cEV and EV in MTT tournaments

[Antilyzer]

I often get into situations were my cEV is positve but I dont know if i should call or not, since i dont know how to evaluate my EV.
What I do know is that my EV is smaller than my cEV meaning when I double up my chips i dont double up my equity at least I read this in cardschat's strategy guide.
But that's just words. I need some mathematical formula too understand this concept and apply it in ervery situation.
Could someone explain this formula to me in simple words?

Here's an exapmle to get the picture of what i mean:
35/45 man left - No Limit Hold'em Tournament - t25/t50 Blinds - 8 players


UTG+1: t3000 60 BBs
MP1: t1272 25.44 BBs
MP2: t1455 29.10 BBs
CO: t1305 26.10 BBs
BTN: t4892 97.84 BBs
SB: t273 5.46 BBs
BB: t2455 49.10 BBs
Hero (UTG): t1450 29 BBs

Pre Flop: (t75) Hero is UTG with Q

Q

Hero raises to t150, 6 folds, BB requests TIME, BB raises to t2455 all in, Hero requests TIME
Let's say BB pushes with 77+,A8s+,KTs+,QJs,JTs,ATo+,KTo+,QJo
cEV=0,68(t1525)+0,32(t1300)=+621
EV=???

How can I evaluate this and exactly??What's the formula??

the puzzled Antilyzer

 

[Lofwyr]

Basically your cEV and $EV are almost identical in the above spot. cEV/$EV don't start to deviate too much until you get close/into the money. In this case the difference is probably negligible.

The range you assign to villain is pretty damn wide though...why do you think they'll be shoving here with stuff as weak as QJo?

 

[tusabes]

That range does seem a bit wide. Taking into account he requested time and took it usually is a tell that he/she is trying to project weakness when actually they are strong.

The range I'd put them on is something like JJ+, AQs+. I could be way off here (let me know if I am) but I'm very weary about preflop decisions that take a long time and then culminate with a huge raise.

 

[pat3392]

Read Kill Everyone, it has methods to help work this stuff out

Snap call the hand, villain is never pushing AA and probably never KK, expect to see AK/JJ/TT a lot of the time

 

[Antilyzer]

I know it's wide range but its a micro buy in..
anyway! Does someone know how too evaluate the $EV exactly?

 

[pat3392]

I know it's wide range but its a micro buy in..
anyway! Does someone know how too evaluate the $EV exactly?

I was asking the same thing on multi-forums. As far as I'm aware, no such thing exists

 

[bonflizubi]

Basically your cEV and $EV are almost identical in the above spot. cEV/$EV don't start to deviate too much until you get close/into the money. In this case the difference is probably negligible.

This is the correct answer. Until nearing the bubble or in the money, cEV = $EV

I know it's wide range but its a micro buy in..
anyway! Does someone know how too evaluate the $EV exactly?

I was asking the same thing on multi-forums. As far as I'm aware, no such thing exists

Yes, it is called ICM, but again it doesn't really apply until a bubble or in the money situation

 

[pat3392]

This is the correct answer. Until nearing the bubble or in the money, cEV = $EV






Yes, it is called ICM, but again it doesn't really apply until a bubble or in the money situation

I think you're making it overly simple

And one can calculate ICM on a non-final table how?

 

[bonflizubi]

I think you're making it overly simple

And one can calculate ICM on a non-final table how?

It would be painful to calculate whenever you weren't at a final table.

However, you could calculate an approximation on the bubble where payouts are zero or non-zero, though again it would be to painful to do.

ICM is the only correct answer to OP's question though... and until you are at the money bubble, cEV will always be equal to $EV unless you are at a distinct advantage to the field or disadvantage to the field. And there will be precious few cases where anyone posting on this board will be at a distinctively large enough advantage to the field to adjust for that. (Though the converse is true, people will definitely be at distinct disadvantages to the field all the time)

Doing anything other than calculating where cEV = $EV is in 99% of cases an example of taking some theory and attempting to apply it to a situation that is in fact, quite simple. Overcomplicating the analysis, and something that would be impossible to do in the real-time of game flow anyway.

For all practical purposes, there are only two non-in the money circumstances where cEV <> $EV and even in these cases you can't calculate the difference so much as appreciate that there is a difference.

