the calculation seems highly suspect. with no money paid out of the prize pool I don't see how there could possibly be that dramatic of a difference.

in any case, his chips being worth less if anything increases the relative value of a mincash vs chip ev.

It's not a calculation it's a back of the envelop estimate. Even a tool like ICMizer only goes up to 100 players--past that it's just too complicated to calculate.

If you think about it another way, OP having slightly above average to moderately above average chips probably puts him in the top 55th percentile or so of players meaning he projects to finish from here about whatever place represents half the remaining player pool so whatever prize goes to that place is approximately the $EV of his stack--at this point, still gonna assume that prize value is much less than 4x. I'm sure the payouts are available if you wanted to pursue it further. To put some rough #'s I assume something like 20% remain, maybe OP projects to finish Top 10% or so with his stack--is that worth 4x? I genuinely don't know.

But it really just doesn't matter because the whole premise revolves around the idea that a mincash is actually worth something relative to continuing to fight for pots. It's just not. I concede some players at the table may be big enough bankroll nits to forgo provably +cEV spots (which should invite wider opens from us) but we do not have to be that way--mincash is so trivial relative to winning that we still have to just go balls to the wall win those chips.

It's not at all about being a bankroll nit.

it's worth 2 buy ins!

You're imputing a value to the chips that makes the mincash almost of equal value to your ENTIRE stack. I'd argue the value of the stack is closer to the proportional chip equity (given the amount remaining in the prize pool) for medium sized stacks, but your position supports my broader point. Ill demonstrate why tomorrow using an ICM calc for a smaller number of people where the basic premise still holds.


How is materially increasing the chances of winning 2 full buy ins not worth foregoing situations that show 0.x cEV gains?

Because 1st place is over 1,000 buy ins and winning cEV furthers my goal of achieving that and choosing to forgo winning cEV at this point in favor of making mincash more likely must necessarily therefore sacrifice my chances of WINNING in favor of doing so.

There needs to be some sort of real life threshold below which fighting for that mincash becomes irrelevant. $50 is definitely below that threshold for me. This isn't a $10k event, no one cares about mincashing and nor should they and that should be reflected in continued dogged persistence in trying to win those chips, now is not the stage of the event to become a nit.

And the probability that you'll win first place, or second place... or all of those pay spots is reflected in the number of chips you have. if you have 4 buy ins worth of chips, and nothing has been paid out yet, your stack is worth approximately $200 - because the number of chips you have as a percentage of total chips in play serves as a rough approximation of the weighted probability of all possible outcomes.

If chips are worth proportionally what people paid for them (before any payouts) 0.2bb's of cEV is worth about $4.

You want to make the case that 400k in chips is actually only worth 2 buyins. Ok. So you're suggesting that 0.2bb in cEV is worth $2.
I disagree but those numbers into perspective.

The mincash is $100. if you reduce the probability of winning $100 by any more than 2-4% by entering the pot in a spot that shows a 0.2bb of cEV, you're just losing money.

It has nothing to do with being nitty and trying to avoid conflicts. You're choosing a play that is both higher variance and lower $EV.

OK, go ahead and be content with mincashing, see if I care.

What kind of a response is that? You're willing to make huge detailed posts explaining the merits of a spot that shows a 0.2bb cEV gain while reaming people out for downplaying the significance of it,

but then you want to turn a blind eye to a common scenario that's worth far more in $ev because you're too strong and brave of a player to concern yourself with 2 buy ins worth of value?


it may not apply to this hand because you cover the guy who 3bet by a fair margin, but even still it carries implications wrt how HE should be responding to your bets.

because now if he's making the decision to call your river bet, he has to do a lot better than break even cEV since when he calls and loses, it usually is what makes the difference between winning the additional 2 buy ins and not winning the 2 buyins. and that's not a trivial factor considering his entire stack is worth about 2 buyins.

It's the kind of response that should imply I'm tired of debating the merits of forgoing +cEV opportunities up in order to guarantee I win $100, thus preventing me from continuing to win chips and perhaps win $50k+. That's what this entire discussion boils down to.

