

Hand 101:

Here Octavian the chip leader makes a weird 988-chip UTG raise. If he had fewer chips so that I could do him some serious damage I would consider re-shoving on him, but as it is I have no idea what his raise means and my hand is decent but not great and I fold. I’d love to know what sort of hand he would choose to do that with, but for now I just have to wonder.

[edited] In a recent comment, V7i7c brings up hand 101 in which I fold K7s to an odd 2.5x raise form the UTG chip leader. He didn’t compare the two, but it made me try to justify folding here as opposed to re-shoving on hand 106 when DDBeast raised me from the small blind. I was tempted to shove the K7s, but I think there are several reasons to fold K7s in hand 101 and shove with the AJ in hand 106. Interestingly I think that the LEAST important reason is that AJ is better than K7s. The most important reason (to my mind) is that in hand 101 I can’t bust or even cripple Octavian_C. This means that he can call me with a pretty good hand and not be too afraid of losing, so my reshove is less likely to yield the desired result. The second most important reason is that in hand 101 I can’t bust or even cripple Octavian_C … no, that’s not a typo … that reason counts twice, because there’s another branch to it –if I shove, get called, and win on hand 101, it will be a great result, but I won’t (virtually) eliminate an opponent (hugely important in a satellite), whereas in hand 106 if I shove, get called and win, the tournament will be nearly over for me – I’ll have the dominant chip lead and dirty4b will have 4 big blinds and DDBeast will have less than one, so my gain from the best possible outcome of the hand is much better in 106 than it is in 101. The corollary to that is that I have more to lose in hand 101 than I do in 106 – in hand 101 I’m in a pretty comfy spot: I’m 3rd in chips, so if all goes according to plan (lol) the two shorter stacks will bust out and I’ll win. In hand 106, there’s one shorter stack, but the other three non-chip-leaders are bunched closer together, so the chip leader can put a lot of pressure on us while we all wait for one of the others to bust out. So in 106 I’m a little less gamble-averse, whereas in 101 I’m more inclined to sit back in my armchair and see if anything good can happen elsewhere. Also, the fact that in 101 Octavian_C is making that raise into 4 opponents, pretty much just inviting them to reraise him, makes me more nervous that he might have a big hand – in 106 DDBeast only has to get one player to fold, so I don’t give him as much credit. And lastly, AJ is a better hand than K7s.

Hand 102:

I finally land in a spot where I could profitably shove a whole lot of hands (72.9%, as weak as 96o), it’s folded around to me in the small blind, and I have 8-2o. Even 8-2s (aka “the Larry” as dubbed from my home game) isn’t quite good enough.

Hand 103:

Finally some action! (and we get to see some cards to evaluate decisions) DDBeast shoves from the cutoff and big stack Octavian_C calls from the SB. Clearly the shove with QQ is correct, but what about the call with AT? My gut says it’s an easy call – his stack won’t be dented too badly if he loses and DDBeast could easily be shoving a weaker Ace or a non-Ace hand. Nash says the call is correct, but not as clearly as my gut thought. A9 is the threshold according to Nash – A9 is a call but A8 is not. This reflects the fact that Octavian_C has no real need to gamble – he can sit back and wait for a better spot. This makes me think that even though the call is theoretically correct, maybe the AT should actually be folded here, since (1) DDBeast might be shoving a narrower range than theory dictates, and (B) Octavian knows what he’s doing and can’t assume everyone else does, so there’s potential for other people to make bad mistakes, in which case it makes sense to play a little on the conservative side with the big stack. But whatever you think about that, certainly calling with AT here is not much of a mistake, if at all. The poker gods torment him for it – an Ace on the flop looks great but the Queen on the river taketh away, and we’re still 5-handed.

Hand 104:

With DDBeast doubling up my stack has now dropped out of the top 3, which sucks. This will probably result in me having to make something happen instead of sitting back and waiting for others to implode. I thought K7o was a good enough hand to use for that purpose, but Nash says I’m (just barely) wrong. He says I need KTo or better to shove here. I’m inclined to defend my decision and argue that woltas and Octavian are probably calling a little tighter than equilibrium here (although perhaps I’ll be proved wrong about that in the case of woltas – see hand 123) so that I can shove a little wider than equilibrium. Even so it’s close, and a fold would clearly have been fine. But I get what I want as everyone folds.

