50-50 Final Table Hand Revisited

On Thursday I wrote about the silly suckout that knocked me out of the 50-50 on the final table bubble on Wednesday night, netting me about $900 cash but raping me of an expected value from the tournament that was probably closer to $3000 or so before the suckout occurred, and significantly higher once I was a better than 4-to-1 favorite to become the chip leader with ten players remaining in the tournament with just one river card to come. In the comments to Thursday's post it was suggested that my opponent did not make a bad play by pushing in his entire chip-leading stack on a massive overbet to the size of the pot when he flopped 743 rainbow with his holding of 75o. This strikes me as a particuarly bad play -- in fact as the very worst of the chipleader's options in this spot -- but I always focus on keeping an open mind about things so I spent my entire train ride home on Thursday with a pen and some paper trying to work this question out and see if my math instincts, which do not usually lead my astray, might have done just that on this one. As I worked through the problem it occurred to me this might be a fun blog post. So here we are. And keep in mind, I am well aware that solving this sort of problem in a poker context requires one to make about 8500 assumptions, all of which are challengeable if you want to, but without assuming many things there is simply no way to compare the worth of one play versus another. So I'm going to solve this the way I believe Sklansky, Harrington, etc. would approach it, having read pretty much all of their books.

OK so to review and give you the whole setup, there are 10 players left in the 50-50. This was a larger than usual 50-50 with just under 1100 runners, a good 10-15% more entrants than this thing has been attracting most weeknights these days, and this number of players equates to approximately 2.1 million chips in play. The approximate payouts for the top 10 spots range from $900 for 10th place, $1000 for 9th, $1200 for 8th, $1600 for 7th, $2100 for 6th, $2700 for 5th, $3500 for 4th, $4600 for 3rd, $7000 for 2nd place and up to just about $11,000 for first place, for a total distrubtion to the final 10 finishers of $35,600. For lack of any better way of determining the players' relative Expected Value of the Tournament in cold, hard cash (TEV), I will add up all the money available in the remaining prize pool ($35,600), and I will assume that each player's TEV share of that $35,600 prize pool is equal to their proportion of the total chips in play with 10 players remaining, multiplied by the total prize pool left to be distributed. As I mentioned above, this obviously is not an exact science, but I can't think of a more accurate way than this of determining what each player is likely to win given their current chip stack and the money available to the remaining players in payouts in this event.

One important caveat I will have to follow about using this TEV formula, however, is that it very quickly gets out of whack once one player amasses more than, say, 20% of the outstanding chips with still a full table of players remaining. This is because the first prize of 11k is itself only less than a third of the total $35,600 prize pool to be paid out to the top 10 finishers in the 50-50, so if one player has, say, half the chips, it's not like his Tournament EV is actually half of $35,600, since the maximum he could possibly win by taking down the entire tournament is only the 11k first prize. So, once we get above around 20% of the chips in play with ten players remaining, I can't use this simple TEV formula anymore since it leads to TEV outcomes that are highly skewed to the upside. So for those calculations in the below solution, I will explain the alternative formula I have opted to use instead as I go through it.

So here is a chart of the approximate chipcounts of the 10 remaining players and the respective Tournament Expected Value (TEV) of each player in the tournament given their current chip stack when this problem occurred:

Player     Chips  TEV
Player 1   440k  $7120 (Villian)
Player 2   290k  $4692
Player 3   270k  $4369
Player 4   250k  $4045
Player 5   240k  $3883 (Me)
Player 6   190k  $3075
Player 7   170k   $2750
Player 8   140k  $2265
Player 9   120k  $1942
Player 10  90k   $1456

Again, these TEV figures come from simply taking each player's proportion of the total 2.2 million chips in play, and calculating an equal proportion of the $35,600 in total prize money available.