Look, I'm not even saying you're wrong in theory it's just--c'mon man, it's $100 bucks. Who cares if that's 2 buy ins or a 100% ROI--I earned 100% ROI using a buy-1-get-1 free coupon at McDonalds the other day, and I still walked out unsatisfied.


This hand is actually an amazingly interesting spot especially postflop where OP could've done a million different cool things (donk ship turn, bluff river, et al).

how should this crusher be altering his approach now that he's almost locked up a $100 prize?

Imagine thinking preflop is important

You're playing a $50 tournament and you don't think $100 is important?

More importantly, you're dwelling on the significance of preflop decisions that are worth < $5 by your metrics, and yet you don't think that a 10-20% increased chance of winning $100 is important?

You're not being consistent.

What does it mean to say that maybe i'm right in theory? Hand analysis is always theory. You're the PIO solver guy. You're the one emphasizing the significance of small edges, and how overlooking them isn't a tenable option in todays games.

This is something that comes up very, very often and not accounting for it is a HUGE leak.

This is the sentiment of the side you're choosing.

Nope, I think winning $50k is important and I don't give a rats ass about some token $100 "thanks for playing" prize. You think not winning $100 in a single special event is gonna have a big effect on one's winrate?

Notice I didn't say these considerations aren't valid in smallerm ordinary events. This is a special event--it requires special considerations, like not caring about mincashing.

Nope, I think maximizing my chances of winning, not merely mincashing, are important



If the buy in were $5k or higher meaning the mincash meant something you'd be right. Sure, are chips are changing in value--you're absolutely right. The same phenomenon is happening here to a very very small (essentially infinitesimally small) degree. You're right in theory.

But the buy in is $50 and the mincash means nothing so you're wrong in practice.

In other words, I'm being perfectly consistent. I'm advocating not passing on a .2bb cEV spot at a point in the event where cEV decisions still rule. This is not an ICM problem.

I made several posts detailing optimal preflop based on the modeled ranges I used. And TBH he could be talking about both of us.

Really what his post should say is "Imagine thinking ICM in this spot is important". That's all this comes down to--I say it isn't because I wanna win $50k, you say it is because you wanna not lose $100.

A marginally winning call to your river shove is now a loser.

Let's say you shove the pot on the river, and he has a hand that is good 40% of the time (a bluff catcher with a blocker for instance). he has a clear +cEV call. And the value in terms of chips (if they're valued proportional to the buyin) is about 4bb's. this seems like a big edge.

On the other hand, calling means he busts 60% of the time. Folding means he survives with a 20bb stack, which will result in a mincash (for arguments sake) 75% of the time. That means calling reduces the chances of the mincash (worth about 20bbs in chips) by 35%. That's 7 blinds worth of value depending on exactly how close it is to the bubble.

instead of needing to be good 33% of the time to break even in cEV on the call, you have to be good somewhere in the low 40%s when you're on the bubble.

this therefor has an impact on the ratio of your bluffs to value.

now you want more bluffs relative to value bets, and you want your value range to be a bit stronger, because he's not calling the bottom of his bluff catchers.



This math isn't perfect because chips aren't all valued exactly at parity. Your first 10bb's in your stack are for instance worth much more proportionally than 10 additional blinds in a 50 blind stack, and it's to reflect the benefits of survival. We could be more precise in the calcs but the basic premise holds true.

Well, then you're thinking about it in a highly irrational way, because money is money. They're equally important in proportion to the probability of them occurring * the value when it happens.


Yes. A huge impact. You're routinely put in these situations on the bubbles. If you were playing sit and goes and flubbing these decisions as badly as your approach would imply you'd have no shot at being a winner. In MTTs its not that big of a deal since it's only a small subset of hands that're impacted by these considerations but it's not small.

I'm not saying they're different in value to you in terms of marginal utility. I'm saying they're different in terms of their $ev. It has nothing to do with reducing variance.

I want to do both. And you need to have a sense of proportionality between the value of chips to the value of survival.

Fine, let's put some rough #'s to it.

1st place prob at least $40k in this event

$50 buy in gonna assume 4k runners.

