

http://www.pokerschoolonline.com/rep...ash=62A1FB5BD1
I posted this hand earlier, but I can't find it. I'll try again, maybe I did something wrong. Above is the link to my hand through the replayer. I don't know how to get the replayer to automatically come up with this new thread. Maybe once this is posted it will. If not, click on link above after you read through the problem. You don't really need to see the hand, the questions are below, with the math calculations. Situation – 27 man mtt, top 5 get paid – 15 players left, 4th level – 7 minutes until blinds double. Hero has 1100 chips, BB has 1700 chips. Blinds 50, 100. Folded to hero on the SB with J8 (11BB stack) against a semitight opponent (17BB stack) that hero thinks villain may defend his BB with any A any broadway any pair 77 plus. This means he’s calling 25% of the time, possibly less given his stack size and stage of tourney. Giving these stats, and reads, should hero shove? Did hero correctly estimate villain’s calling range given villain’s stack size? Would villain tighten up or loosen up with this stack size, and no reads on hero? What if villain thought hero was a solid player, playing 27/17 (vpip/pfr), no steal reads? I thought the above hand was a +EV shove. These are situations that should be studied prior to being faced with them. Off the top of your head, is this a +EV play? If not what would be the minimum hand strength not including suited cards, needed to shove? Below are my calculations. I’m not sure if it is the best way to figure this problem out, but I believe it gets to the correct answer: J8 has 34% equity given the hands I think villain will call with. He will call 25% of the time. 34 x .25 = 8.5 (hero) pot will have 1150 + 1150 = 2300 66 x .25 = 16.5 (villain) villain needs to invest 1050 to win 1250 (needs 46% equity, EV wise) 75% of the time hero wins 150 (75 x 150) +112.50 8.5% of the time hero wins 2300 (.085 x 2300) +195.50 16.5% of the time hero loses 2300 (.165 x 2300)  379.50  71 EV I was sure K9 would be +EV, but: K9 has 38% equity 38 x .25 = 9.5 (hero) pot will have 1150 + 1150 = 2300 62 x .25 = 15.5 (villain) 75% of the time hero wins 150 (75 x 150) +112.50 9.5% of the time hero wins 2300 (.095 x 2300) +218.50 15.5% of the time hero loses 2300 (.155 x 2300)  356.50  25.50 EV With a 9BB hero stack, (finally an almost break even situation, but does villain loosen up?): K9 has 38% equity given the hands I think villain will call with. He will call 25% of the time. 38 x .25 = 9.5 (hero) pot will have 950 + 950 = 1900 62 x .25 = 15.5 (villain) villain needs to invest 850 to win 1050 (needs 45% equity) 75% of the time hero wins 150 (75 x 150) +112.50 9.5% of the time hero wins 1900 (.095 x 2100) +180.50 15.5% of the time hero loses 1900 (.155 x 2100)  294.50  1.50 EV Should this deter me from stealing on SB over a BB that will call 25% of the time? Math says yes. Looks like this will only be +EV against a NIT. I also figured K9 (J9 was EV) against a loose player that will call with the top 70% of hands: K9 has 54% equity given the hands I think villain will call with. He will call 70% of the time. 54 x .7 = 37.8 (hero) pot will have 1150 + 1150 = 2300 46 x .7 = 32.2 (villain) villain needs to invest 1050 to win 1250 (needs 46% equity, EV wise) 30% of the time hero wins 150 (.3 x 150) + 45 37.8% of the time hero wins 2300 (.378 x 2300) +869.40 32.2% of the time hero loses 2300 (.322 x 2300)  740.60 +173.80 EV The villain’s call is also correct (EV wise) if he feels we will be shoving with the top 45% of our hands. He is getting 46% equity needed to break even (EV wise). All that being said, I feel knowing your opponent, and knowing if he is willing to risk crippling himself in this situation, plays a big part in your decision to shove, if on the SB. The same is true on the BB, is your opponent willing to end his tournament with this shove? I welcome any and all feedback  I hope this isn't too long or has too much math. 