Hand 105:

A pretty easy decision – I have KQo UTG, and I can cripple or bust everyone else at the table. Note how narrow everyone else’s calling ranges are against me – other than the short stack everyone else has to have a hand like Tens to call me. My KQ is easily good enough to shove – KTo would have been good enough.

Hand 106:

Before looking at what actually happened in the hand, note that both Octavian and woltas should have been shoving with close to half of their hands, and neither of them did. They might have both had trash, but it just gives a little more weight to the idea that they’re likely shoving a little tighter than equilibrium, in situations where Nash would say for them to push some pretty ugly hands. So it’s folded around to DDBeast, who raises my big blind to 1000 instead of just shoving. Luckily I have a good hand and have an easy shove, but I think I could have done this with a much weaker hand here. DDBeast is really offering up his neck – he pretty clearly just wants to take my blind without risking much, and I just don’t think he’s going to throw away his tournament on the bubble unless he’s trapping me with a monster, so I can pretty much shove here with just about any two.

[edited] Ace asked a good question about this hand in the comments - What do I do if DDBeast shoves instead of standard raising. The Nash answer is on the calculator link for this hand - on the last two lines of the table with all the percentages and ranges, it says:

SB 100.0%, Any two
BB 4.2%, 77+ AQs+

So DDBeast is supposed to shove no matter what his cards are, and even if I know that, I should call with only my best 4.2%, namely pairs 77 or higher or AQs or AKs (that seems a little odd - is AQs being ranked higher than AKo? Sure enough - pokerstove says AQs is better against a random hand than AKo even though AKo is better against a top-10% hand - cool). So AJo doesn’t make the cut and I should fold. I think I would even make my range tighter than that, because I’m not sure DDBeast is likely to shove his worst hands - lots of people including me wimp out in spots like this, and later on hand 111 when DDBeast is supposed to shove 81% he gives me a walk instead, which might mean he’s too careful in that spot. If I think he’s only shoving the top 80% of his hands I need to tighten my range to 88+,AKs to get the same edge that I would have against a random hand with 77+,AQs+. If he’s shoving 70% I need to drop AKs and only call with 88+, and if he’s really wimpy and only shoves 50% (I think lots of weaker players might fit this mold) then I can only call with TT or better AND if he’s that wimpy then he’s going to give me more walks in the future so I really don’t want to gamble here, so maybe I should drop TT and only call with JJ+. But I don’t think DDBeast is that wimpy, so maybe 88+,AKs is a good calling range here. Excellent question, I should have thought of it. It really shows what a mistake he made - by shoving he puts me in a very difficult spot, and instead he gave me a pile of chips on a silver platter. The followup question is what do I think his range is when he raises to 1000 and then can I really shove all-in with Any 2? Would he do it with AA or KK to try and trap me? I don’t think that would be wise - even with AA or KK he should prefer to just shove and take the blinds I think - if he takes the blinds his equity goes up to about $2950, if he traps and loses it drops to near zero, and if he traps and wins it goes up close to $4100, let’s say $3950. So he gains $1000 if his trap succeeds, loses $2900 if it fails, so he needs to have almost 3:1 winning chances against the hands I will re-raise with - OK that works - he’ll have better than that with AA but just about 3:1 with KK. So in his spot trying to induce me to shove with AA is a good plan. So if I think that he thinks that I’ll shove a lot of hands against him and that I’ll rarely fold, then it makes sense for him to do this with (and only with) AA. But in that moment I decided (obviously correctly) that he wasn’t trying to induce me into shoving, he was trying to trick me into folding without risking his whole stack. And if that’s right then I think I can re-shove with Any 2 … or I could get really tricky and fold some of my worst hands (A) just in case he’s got AA and (B) to encourage him to do it again so I can shove. Maybe that’s a bit much. Again, great question.

Hand 107:

With that last hand my standing has dramatically improved. I’m now in 2nd, not far off the chip leader, and DDBeast has put himself in a precarious position. Before looking at the actual hand, note that if everyone folded to me I could shove into the chip leader with Any Two Cards. That would be a terrifying choice to make, and I might wimp out if my hand were really weak, but it makes sense: Octavian just can’t call me, because losing would be so catastrophic for him … Nash says he could call me with 99 or better, but that’s if he assumes I’m shoving any two, and he can’t really assume that – I wonder if he might fold JJ or maybe even QQ, and if that’s true then I’m completely justified in shoving any two, and I should remember not to be a wimp when situations like that come up. OK so dirty4b is getting desperate and should be shoving 30% (I bet he’s shoving even wider than that), which he does, and everyone folds.