1) You have the big stack and are playing table captain, where generally you are stealing and owning most hands and on a steady upward chip stack. In that case, to take a marginally cEV spot that (if you lose the spot) would keep you from bullying the table and hurt you come bubble time would often be -$EV (since $EV thinks about your likelihood of making more money vs the sole outcome of one hand)

2) You are a short-stack, or you are surrounded by better players, or you are up vs the guy that is the only other competent player at the table, or against the guy who is on your left giving you fits all night long who you want gone. in those cases, it may well be +$EV to take a -cEV spot, since you have a better chance of winning/finishing higher if you are to win that spot.

Unfortunately none of that is quantifiable, but IMO are the pretty small list of times when outside the bubble where you would even think about anything in a fashion other than cEV.

p.s. For OP - you can go to any number of online ICM calculators where you can put in the stacks for a 9man or less SNG and the proze amounts and get the ICM results.

For 9man SNG's this one works great. punch in the variables as it asks and you'll get teh Nash equilibrium results for push/call ranges. (remember they assume that everyone is playing mathematically optimal, which they aren't but you should be able to work from there.)

http://www.holdemresources.net/hr/sngs/icmcalculator.html


Assuming you don't have one at your disposal, use cEV, but decide how much of an edge you feel you need to adjust for. Me personally, I'm never passing up a 51% edge, where I know it is a 51% edge precisely. However, since we assign ranges and what not and can never be sure, people often look for 55% or whatever their number is. SO if to be on the safe side, you want a 55% edge, then you might pass on a proposition where given the ranges you get a slight +cEV but it's only like a 51% edge.

 

[pat3392]

How would one be able to calculate the ICM at a bubble? As far as I'm aware, it can't be done. I find it pecuilar how all you guys say that $EV=cEV without showing some sort of proof. Oh and giving the ICM calculator for a STT is incredibly absurd as this is a MTT

 

[loopmeister]

Pat,

The key difference between cEV and $EV is that the change in $EV decreases for every additional chip you accumulate, while for cEV it is constant.

Therefore, if for certain situations you can show that $ev is constant with respect to stacksize, or nearly constant, would you agree that cEV = $EV?

Case 1:
First hand of tourney. (I'll use the same notation as here).


cEV by Curly77, on Flickr

 

[loopmeister]

cEV2 by Curly77, on Flickr

 

[Lofwyr]

How would one be able to calculate the ICM at a bubble? As far as I'm aware, it can't be done. I find it pecuilar how all you guys say that $EV=cEV without showing some sort of proof. Oh and giving the ICM calculator for a STT is incredibly absurd as this is a MTT

The whole cEV~= $EV thing has to do with where the idea of $EV came from to begin with. $EV became an issue purely because people realized that decision making late in the tournament, when payouts started to matter, didn't line up with standard decision making. Equity calculations weren't precise to how much $$ you'd make. The concept of $EV was developed into ICM and by its very nature $EV/ICM doesn't apply to situations where decision making has little effect on your immediate payout. Thus the early stages of an MTT ignore $EV because decisions at that time are not critical to how you're getting paid, so for practical purposes your cEV=$EV.

ICM in an MTT-bubble situation is a pain in the arse to calculate because you have to track stacks over multiple tables (for the most part). Anyway, in these spots your cEV&$EV will still be very close because the major payment jumps don't appear until very late in these tournaments. Basically, even though it's the difference between $0 and $X, MTT bubbles are such small jumps in payment that $EV doesn't really mean much, though it will mean more on/around the bubble than it did at any time prior in the tourney (and likely any time from ITM on until the big pay spots).

 

[pat3392]

@loopmeister:

thanks for the math, cheers! will check out in detail some time

The whole cEV~= $EV thing has to do with where the idea of $EV came from to begin with. $EV became an issue purely because people realized that decision making late in the tournament, when payouts started to matter, didn't line up with standard decision making. Equity calculations weren't precise to how much $$ you'd make. The concept of $EV was developed into ICM and by its very nature $EV/ICM doesn't apply to situations where decision making has little effect on your immediate payout. Thus the early stages of an MTT ignore $EV because decisions at that time are not critical to how you're getting paid, so for practical purposes your cEV=$EV.

ICM in an MTT-bubble situation is a pain in the arse to calculate because you have to track stacks over multiple tables (for the most part). Anyway, in these spots your cEV&$EV will still be very close because the major payment jumps don't appear until very late in these tournaments. Basically, even though it's the difference between $0 and $X, MTT bubbles are such small jumps in payment that $EV doesn't really mean much, though it will mean more on/around the bubble than it did at any time prior in the tourney (and likely any time from ITM on until the big pay spots).