On top of all that there is the ICM effect: The chips you stand to lose are more valuable than the chips you stand to gain, so you need to be somewhat tighter.
On top of my head, you shouldn't start pushing ultralight until you're down to about 6BB. K9 is probably good around 78BB. How to embed the Replayer: It's step 7 in the Replayer instructions 




This particular type of calculation isn't my strong area, but I'll figure out the math later, if none of the evaluators do it before me. I'm not sure exactly how much ICM considerations influence your shoving range here, so maybe some of the sit & go specialists can weigh in on that.
I think this is a EV spot, though, from my initial attempt at the math on my notepad, which kind of surprised me, since I would have figured this to be borderline +EV. The simple solution is to tighten up a bit. Maybe cut 5 hands out of your range to make your shove +EV, and maybe cut out another 5 hands for ICM considerations. It's not a precise solution, but it's simple and effective. 




Actually, for this spot the BB is only going to be "right" in calling this shove on a WAY TIGHTER range than the one postulated. Risking the loss of 1100 of his 1700 versus an open shover is way too damaging to do on a near 25% range.
But given the info here, that Hero BELIEVES BB will call on Any A, Any 2 broadways, and pp 7+, THAT is the operative question...afterall, sometimes an opponent will not KNOW he should be way tighter So... 25% of the time Villain calls. 75% of the time he folds. when he calls, he holds a 66/34 equity "edge'. 75 x 150 = +11250 chips won when Villain folds. .66 x 25 = 16.5 times villain calls and hero loses 1100 = 18150 .34 x 25 = 8.5 times villain calls and hero wins 1100 = +9350 .....20,600 won in various scenarioes ....18,150 lost in various scenarioes  ......+2,450 / 100 = +245 cEV I think the "skew" in your numbers is occuring because you have the Hero LOSING 2300. He starts the hand with 1100, and cannot lose more than that. Also, you show him winning 2300, but 1100 of that 2300 is his already, so he is only "winning" 1100. PLUS... Not to be pendantic, but if the Hero STARTS with 1100, posts 50, and shoves to open, the BB has posted 100, so will need only CALL 1000. 2300 you show is considering the Hero to be doubling up, PLUS winning the amount of the BB, but the BB is part of pot already, and reduces the amount the Villain must call...see? the action ACTUALLY proceeds: Hero = 1100, 50 is posted in SB (1050 behind) Villain = 1700, 100 is posted in BB (1600 behind) Pre Flop Pot = 150. Action folds to hero, who shoves allin Pot = 1200 Villain CALLS 1000 Pot = 2200 




Dan Harrington’s solution may be right for this problem hand
I dusted off my Harrington on Hold ‘Em Volume 3, and found this on page 153 (problem 21). Dan is on the BTN with 4800 (AQ), blinds are 400, 800, 8 players at his table, 50 players left, 40 get paid. UTG has 18000, opens for 2500, and is folded to BTN. Should he shove or not? Dan’s math goes like this: (to simplify this we’re going to assume SB and BB are folding – however because of combinatorics, there is a 3% chance of them holding QQ+, and 4 betting). Dan surmises that UTG will call his shove 100% of the time given the pot odds. He Ranges UTG, 90% = 88+, AJ+, and KQ, 10% = bluff (he sets bluff on 98s, for his calculations). OK, that’s the setup, here’s the math, the way Dan would do it. He doesn’t consider his loses, just his wins! Dan wants to see if his stack would be bigger by folding or bigger by shoving. Pot is 10800 = 1200 + 4800 + 4800 90% = Dan’s equity is 46.5 (I poker stoved it, it came up 47.4) .9 x .474 x 10800 = 4607.28 10% = Dan’s equity is 60 (I poker stoved it, it came up 59.3) .1 x .593 x 10800 = 640.44 Dan’s total equity when shoving is, 4607.28 + 640.44 = 5247.72. That’s 447.72 better than folding. He continues to state that even without considering a bluff, it’s still +EV, but you should always consider the bluff as a possibility. Lets apply this math to my problem: I’m not using the chip stacks from the original replayer hand. I’m using the chip stacks from the problem presented, because in a game situation you need to round off to figure out problems quickly. Pot is 150 75% = hero’s fold equity .75 x 150 = 112.50 Pot is 2300 (when called) 25% = hero’s equity is 34% .34 x 2300 = 782 Hero’s equity when shoving is, 112.50 + 782 = 894.50. Using Dan’s math, it is a –EV play. Horrible68 has a good point when he brings up ICM (not familiar with the term, but from the explanation Horrible68 gave, I understand it), is gaining 14% of my stack worth losing the tourney? That’s another point to weigh. I’m guessing that when you consider other factors, like ICM, that would put addition pressure on the villain. JDean also feels that this pressure will tighten up the villains range drastically. Being that I’m well below average chip stack (2700) and needing to chip up to get through another orbit, it might be correct to shove. I’m Still in a quandary on what to do with this hand. Well that’s poker! Thanks PanickyPoker, I felt the same way about this hand (+EV), until I did the math. Thanks JDean, you put a lot of time and effort in your reply. I think I’ve seen the breakdown you did in other poker books. But which math is right? I understand one way considers total pot value and the other considers effective chip stack. I’ve only been studying poker for a few months, and find it very intriguing, and frustrating. Thank you all so much for your input. I hope the discussion continues. 