So, Player 1, the Villain in this hand, has an expected value from this tournament of $7120 right now before the hand in question, due mainly to the fact that he has almst exactly one-fifth of the total chips in play, giving his an excellent chance of nabbing one of the top few cash payouts in the prize pool. I should note that his nearly 20% of the outstanding chips is right up against the point I mentioned above where my simple TEV formula starts to skew, but even if this $7120 figure is skewed by his 20% of the outstanding chips, it is only skewed by a little bit, a couple hundred chips maximum in any event. So I'm sticking with the $7120 as Villain's starting TEV for this problem, although if you prefer to think of it as $7000, or even as low as maybe $6800 or so, I can't really say that is any more or less accurate than the $7120 figure I am using. Anyways, my TEV at the time this hand occurred was $3883, as I had just over 10% of the chips in play and thus my TEV is very close to the average of all payouts remaining in the pool.

OK on to the hand in question. Villain, the significant chip leader, is in the small blind and the action folds around to him. He looks down to find 75o. He should probably fold here, but I'm not gonna kill him for trying to pad his chip lead at a time when everyone else is probably going to be playing tight, scared of missing the final table. So he raises the 5000-chip blind around the size of the pot to $18,500, bringing his chip stack down to 421k (these numbers are not necessarily exact, but they're all very close). I wake up in the big blind with pocket Kings, my first premium pair of the entire tournament. No point in slow-playing this, I don't want to go up against the big stack here on the literal final table bubble with a hand that's going to be hard to lay down, so I bump it up by the size of the pot again, to 55k, bringing my chip stack down to 185k. Villain calls -- with 75o!! -- which was a horrible, horrid, putrid play that stinks so bad I can still smell it here more than 30 hours later, making his stack now 384k.

The flop comes down 743, rainbow. Villain has flopped top pair and a 5 kicker. He also has an inside straight draw. As I even just begin to ponder how much I love this raggy flop in this key spot for me, Villain instantly pushes allin for 384k into a 113k pot. I think for about 2 seconds and then of course I call for all my chips, the turn is a raggy 9 but the river brings a 7, giving the Villain trips and sending me home in 10th place for the $900 final table bubble payout. I know I played this hand optimally, so I don't have any doubts at all about my own play, but my feeling when I posted on Thursday was that Villain's allin insta-overpush on the flop against my preflop reraise was a bad move that clearly cost Villain TEV over time. Some comments said otherwise. So let's work it out.

Remember, the starting point here is that Villain comes into the hand with 440k in chips, and thus an TEV of this tournament of $7120.

The first, and really the central, issue in this hand is what is my hand range for me to pot-reraise the chip leader preflop for over 25% of my stack here on the final table bubble. The answer is that this is a hugely tight range of only the absolute very best hands. He is the chip leader, and we're right on the final table bubble. Now, with ATs or something like that, it is unlikely but I suppose conceivable that I might push allin on a reraise. I actually would fold a hand like that in this spot, but trying to get into Villain's head, maybe he could think that way. But to only pot-reraise as opposed to pushing allin, with about 27% of my stack into the pot preflop, against the chip leader, on the literal final table bubble with the payouts just about to start really escalating, a reasonable hand range for me is AA-JJ, and AK. That's it. Perhaps he could think I would make this move with AQ as well, although of course in reality I would not. I might reraise allin, and I might (more likely) fold to his preflop raise given that this is the final table bubble and he is the chip leader, but no way in hike I pot-reraise with AQ there. So it's AA-JJ or AK, and maybe he would throw AQ in there as well. That's it.

The next assumption is to predict what I'm going to do with each of those hands to his massive insta-allin overbet on the flop. This one is easy. I'm folding the AK (or AQ), and I'm calling with all the big pairs. He was making a move from the small blind, I had been playing fairly tight while he had been an uber-calling donkey for the last hour or so, and I felt more or less positive that I was well ahead of anything he might have been holding as soon as he did not re-reraise me before the flop. His allin massive overbet insta-push on the flop absolutely iced it for me. AA or a flopped set would never, ever do that in this spot for fear of losing me, and would surely require at least a few moments of thought as to how to extract the most chips from me with such a flop. So I'm calling 100% of the time with AA-JJ, and folding 100% of the time with AK, or AQ if you think that's in my range.

So let's look at the structured hand analysis of how likely each of those hands is for me. There are 6 ways to make each pocket pair of JJ, QQ, KK and AA, and there are 12 ways to make AK (and AQ). So there are either 36 hands in my total range (if AQ is not included), or 48 hands in the range (if AQ is included), and in both cases 24 of them are pocket pairs which call 100% of the time in this spot.