Gonna therefore assume 700 players remain. OP has ~.215% probability of winning the event (hes got approx 1.5x an average stack)

Adding .2bb in EV gives OP ~1.54x an average stack which increases his Pr(Win) to ~.22% For a 1st place price of $40k, that incremental increase to Pr(Win) alone is worth $2.30

Now do the same exercise for all probabilities of finishing in all possible places and you see an incremental addition of .2bb is worth a **** ton of $EV--more than enough to justify continuing here. Probably a good $4.50-$5.00 in $EV depending on just how big this event got. Keep ignoring $5 $EV opportunities (immediate 10% ROI on your buy in) and see what happens.

You're also ignoring this is a special event that does not happen often, there's an opportunity cost of punting on Pr(Win) over Pr(mincash). A sum like $40k+ also has utility off the table--$100 does not. There's an implicit bonus built into winning this event you're not capturing--I can much more easily turn $40k into a whole lot more than I can $100.

Stop confusing my approach in THIS EVENT--this SPECIAL event--with a typical bubble approach in a typical small event where 1st pays 20x, not 800x+.

This is not the stage to forgo .2bb +cEV opportunities.

Basically my argument has been, in special events that don't happen often where 1st is so large relative to mincash and also so potentially impactful (meaning the prize would be impactful outside of poker--life changing $$, money for a down payment for a house, enough money to start a small business, etc), it's ok to relax strict ICM considerations around the bubble. Especially if the buy in is trivial.

You don't even need to agree with that to justify continuing here though--800x to 1st compared to 2x for mincash tells the whole story really. This is just a pure slamdunk continue (using ANY EV metric) and you're a being a huge nit if you think otherwise.

Great thread - one of the most interesting that I’ve seen for a while. Gotta agree with Eggs that up-top is all that matters in this specific event. When I’m playing the big 55 and daily marathon on a daily basis then the min-cash has some merit and I may be inclined to agree with Abadabbadabba to some extent. But in SCOOP/WCOOP, where the money up-top is astronomical compared to BI, we have to focus on going super deep. Only exception may be if we’re taking a massive shot and a min-cash would be relatively significant to our bankroll

There’s also a Series leaderboard with some pretty significant prizes for most cashes - obviously if we’re doing well here then min-cashing becomes drastically more important, so there is an exception to Eggs’s arguments validity

Yes, it's in $4-5 range. And the value of cashing is $100, in which case if continuing in a hand increases your probability of busting before the money any more than 5% it's a mistake, which it WILL be in many spots.

Do we disagree about the numbers? It seems you've now agreed that there are many spots where laddering has more than enough value to change your decisions near a bubble in normal tournaments.


Is this tournament special? $200 worth of chips in a tournament with a 40k top prize. Isn't that basically the sunday warmup? You can find tons of tournaments with similar buyins that have top prizes close to that. The fact that it has a higher top prize doesn't make it special, and definitely doesn't change the basic premise of what constitutes a winning or losing play.

As for $40k having more utility than $100…? You mean greater marginal utility? Obviously it has more utility, the question is whether it has more than 400x the utility. I think you might want to try and think about this a bit more objectively. It seems like you're just finding ways to rationalize your original position.

Increase your probability of busting over what? There's no steady state rate of busting.

By this logic, why ever play a hand around the bubble?

No you can't, and yes of course the size of 1st place makes it special.

I’m torn. Can’t remember the last time I played an mtt that had almost 1000x BI for 1st though, outside of the series events. Except for the Sunday mil, which is another tourney where I don’t care about the min-cash. 6/7/8 hours or whatever it takes to get the min-cash isn’t worth my time unless I’m in it for recreation alone. I might as well go to work for the day and earn a whole-lot more. Maybe if I played professionally then I’d look at this differently? It’s not as though we’re giving up our shot at the big money by turning down one or two close spots and if we lock-in two BI’s then we get another two shots at 55’s. Maybe the answer to this is a little more subjective/circumstantial rather than purely objective/mathematical

The probability of busting if you continue vs if you fold. Because there isn't a mathematical formula to tell you how often you're busting doesn't mean there aren't reasonable estimates to be made.

If pio introduces a bubble cruncher function you'd be able to get more reliable estimates but in the absence of these programs you don't assume these considerations don't exist.