Hand 108:

An interesting hand. It’s folded around to Octavian, and you might think, as he apparently did, that he could shove any 2 here. That would have been true before dirty4b bolstered his stack with a blind steal, but with his stack up to 2400 Octavian should be a little more careful – Nash says 52s is OK but 52o is not, so theoretically it’s a bad shove. In Oct’s defense, he might reasonably have thought that dirty4b would not be calling wide enough (Nash says 45%) in which case shoving 52o is probably OK. I think I would choose to err on the side of being conservative though, if for no other reason than to avoid letting everyone at the table know that there are situations in which you will shove 52o. Clearly dirty’s call with 66 is correct, and he is vindicated with a full house on the river.

Hand 109:

Guess who just became the chip leader (by mostly sitting on his ass)! That’s the good news. The bad news is that a player has not been eliminated, all the stacks are close together so anyone can cripple me – we’re in minefield territory now. Ironically, the fact that I’ve been getting crappy cards and have not showed much aggression might make people think I’m being careful or timid, which might make them more likely to fold when I come out of my shell, which would be fabulous. After DDBeast folds, any of the rest of us have the right to go after the pot without much of a hand, Octavian does and gets the blinds.

Hand 110:

Nash actually says I could have shoved T7s here, but it’s right at the bottom of the range and I think folding it is fine. Octavian either has a better hand, more guts, or just a determination to regain the chip lead, as he shoves and everyone else folds.

Hand 111:

A WALK! What a blessed gift! Woltas should be shoving 46%, but doesn’t … DDBeast should be shoving 81%, but doesn’t … someone is probably playing too tight. And perhaps I’m reaping some dividends from hand 106 when DDBeast tried to take my BB cheaply and I bitch-slapped him. Maybe he had a bottom-20% hand, I don’t know, but I’m going to guess he’s wimping out a bit (and so I should tighten up my calling range when he does get his backbone in place enough to shove)

Hand 112:

Before I replayed the hand I looked at the Nash numbers and I was afraid I might have to eat my words from the previous hand. It’s folded around to me and as the chip leader I should be shoving any two cards. I would have been sorely tempted to wimp out if I had a crap hand, but as it is I had an easy shove with 77.

Hand 113:

Again I’m spared any real temptation to wimp out – it’s folded to me on the button and QJ is more than enough – J2 would have been enough, or T3, or 95. The blinds can’t call and I improve my chip lead.

Hand 114:

Again Nash puts my 98o near the bottom of my pushing range, but I think my decision to fold is sound. I’ve just shoved the last two hands and people might think I’m just big-stack-bullying. Dirty4b should be shoving 82% from the SB and he gives a walk – I’ve got to think that’s probably a mistake. Even though Nash says 82% I would probably shove any 2 here, because I just wouldn’t expect woltas to call lightly (again – I’m about to get evidence to the contrary on hand 123, but that’s what I would be thinking in dirty’s shoes). So I’m thinking dirty is playing a little too tight in must-shove situations, so when he does shove I’ll give him a little extra respect.

Hand 115:

33 is a pretty easy shove here, and no-one can call me without heavy artillery.

Hand 116:

DDBeast couldn’t give me another walk. Note that because my stack has grown so nicely his decision is more difficult. His stack won’t wound me so badly anymore, so I could call more easily, so he has to be more careful. I’m guessing he had a real hand here.

Hand 117:

Finally what we’ve been waiting for … both plays are clearly correct … DDBeast can happily shove any Ace, and Octavian could have called with 77 let alone Queens. We’re down to 4, the final bubble, Octavian has regained the chip lead but I’m in great shape.

Hand 118:

Once again I have a hand near the bottom of the Nash barrel, so Nash says I should shove, but I think I’m right to fold here. For me to shove here I have to believe that Octavian will only call with KK and dirty4b will only call with 88, AJs, AQo or better, and I think there’s a significant chance that one or both of them might call lighter than that. Octavian has to shove any 2 and dirty pretty much has to fold, and that’s what happens.

Hand 119:

This time I get a hand just underneath the Nash chalk-line, but not by much. If I had T6 I could shove (but I probably wouldn’t). Octavian has to shove any 2, does, takes the blinds, grows his chip lead.