Again...
You math skew seems to come when considerng that the Hero will lose too MUCH when he loses, and doesnt win ENOUGH when he wins... Here: 75% = hero’s fold equity .75 x 150 = 112.50 out of 100 hands, 75 of 'em villain folds. every time villain folds, hero wins 150 (the blinds). so that is 75 x 150 = chips won on 75 of the hands tested. Now... 25 of the 100 hands tested the villain calls. 34% of that 25 times hero wins 66% of that 25 times, hero loses When hero WINS, he wins only 2 times his stack, or 2200. NOT 2300. Hero 1100 in stack total, posts 50. 1050 behind. open jams 1050, making the pot size 100 + 50 + 1050 = 1200. total call amount for villain = 1100 (50 posted + 1050 behind) villain has posted 100 already, so must only call 1000 more. He calls, pot = 2200, not 2300. .34 x 25 = 8.5 times hero WINS 1100 .66 x 25 = 16.5 times hero LOSES 1100 8.5 + 16.5 = 25 times the villain calls...see? 8.5 x 1100 = +9350 16.5 x 1100 = 18150 and... This is where I made MY "mistake"... If I am only considering the amount the hero wins when he takes the pot down, and assigning this as 1100 for the double up, then when I evaluate the amount he WINS when the blinds are folded to him cannot "include" the 50 he posted. Therefore... 75 x 100 = 7500 (won, when he takes down the blinds) NOW... ...7500 .+9350  .+16850 .18150  .1300!! 1300 / 100 = 130 cEV. so while i'm "complaining" that you are adding 100 extra chips to the pot because you are not considering the fact the BB already has 100 in, I was doing the same thing and "creditting" the SB with winning an extra 50, over his posted 50. Doh! Sorry for misinterepretation. (btw...2300  894.5 = 1405.5. if you lower that to make it 2200  894.5 you get 1305.5. since Dan is working on estimates, that is right on what I was arriving at, when you divide it across 100 trials.) 




Here's my math:
According to the range estimate you provided, the villain will call 25.3% of the time, and of this time, you'll have 35% equity. The rest of the time, you'll win the initial pot. Using the effective stack of T1100 before blinds are posted with no ante, and assuming that the hero has all combos of J8s and J8o since that seems to have been unspecified, here's how it breaks down: 25.3 times, you'll have 35% equity in a T2200 pot. 74.7 times, you'll have a final stack of T1250. [(25.3 x .35 x T2200) + (74.7 x T1250)] / 100 = T1128.56 Since you started with T1100, this shove should be +EV by roughly 29 chips, or a little over a quarter of a big blind. I was right to begin with; it's borderline +EV. This should be the bottom end of your equilibrium shoves in this spot, and you might actually want to tighten them a little bit for ICM considerations (again, not sure how those factor in, if at all). 