So, moving on to the math, let's see what happens to his stack and with what probabilities, and thus what happens to that $7120 TEV he started the hand with, once he pushes allin on the flop. He should figure, if he is behind (he always will be if I call), he has 9 outs (two more 7s, four 6s and three 5s), discounted a bit for my redraws to trips with my pocket pair and better two-pair hands:

If AQ is not in my hand range, so it is just AA-JJ and AK:

66.7% of the time, I have a pocket pair (24 out of 36 possible hands), which I call with every time given the circumstances. In this case:

(1) Villain will win 36% of the time with his 9 outs twice, discounted slightly for my redraws. If he wins the 483k pot, his stack jumps to 682k, giving him around 31% of the chips in play and a very high likelihood of nabbing one of the top 3 payouts. Unfortunately here we cannot use my Tournament EV formula, because it would equate with him having a TEV of around $11,100, or higher than the first place payout, which of course makes no sense whatsoever since the maximum he can possibly win by winning this tournament outright is the $11,000 first prize, and there is still an entire final table of players to get through. This is exactly the skew I was referencing earlier with my TEV formula once someone starts amassing a huge portion of the remaining chips with more than a few players remaining. So for Villain if he beats me here, we will have to devise a different method of computing his Tournament EV. To do this, let's instead just intuit that, with 31% of the chips outstanding and 10 players remaining, he has just a 10% chance of missing the top 3 payouts, paying him an average of $2000 if he does, and a 20% chance of ending in 3rd place ($4600), 30% of second place ($7000) and 40% of ending in 1st place ($11,000). This equates to a Tournament EV of $200 + $920 + $2100 + $4400 = $7620.

At first glance this may not sound right because his TEV with 440k in chips was already $7120, and now with another 245k in chips on top, the TEV only rises another $500 or so. But in reality this makes perfect sense. With ten players left, there is only so close to the $11,000 first prize that one's Tournament EV can ever come. So much can happen, so much is still dependent on luck, that with 10 players left it's going to be nearly impossible to nab a TEV much higher than 2/3 or so of the first prize payout. So $7620 for Villain's TEV if he wins my stack seems about right to me.

(2) Villain will lose 64% of the time to my higher pocket pair, in which case his stack drops to 199k. At 199k, his TEV drops to $3220 from the $7120 it began the hand with.

So, to summarize, 66.7% of the time when he pushes, I have a pocket pair and will call. When that happens, 36% of the time he wins anyways and his TEV climbs to $7620. 64% of the time he loses and his TEV drops to $3220.

What happens the other 33.3% of the time, when I have AK? I fold, so Villain automatically wins the 483k pot, bringing his stack up to 517k. Once again my original TEV formula is going to produce a TEV value skewed too high with Villain then holding nearly a quarter of the total chips in play with still 10 players remaining, so let's intuit again for a bit. With 517,000 out of 2.2 million chips, let's figure he has a 15% chance of missing the top 3 payouts for an average payout of $2000, an 18% chance of 3rd place for $4600, a 28% chance of 2nd place for $7000 and a 39% chance of first place for $11,000. This equates to a Tournament EV of $300 + $828 + $1960 + $4290 = $7378. Again, not much higher than his TEV with 440k chips and ten players remaining before the hand even started. Of course these numbers are all so inexact and you could adjust them here and there however you want, but my point is, his TEV does not rise much by getting me to fold and bumping his stack up another 113k with still ten players left.

OK, so for the grand summary, when Villain pushes allin on this flop, 66.7% of the time, I have a pocket pair and will call. When that happens, 36% of those times he wins anyways and his TEV climbs to $7620. 64% of those times he loses and his TEV drops to $3220. In the other 33.3% of cases, I have AK and I fold, raising his TEV to $7378.

Now we can easily figure out his overall TEV from the above probabilities and values. Remember, he started with a TEV of $7120 before this hand began.