No you can't? The last normal sunday warmup had a top prize of 30k with a buyin of 200. your chips at this point are worth about 200 and the top prize is 40k. this is materially different? This means you put aside all $ev concepts in the name of marginally increasing your chances of winning a slightly higher first place prize?

Even if there weren't other tournaments with a similar payout ratio the argument would make no sense. Money isn't special. It's the same game and the same money as when you're playing a $100 freezeout with a $10k first prize.

First bolded, actually the null hypothesis is gonna be there are no ICM considerations and its up to you to prove that there are, not for me to disprove. And BTW you open and get 3b, you better believe you have a >5% chance of busting if you ship. Guess we should fold KK pre to the 3b too? I mean we ship he snaps prob ~50% of the time we lose ~25% of the time--KK a slamdunk open/f23b in your world because of the "soft bubble"?

2nd bolded: Yes an event with a top prize of $40k for a buy in of $50 if materially different from an event w/ 1st place of $30k and a buy in of $200. One pays 800x+ to first, the other 150x.

3rd bolded: great, sounds like you're coming around to the idea the cEV rules here! And you misinterpret my argument. My argument is, the value of 1st place is so high, incremental increases to Pr(Win) are more impactful to $EV than are incremental increases to Pr(mincash). It's literally a 1st principles, as-basic-as-you-can-get ICM argument. I put rough numbers to it; you did not.

I don't even know how to continue. It seems like you're arguing in bad faith. I've gone into great depth to explain the icm consideration, and you even acknowledge it - so you shifted the argument to there being some magical ineffable quality to tournaments that pay >x buyins to first. And then you want to backtrack to say that the burden of proof is on me to show the value of the icm considerations? Which is it?


The 5% increased pr of busting is the break even point for a cev of a fraction of a bb.

A shove that shows a 10-15bb chip gain that has 70%ish equity when called (that will usually get folds) is not analogous. Do you not see why?

I feel like you understood what I was saying 10 posts ago but don't want to back down / want to get in the last word to save face.

You can come up with comparably weak justifications why every tournament is special if you really wanted to, and then proceed to use that as an excuse to take the lower $ev decision.

That isn't your argument. We've already been through the numbers of the relative value. Your revised argument was something about $50k being such a big number that it would give you the bankroll to play in bigger tournaments.

"A sum like $40k+ also has utility off the table--$100 does not. There's an implicit bonus built into winning this event you're not capturing--I can much more easily turn $40k into a whole lot more than I can $100."

I feel like you don't get that literally no one else in the entire thread (perhaps even the entire forum) thinks (with good justification for thinking so) ICM is even remotely relevant here.

I threw out some rough #'s to entertain you, no other reason.

If you wanna keep punting on +cEV spot in the "soft bubble" (again whatever that means--you have passionately "Argued" [if you wanna call it that--argument implies the other person actually cares about being right, which I am, but I don't care either way] for something 20 other posters felt was entirely irrelevant without even knowning the full context of the hand--seriously, what is a "soft bubble"?), then you may do so and you may even believe you are maximizing your $EV in the process.

You're wrong, but you can go ahead with being a huge $EV nit and enjoying your mincashes all you like.

And you can easily lump all MTTs into one ategory and disregard what makes them special. You really don't think 800x for 1st is materially different than 150x for 1st?

Yes it is, again I even threw out the rough #'s (which while rough are a hell of a lot closer than yours--seriously you think having 4x starting stack implies a stack is worth 4 buyins? The nonlinear relationship between stack size and $EV value is like ICM 101, you don't know that basic fact and you're saying I'm here in bad faith, the only one who's actually engaging you, sitting here typing out page after page of message, and you say I'm here in bad faith?). There can be no other approach--that's how $EV is calculated. So either you don't understand MY approach--very rich coming from someone saying the same thing about me--or you're willfully ignoring it in favor of something wrong and irrelevant.

I never "revised" my "argument"--I did realize though that winning does indeed have value off the table, which you can't ignore. Also never said anything about playing bigger MTTS--$50k is a down payments for a house (hello interest tax deduction), it's enough to start a small business--you're actually the one who's here in pretty bad faith advocating for maximizing the chances of mincashing if you're ignoring all these cool things that can happen to someone who wins this event.