Hand 120:

Same deal – Octavian should shove any 2, and none of us can call. Note that I can’t call with Aces here even if I know Octavian is shoving any 2. Even the short stacks need big hands to call, although I think dirty4b should widen his range a bit because the big blind is about to hit him, and Nash doesn’t take that into account.

Hand 121:

Here Nash says I dropped the ball, and maybe he’s right. If I shove here Octavian just can’t call – Nash says he can call with TT but I wonder if he might even fold JJ here. So I should be shoving any 2, and I just couldn’t do it with 8-2o. I guess a possible justification for folding is that the blinds are about to hit the shortstacks, and it’s more likely than normal that we’re about to see an elimination, which gives some extra value to folding. I should run the numbers to see how much equity I’m giving up by folding – my guess is not much.

FOLLOWING ARE THE THREE HANDS PETE WAS REFERRING TO…

Hand 122:

Straightforward – Octavian should be shoving any two cards, but he actually has a good hand. Dirty4b has to call pretty tightly, but he has a monster heads-up in AK. Nash actually says he should fold AQ here, but I bet he wouldn’t. dirty doubles up, Octavian still has a healthy chip lead, and I’m feeling just a hint of anxiety.

Hand 123:

Nash says I’m a pussy again, and that not only should I shove K7, but Q2s, or Q8o would have been good enough. And using the same logic I applied before, the fact that the blinds are about to hit me should weigh in favor of pushing (though that doesn’t matter as much here since I have a much bigger stack than dirty did when I brought up that angle). The other thing I can try to weasel out with is that Nash expects Octavian and dirty to only call with KK or AA if I shove, and I just don’t think they’re going to be quite so tight – hard to imagine dirty4b folding Queens to me here. But K7 isn’t on the Nash borderline, it’s firmly in the shove range, so this is probably a mistake. After I fold, things get really hairy. Octavian shoves with Q8 and woltas calls with KT. Nash says both plays are mistakes, but that Octavian’s shove is a small mistake whereas woltas’ call is a major blunder. I think I agree. If I’m Octavian, I can make a case for shoving here – dirty can’t call at all, and woltas is a strong, very successful player in these things – I would expect him to know his calling range well, and I would expect him to narrow it a bit to compensate for his perceived skill advantage over the rest of us, and apparently I would be wrong on all counts. All I can say for woltas is maybe he thought Octavian was shoving any 2, in which case *maybe* his call is correct (though I’m not even sure of that). I don’t know, I think it’s a stinky call. But the poker gods reward him for it, and Octavian has fallen in 2 hands from dominant chip leader to short stack, without doing anything seriously wrong.

[edited] I just ran the numbers to figure out if woltas’ call would be correct if Octavian were shoving any 2. It came up as a tossup - he can call, he can fold, it doesn’t really change his equity either way. And I think it would be silly to think that Octavian is pushing any 2 here, so I think it’s just a bad call.

Hand 124 (final hand):

OK this is just rubbing salt in the wound. Octavian is correct to shove with A7o according to Nash, but I think after the last hand seeing woltas make such a loose call with KTo, maybe we need to re-evaluate our assessment of his calling range. If he’s calling wider than equilibrium, then A7o probably drops off the list and can be folded comfortably (though, again, the blinds are about to bite into Octavian so that puts a little extra pressure on him to make something happen). Whether it’s a mistake or not, it’s certainly not a big mistake … and then woltas is just a lucky-ass bastard to wake up with KK.

So Octavian goes from having about 94% chance to win the tournament to zero in three hands, the worst fear of chip-leaders everywhere. But it is exactly that fear that you have to conquer if you want to play correctly on the bubble – you have to take the calculated risk of that worst-case scenario in order to keep the pressure on your opponents.

I guess it’s kind of funny that in my last post I said I should show some self-restraint in long-ass blog-writing, and then I go and produce this little magnum, but this has been a good exercise for me in going through hand by hand and looking at each decision critically. It looks like there are some situations where I am a little gun-shy about shoving my chips in with crappy or marginal cards, but I think for the most part I did a good job of playing situational bubble poker. Writing this up has helped me to look at this stuff – if anyone else gets something out of it that’s just a bonus (as long as you don’t bust me out on the bubble in my next tournament).

If you have questions, comments or criticisms about how I played a hand or my explanations or whatever, fire away…

-huge