66.7% (I call) x 36% (he wins anyways) = TEV of $7620.
66.7% (I call) x 64% (he loses) = TEV of $3220
33.3% (I fold) = TEV of $7378

Adding these three mutually exclusive outcomes up, we have $1829.71 + $1374.55 + $2456.87 = $5661.13. Villain's Tournament EV from pushing allin on the flop against a guy with a range of AA-JJ or AK who will call with any of the pairs and fold the AK, drops from $7120 to $5661.13. That right there is a hugely bad play for Villain, which is what I felt at the time. As chip leader with these payouts now all within reach, making that overpush is a major mistake. Now of course there are a million different assumptions and guesses thrown in to the above calculation, but hopefully it is clear that my results are so far below the $7120 TEV that he started with, that it is obvious the play is a bad one regardless of my being a little bit off here or there. He simply cannot increase his TEV very much no matter what he does in this particular hand with ten players still remaining in the tournament, but he has an overall 42% chance of decreasing his TEV to $3220 if he doubles me through. This is a gamble he should never make given that he is in position to make a serious run to the hefty top few payouts in the tournament given where he is already situated.

For interest's sake, let's throw AQ into my range as well. Like I said, there is no way I pot-reraise the chip leader with AQ in this spot, absolutely none (I might reraise allin, or I might more likely fold, but never a pot-reraise for 27% of my stack), and I refuse to even consider my doing that with a shithand like AJ or KQ or worse because that is just plain looptidin this spot. But let's throw in AQ, because it makes a whole new 12 hands in the structured hand analysis that I would fold to his flop push. I will try to simplify some of these calculations now since I've already been through how it all works once above.

So, if AQ is in my range, so it's AA-JJ, AK and AQ:

(1) Now only 50% of the time do I have one of the pairs (24 out of 48 possible hands). So I call 50% of the time, and once again when that happens, 36% of the time he wins anyways and his TEV climbs to $7620. 64% of the time he loses and his TEV drops to $3220.

(2) Now the other 50% of the time, I have AK or AQ, and I fold, raising Villain's TEV to $7378.

Again, we can easily figure out his overall TEV from the above probabilities and values, given a range of AA-JJ, AK and AQ for me:

50% (I call) x 36% (he wins anyways) = TEV of $7620.
50% (I call) x 64% (he loses) = TEV of $3220
50% (I fold) = TEV of $7378

Adding the TEV's of these three outcomes up, we have $1373.04 + $1030.40 + $3689 = $6092.44.

So, in sum, if I would pot-reraise Villain before the flop in this spot with AA-JJ or AK only, Villain's TEV by overpushing allin on the 743 flop drops from $7120 to $5661. If I would pot-reraise preflop with AA-JJ, AK or AQ, his TEV drops from $7120 to $6092. As I said, I won't even consider adding AJ, KQ or weaker hands to the mix, because that is a ludicrous assumption given that we're on the final table bubble and I'm going up against the chip leader. I suppose we could add TT to my hand range as well, but hopefully it is intuitive to you that adding another big pair to my range is only going to lower Villain's TEV from the move, because that is another hand that I will call with and be ahead of him on the flop. And I wouldn't pot-reraise with TT anyways preflop in this spot. Again, as with AQ, I might reraise allin preflop with it, and I might more likely fold it in this spot, but pot-reraise with a vulnerable and hard-to-play hand on the flop like TT? Not happening. And equally unthinkable is sinking 27% of my chips into this pot before the flop here on the final table bubble, and then folding an overpair to hsi insta-overbet allin push. Not in a million years.

So there it is, in all its boring and overcomplicated glory. It is definitively a bad play for Villain to push allin on that 734 rainbow flop with his 75o, only because the range of hands I would need to have in order to have reraised the chip leader the size of the pot on the final table bubble is so strong that his 75 is behind more often than not. If he wants to push way earlier in the tournament with 9 outs twice and possibly being in the lead in the hand in any event, there is some math to at least make that not an objectively poor play. But once you're down to the final table like this, the cash payouts take on utmost importance and the relevant calculation for many allin moves like this becomes not EV but Tournament EV -- at least the way I view it, it does.