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Since he is still far away form the money, and since he is short enough that he has little chance of getting there on his current stack, he NEEDS it more. It is a matter of 'go big or go home" here. Were it 6 left, 5 get paid, and there are a couple stacks near his in size, ICM tilts toward a fold more often...simply because one of the other shorties may "stand", getitng him itm. THEN it would be more a matter of cashing SOMETHING of a return for the event, so you should be less willing to go bust on the same relative size stack. So if you are showing +29, I'd go for it with 15 left... TBH though, we've all arrived at such divergeant answers, that I'd question +29...or 130! Fact is...I still think a CALL RANGE for BB is much narrower than 25%, and I think that alone tilts me towards "going for it" here more often than not. If that 25% is rock solid though, I think I just have to "accept" the fact I have a loose cannon in the BB, and fold about as often as I would if the BB were such a LARGE stack that losing a double up to me would not really hurt his chances of running deep (like a 20k stack or so). 




I also think that the stated calling range is certainly off of an optimal calling range by a wide margin, but some people play that way, so I didn't bring it up. I wouldn't say that calling with 25% is totally loose cannony, since I've actually seen people call shoves on deeper stacks than these with well beyond 50% of all hands, to which I say, WTF. It's an awkward 25% as well, since it's too broadwayheavy and way too unsuited aceheavy.
The great thing about equilibrium shoves is that your opponent loses money when they play tight because they don't call enough to win enough to make up for the blinds they're folding, and when they play loose because they're behind to your range. So in this spot, it doesn't matter what their stats are when deciding if the spot is +EV or EV because it's always +EV. But the more they lean toward either end of the spectrum, the more they lose. 




PanickyPoker posted a math solution that is the same as Dan Harrington’s math.
I’m sorry the following line in my original post is a bit ambiguous, and it may lead the reader to conclude that the stacks are before the blinds were posted: Hero has 1100 chips, BB has 1700 chips. Blinds 50, 100 The next line however states: Folded to hero on the SB with J8 (11BB stack) against a semitight opponent (17BB stack) As a clarification, when I wrote J8, and didn’t specify suited or not, it’s just because I always distinguish the two by J8 or J8s. Also there needs to be a slight correction to the math. Panicky was under the assumption that the SB had 1100 before the blinds were posted, if so the pot would be 1200 not 1250 when hero shoves: [(25.3 x .35 x T2200) + (74.7 x T1250)] / 100 = 1128.56 – original formula [(25.3 x .35 x T2200) + (74.7 x T1200)] / 100 = 1091.20 – corrected formula = 41.20 +EV. 1091.20 is greater than 1050 (if you fold) so it’s +EV. You can’t count the 50 blind that you put in the pot. To follow up Panicky’s math with this new information, the formula now reads: [(25.3 x .34 x T2300) + (74.7 x T1250)] / 100 = 1131.60 (1131.60 – 1100) = 31.60 +EV Harrington’s math method (correction from my last post): [(25.3 x .34 x T2300) + (74.7 x T150)] / 100 – I used this formula, however it should have been: [(25.3 x .34 x T2300) + (74.7 x T1250)] / 100 = 1131.60 – The same as the formula Panicky presented. Thanks Panicky, I think this is the correct way to figure EV with this hand. JDean, I think the reason there is quite a different outcome between this formula and ours (which had similar results) is that this one doesn’t include loses. But I still feel that I’ve seen your formula in poker books. As a side note, in the example from Harrington’s book, he didn’t consider ICM. He wanted to double up and get deeper in the tourney. He stated that he was going for the win, and didn’t care about getting ITM. He knew he was getting called and that at best it was going to be a coin flip. Granted he was a bit shorter stacked, which may or may not have been a factor. Let’s ask him. Is he a Poker Stars pro? Thanks again guys! Keep the thread going. 