I acknowledged nothing. I entertained your discussion--which no one else bothered to do because they know it's a silly discussion to have at this point in the event--nothing more.

You'd be surprised. But it's lovely that you think you speak for the entirety of the forum because 1 person with a reg date of 2018 kinda/sorta agreed with you.

Do you want to choose someone whose mutually respected to give their thoughts? We can condense the argument down to the most basic elements and pitch it.


I'm agnostic to what a soft bubble is. I'm framing it purely in terms of the relative probability of busting, which is up to the reader to make an assessment of. Being a $EV nit? What does that even mean? Making the highest $ev play is the one that makes you the most money. I guess I am being a nit in that respect.



No. And especially not when we're evaluating a position where we have $200 in chips vs a 40k first prize, to a tournament with a $200 buyin with a $30k first prize. The difference in not material in terms of how you'd approach hands.


I'm perfectly aware that each chip is not equally valuable. The ICM model makes a probabilistic assessment of making each pay jump given your stack size, and factors that in to the value of decisions. Because ICM calculators don't apply to this large a field, I'm giving a basic overview of what that would look like. It's not perfect and you could definitely critique it (and I can think of a few legitimate critiques of the way im arriving at it) but the position you're taking is not one of them.


You were initially saying that pay jumps are too insignificant to impact a 0.2bbcEV decision in terms of $ev. Notwithstanding the details of this particular hand, do you really not think you aren't routinely faced with situations you're put in that are (in terms of $ev) greater than 0.2bb of cev?

I've already said that it doesn't apply to you in this case because you have the other guy covered by 15 blinds, and in fact it should alter things like your bluff ratio on the river. Which I already thought was a bluff even before you account for his slightly higher incentive to fold to all ins.

The pivot is when you want to get away from actually examining how you'd go about constructing a $ev estimate, and introduce this bizarre argument about large first prizes being worth more than their proportional value.

The marginal utility of money almost definitionally decreases as the amount gets larger. Yes, in very rare cases you have a downpayment for a home. Alternatively the $200 mincash reliably puts you a step closer to making a down payment on a home, for a scenario that you'll be faced with routinely that you'll capitalize on hundreds of times before you actually win one of these things on average. If you're going to deviate from the highest $ev decision, doing it in the name of increasing variance is highly irrational for any rational human beings utility curve / preferences.

Your argument is essentially the same argument that some guy lining up to buy lottery tickets would make.


It's silly in the same way dwelling on any specific situation is silly. But it's significant if you extrapolate it to all the situations that are analogous, and ignoring ICM decisions around the bubble in large field events is a huge net loser.

Your assessment of the assumptions makes you a nit--you assign too much value to the mincash and too little to the win. To wit, you've (again, after being told multiple times you're wrong) assumed OPs chips are worth close to double their actual value (see below)

JFC how many times do you have to be told you do not have 4 buy ins worth of chips just because you have 4x starting stack. Your entire premise is based on shitty arithmetic and even shittier (just plain incorrect) logic.

You tell me I'm wrong for not digging deep enough, then you just throw up your hands and compare an event where 1st plays 800x to an even where 1st payts 150x and act as though they're exactly the same? Where's YOUR subtlety in your analysis?

Now you circle back and say "Oh well I wasn't taking about THIS HAND!!! I just meant in general hehehe" No, bullshit.

It is ABSURD to see someone say "Well 4x starting stack, I don't even know what the stage of this event is because I don't know what "soft bubble" is but OF COURSE clearly he's got 4 BI's worth of chips." Absurd.

Except you're not even in the same ballpark, you just assumed a linear value of chips in an explicitly nonlinear model. You've filled up 2 pages of this thread on the basis of a mathematical felony.

Waiting for all those forum members who think ICM is critically important here to chime in and tell me I'm wrong. (Oh but it's not THIS HAND you were talking about was it? Gee, now who's here in bad faith...). And my reg date is 2019, go ahead and tell me I'm a shitty poster. And your reg date is 2005 and you think ICM chip values are perfectly linear. Reg date means nothing.

This stuff is "bizarre" to you in the same way the Sun was bizarre to ancient peoples: you do not understand it, hence it is bizarre to you.