By the way, once the guy flopped top pair, you know he could have considered that he had only top pair shit kicker and an inside straight draw, and that it was about 2-to-1 likely that I had a higher pocket pair in my hand, and he could have gone ahead with a bet of approximately half the pot,say 60k into the 113k pot. This would have brought his chip stack from 384k down to 324k, and I would doubtless have raised him allin, and he could have insta-folded there. With 324k chips and still a solid 2nd-place stack, this would have left his Tournament EV at $5196. So he could have made this half-pot bet on the flop, and I'm still going to fold my AK (33.3% of the time) or my AK/AQ (50% of the time). So his TEV of betting half the pot instead of the foolish massive overbet allin looks much better:

With a hand range of AA-JJ and AK, I have the big pair 66.7% of the time, I raise allin on the flop, and he folds, leaving him with a TEV of $5196. The other 33.3% of the time I have AK and I still fold to his half-pot bet, giving him a TEV of $7378. So this equates to an overall TEV of $3465.73 + 2456.87 = $5922.60.

With a hand range of AA-JJ and AK or AQ, I have the big pair 50% of the time, I raise allin on the flop, and he folds, leaving him with a TEV of $5196. The other 50% of the time I have AK or AQ and I fold to his half-pot bet, giving him a TEV of $7378. So this equates to an overall TEV of $2598 + 3689 = $6287.

As you can see, whether my range includes AQ or excludes AQ, the strategy of Villain betting just half the pot on the flop and then folding to any push by me dominates his silly allin overpush, leading to a higher TEV for him in either case. So even if you think him check-folding to me after flopping top pair and an inside straight draw (admittedly, that seems a bit weak to me as well) is too wimpy for the chip leader in this spot, the allin overpush on the flop was truly the worst of all of his available options.

Flame away.

Have a great weekend everyone. I should be in the FTOPS Main Event on Sunday night at 6pm ET, looking to make a big run in the first ME I have played in I think this entire year in the FTOPS.

Bitches, Bracelets and the MATH

Man am I glad I don't have to work with the bitch who got on the subway right behind me this morning. I mean, here we are, all packed in like sardines as is the universal constant for rush hour in Manhattan, and this bitch gets on right after me and starts pushing her way through the crowd. And by "pushing", I mean throwing elbows aggressively and angrily left and right at anybody standing in her way. All so this bitch could -- what? Get to the next overcrowded sardine spot 3 or 4 feet across the train car. She nailed me good in the back a couple of times as she raged her way to the other side of the train, and when it was all done, there were probably 5 or 10 passengers all looking at this bitch to see what the hubbub was about, including me. She must have sat there angrily shaking her head in the "no" sign for a good minute or two even after arriving at her equally-packed destination point. And I was just thinking: how the fuck bad must this bitch's life be to be acting like this in a perfectly innocent situation that affects everyone equally, at 7:30 in the morning on a nice day on the first day of spring in the best city in the world? Then I remembered I don't live in Las Vegas. But, other than the "best city" part, what must be up this bitch's ass so early in the day? First I'm thinking maybe she just really hates her job. But as someone who has worked jobs that I fully hated, despised with every ounce of my being (hint hint...law firm), I just don't see that person acting quite like that. That was typically more of a depressed, mopey attitude for the morning commuter, not the raging bitch thing that this whore had going on first thing in the morning today. No, this struck me as more of a family thing. She's probably got a husband (she looks to be about 40, 45 years old) at home, who's probably nailing the 18-year-old babysitter, or worse yet the 50-year-old next door neighbor, all because his own wife has turned into such a fucking bitchcow that he can barely stand to be in the same room as her. She must have something going on at home that angers her so much, that she is showing up at the subway at 7 fucking 30 in the morning already pissed off to the point of launching physical violence on numerous fellow citizens just because she has the slightest excuse to do so. I can't imagine being that kind of bitchwhore, or having that kind of life that I'm that kind of angry that early in the day for no good reason. Poor little bitchcock. And poor little bitchcock's co-workers, as she looked dressed for some kind of an office job. I can only imagine working with that scumbitch has got to be like playing at a full tilt table with me or Chad when we're fully tilted and raring to go in the chat. Hah. Love that fuckin post man.