I agree with you, and as stated in my original text:
hero thinks villain may defend his BB with any A any broadway any pair 77 plus. This means he’s calling 25% of the time, possibly less given his stack size and stage of tourney. Others also feel the same way. JDean thought the villain would be 'way tighter'. But Horrible68 thought that because of ICM we should fold. I love the discussion and I'm sure this topic will get a mixed response for and against the shove. Anyone out there want to take a look at this from the villains viewpoint? You're faced with a crippling shove from a solid player from the SB, with no steal reads on him. It will cost you 65% of your stack. What do you do? To see the exact stack sizes and stage of the tourney, check page #1 of this thread. 




BTW...
For reference I checked my Harrington Grey book (Vol 3). The hand in question you cite is on page 153, Problem 21 "Calling With Low M"? If so, that is pretty different from the hand posted here. It differs thusly: 1) That is considering a "stand range" versus an open raiser, vs. a shove range to get a call. 2) That is an exercise in first in vig, versus calling or shoving. 3) That is an exercise in ranging effectively (and the hero in the hand makes a "mistake" by ranging the pfr too tightly per Harrington). The reason why I think that MIGHT be the hand you refer to is the math done for it. situationally though, it this is a VERY different hand. So can you possibly put up the HoH problem number you are refering to? 




This seems to be making misleading assumptions of what ICM is. ICM attempts to determine optimal shoves, calls, and folds given the impact cEV has on $EV. ICM (Independent Chip Modeling) and ITM (In the Money) are different terms. 'Going for the win' and folding +cEV spots based on ICM considerations are not mutually exclusive.





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They work in our FAVOR here beause we are exercising first in vig. Our BB opponent is so short stacked that he cannot risk us shoving the top end hands with a call, because he would be left crippled. Even if he "suspects" us of being light here, folding (by him) still leaves us well behind him in chip count, and with less of a chance than he has to make it thru 10 more for itm. I had a similar hand situation that played out for me in a Cowboy's Corral Event recently. I was BB with blinds at 1k/2k on an 8500 stack. We were final table, 8 handed. There was 1 stack at about 8k, and 1 stack around 9500, the rest were in the 13k+ range, with big stack around 24k. 4 got paid. It folded thru the BTN, who was a player I felt I had a pretty "solid" idea about his play style. This guy (Yes Dougie, it was you!) is a PSO'er named SnafuinMd. Doug is a pretty "aware" player, and also highly aggressive if the situation warrants it. He open shoved the button for his stack of around 14k. SB folded, and I looked down to see 98d. Now this was a case where I had been pretty prone to mucking my BB to big chip moves. Doug also knows enough about me that I am not really going to CALL for too much of my stack with a "weak" hand, and that I recognize committment level for my stack. I know enough aobut HIM to know he knows that about me too... With that said, I was able to actually REMOVE much of the "top end" of his range BECAUSE he shoved. If he had held a pretty strong hand, He's much more likely to try playing me post flop. I also did not harbor any illusions that I was "ahead" with my 98d, the thing to factor though was (in my mind), "how FAR behind am I likely to be"? I don't think Dougie will jam AT+, because that has too MUCH chance of being ahead of my range. I also do not think he is jamming 88+ for the same reasons, altho I'm not completely sure of 88. KQ/QJ, I'm also on the fence...those are exactly the hands Dougie might jam to pressure, but also might fall into the "enough value" thoughts that he'd want to take a flop with 'em. Rag Aces though, are just the sorts of hands he might jam in hopes I just fold, as are pp 2277. I doubt seriously he is jamming ANYTHING LESS than T9, so no matter what, there is not ANY of his range I am ahead of, but with blinds and antes putting a near 4k preflop pot out there, I do not THINK I "need" to be ahead. I am looking for a 40/60 basically, and will consider that "good enough"... If I were closer to the bubble with the same stack distribution, I would not take a 40/60 underneath position, but 4 away, with only 2 other stacks in similar "danger zone" to my stack means I'm probably NOT folding to ITM at a pretty "solid" table. If the table were looser, or more prone to dumb "mistakes", then again, I "need" more here to go, but it wasn't... So the "working range" I had for the open shove Villain was: pp 2288, A2A9, KQKT/QJQT/JT. I'd also put T9s and MAYBE J9s in there. Only AFTER the fact did I find out my "gut" did steer me to what I "wanted", which was a 40/60 stand to add 1.5 times to my stack, and have an almost certainty of cashing. My equity versus this range was: 42.75%. The results were: I flopped an open end straight draw, with a flush draw, Villain had A2s, and I missed all my myriad outs. He won the hand unimproved. I'd be interested in your thoughts on making THAT call, in that spot, on the pretty "weak" hand that I chose... 