OK back to poker....So you want to hear something about me, that is not only just about the dorkiest thing about me, but probably the dorkiest thing you could ever hear about anybody, and then how it relates to my poker play? Well here goes (avert your eyes if you don't want your opinion of me as mister cool n smooth to be shattered forever)....

I won the New Jersey Math League as a teenager, an annual competition of all the students in the entire state at tricky and complex math problems, given once a year state-wide. And if that wasn't enough, I won it twice. I don't know if this has happened since, but at the time nobody connected to the Math League exam had ever heard of someone winning this contest back to back. But that was me. I was also on my high school's math team in my junior and senior year of high school. Yes, the math team that won all of Burlington County and placed third in the state (I can't help it if we didn't have a great cast all throughout!) both of those years. And I was always the anchor of the team. You could hardly come up with a math question that I couldn't quickly figure out how to solve. By the time I was done with high school, I had scored a 5 on the Calculus BC advanced placement exam, and I had placed out of all math requirements at Georgetown. And you know what I did with all this great math experience once I got to college?

I never took another math class again. Despite being really awesome at math all growing up, I never took math after high school. It just didn't fit in with all the rest of the more well-rounded courses I was taking in college, and it's not a decision that I regret a bit. But, the downside is that today, more than 15 years later, I have forgotten the "how" behind many of the more complex math-type of problems, including difficult probability questions, combinations, etc. These are things that I'm sure I could re-learn with probably just a few days of study since I once knew them and was able to combine and manipulate the formulas and concepts like a master chef knows just what to sprinkle and throw in to create a delicious entree or dessert. But nowadays, after upmteen years of not practicing, not even thinking about how to calculate some of the finer complexities of probabilities, you know what I am left with? Very little ability -- or desire, really -- to actually do the computations required to determine with any exactitude the probabilties I often face at the poker table. But one thing never went away -- I still have really, really fine math instincts. I may not care to remember how to calculate exactly the probability, say, that I am dealt KK when another player at the table is dealt AA. But I know it's rare as balls, and I bet I could estimate that probability just based on instinct off the top of my head a heck of a lot closer than mostly anyone else who doesn't already know the answer. That's what I am nowadays at the poker table, math-wise. I may not be in the least bit willing to figure whether a given probability is 20.3% or 20.7%, but I am usually able to "guess" that probability off the top of my head to, say, "somewhere just slightly more than 20%" and usually am right on.

All this is to say, when I'm at the poker table, although I'm not one to do many actual calculations, I generally know with pretty good accuracy how likely or unlikely something really is, moreso I find than mostly anyone but the very best players who have also taken the time and energy (and have the ability) to really understand the math behind this game we love. And this kills my game sometimes as a result. You know how? Because sometimes I get too attached to what I just instinctually know to be true about the probabilities, without regard to the betting action I have actually seen at the table in a given hand. And this is something I have got to work on and get better at. For example, I am just about the last person who will ever lay down the pocket Kings in the small blind, say on a raggy board, even when I can just tell my single opponent in the big blind is playing his hand just like he has Aces. I am just too in tune with how truly unlikely it is that I would be dealt KK in the small blind, nobody behind me would be dealt anything playable, and the big blind would just happen to be dealt Aces at the exact same time. Again, I don't do the calculations, but my head instinctually tells me -- and I know this is true beyond any doubt without sitting down with a calculator or pen and paper -- that we are talking about less than 1% here. Probably more like a third of a percent. Or less. It's rare enough for two players to be dealt KK and AA in the same hand at the same time. But for this to happen in the small blind and big blind, and to have nobody else have anything worth playing, and to have the flop come all low cards, it's just incredibly rare. And because I seem to have a great instinctual grasp of just how rare that really is, I tend to talk myself out of believing that the super-rare event could actually be happening here when I'm sitting at the table. It's just too unlikely, I'll tell myself, and I'll end up calling off all my chips even when by the end I basically know the guy does in fact have the Aces. And sometimes I feel like if I didn't have such a good instinctual grasp of the math, I might not be so unwilling to believe I am beat in situations like this.

Such was the case last night in the midnight bracelet race on full tilt, which I again satellited in to, for the second straight time in the 9:20pm ET $14 rebuy sat with only one initial rebuy. Actually, to be accurate, I bubbled in this satellite thanks to some ultra-annoying collaboration between two players who were obviously friends, with the one big stack to the short-stacked guy's immediate right folding his small blind to the friend's big blind twice instead of stealing to knock the small stack out, and then that same big stack raising big against my big blind on the next hand on those same two separate occasions. The J2o and 64o I had in both instances made it difficult for me to do anything about it, and by the end there the blinds were so big that my own stack quickly went from 4th out of 6 remaining down to 6 out of 6 remaining. But, I scored just over $100 for my efforts in going out in 6th place with the top 5 players winning the full $216 buyin, and I figured, at just $100 for a 10% chance to win the 2k prize package in the midnight bracelet race, I would go ahead and do it anyways.

Anyways, I didn't get shit for cards through most of the first hour of this thing on Monday night, seeing a despicable 5% of flops through my time in the tournament, and then with about 2 minutes left before the first break, I look down to find QQ in the big blind. First position limps UTG, and when it folds around to me, I pop it up significantly, about 4.5x his bet, since I want the limper out of here because UTG limpers generally scare me. He pauses briefly and then called my big raise. Sign #1.

The flop naturally comes out a rainbow 873. I've got the big overpair here, and I need to test the UTG limper to see just how strong he really is. I bet out the size of the pot on the flop, now about 1200 chips of my 4000 or so remaining chipstack. He pauses briefly and then calls. Sign #2.

Before the turn card even came out, I had decided I was going to check it and see what he had to say about it. It came another offsuit rag, and I checked. He paused briefly and then checked behind. Truth be told, if he had gone allin I was going to call him anyways, but he didn't bet it. Then the river came a Jack. I checked it, knowing full well that my fucking Queens never win shiat, and I was completely unsurprised in every way when my opponent responded by moving in his last 2400 chips or so, just enough to cover me. Sign #3.

Now, at this point, I knew in my heart of hearts that I was beat. The guy had limped UTG and then called a big raise from me preflop. That right there screams out "big pair! big pair!". It's not like I don't know this. I did know it. I knew it right then and there in real-time last night. Then when he called my big bet on the flop, that iced it. I knew I was up against Kings or Aces. There was just no other way. I know plenty of donks (the majority of online poker players out there I would say, in fact) who would make the preflop call with AK. But would most also call a large potbet on the raggy flop with just the AK high? Nope. Not the good players anyways. So in my heart, I knew this guy had Aces or Kings.

But that was when those math instincts deep in my brain started kicking in. And this has happened before, many, many times. Suddenly there's this voice in my head saying "Come on, Hoy (ok I don't really call myself "Hoy", but still). What are the odds that this dude just happens to have Aces or Kings, at the exact same time that you get your only premium hand of the tournament with Queens, and that the board comes all raggy like this to boot?" And because I've always had these great math instincts, I have a very good idea of the answer. Do I know it exactly? No. But I know we're talking about in the low single-digit percents here. Like, the percentage of a 1-outer-with-one-card-to-come kind of chances. Now, obviously when you play several hundred hands of poker a night, even something with a 2 or 3% chance ends up happening to you, almost every night in fact. And lord knows we've all lost KK to AA, QQ to KK, etc. more times than we can count (or in my case, KK to AJ, QQ to AJ, 99 to AJ, 66 to AJ, AK to AJ, etc.) But nonetheless, when my math brain starts talking to the rest of my head, I can find it very hard to ignore. And there was me last night, as I've done so many times in the past, letting my math instincts convince me to "go with the odds", instead of paying fucking attention to all the fucking evidence there was that this was, in fact, one of those 2 or 3% of times when my pocket Queens were in fact beat from the getgo. I called, he showed his pocket Kings, and IGH on the second to last hand of the first hour. What a waste of about 3 1/2 hours of satelliting into and then playing in this thing. What a waste of a good read, and what a waste of an hour of solid, patient poker play, finally waiting until I hit a cheap flop hard and was able to double up despite sitting there like a donk and seeing almost no flops for the better part of an hour online, in the dark, after midnight with my wife and kids all asleep around me.