Answers to some questions from earlier posts:
In the actual hand I was called by the BB and he held T9h, which is in the top 25.2% of poker stove hands. So the ranging wasn’t off, even though I thought he might tighten up a bit. In my original range, I thought this guy would protect with any A, so I added them and took away suited connectors and suited gappers that didn’t have 2 broadway cards. Yes, Harrington’s hand was much different I only used it for the math formula. I stated earlier that I was unfamiliar with the term ICM effect. But, it was explained to me by Horrible68 as, “The chips you stand to lose are more valuable than the chips you stand to gain, so you need to be somewhat tighter”. I’m also not familiar with the term cEV. I’ll be researching both terms, thanks. JDean hand: As far as the 98d hand on the BB, with only 4.5BB left, the pot offering you 1.5 odds, and not able to fold to the bubble – you have to get your money in. 98 suited adds up to 9% (in most cases) over nonsuited nonconnected cards. Dogs get around 4% (varies) increase for suited cards, and about 1% (varies) for every gap that’s closed, e.g. 96 if it were 97 you would gain around 1% equity. Doug is a solid player, and the, I know that you know that I know thing might not really play here. You are short stacked and he knows that your range is wider, plus you have your blind money working for you giving you 1.5 odds (40% equity breaks even). You only have one more orbit without as much money working for you (less this blind), and will need to triple up. He’s going in based on the RANK of his cards, any A, any K9+, 88+, and there are other holdings as well. We don’t need to go deeper with our ranging because with those holdings you have 39% equity. Sure you may want to have higher ranking cards for this situation, but you need to get it in now. Beggars can’t be choosers, and the price is right to boot. 




From the OP (I don't know if this has been pointed out or not, but it explains some things):
What was your starting stack again? 




So based on RESULTS, you range him as 25%? Or was it based on your reads before hand?
That is fine to range him thusly, so long as you "knew" he might go that wide preflop (I'm assuming you did have that feeling). If you analyize your play ex post facto using the RESULTS though, you will tend to misapply your data findings. Poker is a game of incomplete information, and you can only decide what to do based on the info you have at the time you decide. For instance: If you have a guy who has jammed every pot for the last 15 hands, and you catch KK and call, just because he "woke up" with AA on that 16th hand does NOT negate the validity of your decision to call...see? Fact is, I thought soemthing like that had happened...that the opponent DID call on a 25% range, right or wrong. That's why I tried to stick with your "read". No matter what "should" or "should not" be done by an opponent, what matters is what you think he MIGHT do. f he is prone to making a mistake by calling you as widely as 25%, then you must account for that in your decision. Very good read. 




More answers to questions about this hand:
Panicky Starting stacks were 1150 (hero) and 1800 (villain), in the problem that I presented. Leaving 1100 (hero) and 1700 (villain), after the blinds were posted. In the actual replayer hand the hero started with 1125 and the villain had 1710 (before blinds were posted). I rounded up the theoretical problem to make it easier to calculate. I don’t think the difference biased the outcome. JDean I ranged him prior to his call, not after when examining hands. I ranged him in favor of higher ranking cards for a shove, as opposed to hands that have playability. So A2 made the range over T9s, even though poker stove will add T9s before A2 when ranging. I could have ranged him down to 13% if I eliminated Ace rag hands, but not for this guy. Being that he called with the bottom of the 25% hand range, he may be looser than I had originally ranged him. 




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