So that's it. I've made this mistake in this exact way too many times now, and today I resolve to finally do something about it. I, King Hoy, hereby proclaim (trumpets sounding in the background) that I am not going to let my math and probability instincts talk me into making calls that the evidence otherwise indicates I should not make. If I am sure I am beat from the action on a hand, I will hereby stop using the fact that I am very good at quickly just "knowing" the chances of something fairly remote to make a decision for me that I otherwise know is wrong. Now all you donks out there, try all you want to push me off of hands because of this. I'll read you like a book and take your chips. But in the specific type of situation I am talking about here, when I know I am beat in a very rare, hard-to-believe, "big blind special" or big-pockets-over-big-pockets type of situation, I've made this mistake for the last time. You have my word on it.

OK briefly I want to review last night's Hoy tournament, which had 21 runners including at least two new faces (to me, anyways) in Shag0103 and Nickedemus (hope I am spelling that one right). I got no cards, saw almost no flops, and ended up going out I think in 13th place. More importantly, however, is that I outlasted both Fuel55 and Bayne, my two closest competitors on the 2007 Hoy money leaderboard, meaning that my top spot was safe for another week, so I felt ok pushing with what I think was just Ace-high on a paired flop against a preflop raiser who I think turned out to have a pocket pair and held on to win. I don't remember who got me, but I donked it as I recall, so way to go whoeveryouare.

In the end, it was Hoy newcomer Shag0103, complete with icon of Shaggy from Scooby Doo fame and all, busting in 3rd place and taking home $84 for his efforts in his first ever Hoy cash. Shag, if you have a blog let me know in the comments and I will link you here. This left fellow bloggers Zeem and Byron to battle it out for heads-up play and for the latest weekly Hoy title, with Zeem starting off the battle up 22k to 8k in chips after Zeem knocked out Shag in third place. These two fierce competitors battled it out two-handed for a good long while, and the 20- or 25-minute clash included some nice consecutive hand-winning streaks by both players that saw Byron take a more than 2-to-1 chip lead from Zeem, and then Zeem getting himself back to his own 2-to-1 lead on at least one other occasion during the tussle. Eventually, once Byron had once again regained the chip lead, Zeem raised preflop, and Byron moved in with what turned out to be KQo. Zeem quickly called with his A6o, the Ace held up and Zeem once again was up 18k to 12k. Five minutes later, Zeem's A9 held up over Byron's pocket 4s when the 9 on the flop sealed the deal, and Zeem had won his first Hoy of 2007 (and I believe at least his second overall). So it was Byron coming in second place for $126, and Zeem taking down this week's tournament along with the $210 prize to go along with it. Congratulations to all three of this week's cashers, including again Shag in what I believe is his first ever Hoy tournament, and I hope to see you all back again next week as the field continues to try to dethrone the long-reigning leading 2007 Hoy moneywinner through almost a quarter of the year so far:

1. Hoyazo $472
2. Fuel55 $458
3. Bayne_s $410
4. Zeem $330
5. VinNay $310
6. Wigginx $288
7. Manik79 $252
8. Byron $234
9. Omega_man_99 $210
10. bartonfa $180
11. Santa Clauss $170
12. Smokkee $162
13. Chad $120
14. Ganton516 $114
15. NewinNov $90
16. Shag0103 $84
17. Columbo $80
17. PhinCity $80
17. jeciimd $80
20. l.e.s.ter000 $72
21. Julius Goat $60

See you next Monday for Mondays at the Hoy!! Tonight I will try to make the Wheatie at 8:30pm ET on pokerstars (password as always is "monkey"), and I should otherwise be in the 9:30pm ET bracelet race on full tilt, which I believe tonight is just straight-up no-limit holdem, even though nobody ever wins these things when it's just winner take all like most of the regular 9:30pm races are. But I can't stay away, on the off chance I can get lucky early and often and maybe hit something big. I still have the Any Two Cards post half-written, but it looks like that is going to wait for tomorrow once again. I'll still be here then if you will.