I'm a semi-perfectionist with big ambitions with poker; it may not be a huge differences in the ranges, but there will be differences for sure. I also like playing very laggy early game but not sure if it's profitable, due to the ICM tax. This discussion though is quite advanced and it's probably safe to assume $EV=cEV until we're a the $60 games/plugged bigger leaks

 

[loopmeister]

I wanted to make some comments but got really frustrated about trying to get the maths posted (BBs aren't designed for maths) and then forgot.

I noticed some things while I was doing the derivation and researching ICM.

1. I thought it would be a 5 second google to find someone having done some proof about cEV ~ mEV far from the bubble. Well, I spent about 90 seconds on it and didn't find anything, which I found odd. It does feel "right" that cEV ~ mEV away from the bubble; but that's not a proof, and people have mostly just accepted it as truth. I reckon there must be a proof out there somewhere though, and one that covers more general cases than the ones I posted.
2. The proofs I posted are solid, I think; but you may find the results pretty academic. They describe to very special cases only. However, I think the value lies in demonstrating that the ICM is at least behaviourly asysmptotic to the standard chip equity model.
3. One of the assumptions of ICM are that everyone has the same skill. This simplifies the math, but it actually wouldn't be a stretch to generalise this. One great application of this would be to see how your decisions change if you assume people are more skilled than you are. Let's say you satellite into a big Sunday tourney and then manage to run deep (final table say ). If it were me, 100% of the remaining field would have a big edge over me. How does this change my decision making? Anyone with more spare time than me keen to give it a bash?

 

[pat3392]

I wanted to make some comments but got really frustrated about trying to get the maths posted (BBs aren't designed for maths) and then forgot.

I noticed some things while I was doing the derivation and researching ICM.

1. I thought it would be a 5 second google to find someone having done some proof about cEV ~ mEV far from the bubble. Well, I spent about 90 seconds on it and didn't find anything, which I found odd. It does feel "right" that cEV ~ mEV away from the bubble; but that's not a proof, and people have mostly just accepted it as truth. I reckon there must be a proof out there somewhere though, and one that covers more general cases than the ones I posted.
2. The proofs I posted are solid, I think; but you may find the results pretty academic. They describe to very special cases only. However, I think the value lies in demonstrating that the ICM is at least behaviourly asysmptotic to the standard chip equity model.
3. One of the assumptions of ICM are that everyone has the same skill. This simplifies the math, but it actually wouldn't be a stretch to generalise this. One great application of this would be to see how your decisions change if you assume people are more skilled than you are. Let's say you satellite into a big Sunday tourney and then manage to run deep (final table say ). If it were me, 100% of the remaining field would have a big edge over me. How does this change my decision making? Anyone with more spare time than me keen to give it a bash?

the book I'm currently reading suggests that cEV=$EV when one times the amount of people that get paid by 5 and there is currently more than that many people in the tournament. Haven't got to the part where it suggests how we should play differently yet

If you're less skilled, that you'd have to take slightly negative spots. A good player takes slighter better spots. However, as a bad player, you wouldn't neccesairly know when a spot is slightly -/+. My, perhaps incorrect advice, is if you're not sure how tight/loose you should be, try to be a little tighter/looser than the average opponent at the table

 

[loopmeister]

If you're less skilled, that you'd have to take slightly negative spots. A good player takes slighter better spots. However, as a bad player, you wouldn't neccesairly know when a spot is slightly -/+.

That makes sense. And of course, the ranges you assign your opponents are always subject to uncertainty.

I'm using SnGWiz to fine-tune my internal neural networks for gaining a "feel" for the correct shipping and calling ranges. I find the 54 man SuperTurbos perfect for practicing this.

But, I've begun wondering what adjustments you'd need to make if you gave your opponents a 10% skill edge. I'm not sure it translates linearly to a x% equity edge using std ICM assumptions, though maybe it does. (I don't know if I'm making myself clear here or not).

 

[Lofwyr]

Absolute proofs for cEV=$EV are just a nightmare to do which is probably why you didn't find any through a quick online search.

http://www.pokerhelper.com/articles/independent-chip-modeling-part-1-derivation-and-sample-analysis/

The above link shows how you arrive at $EV and doing those calculations for only 4 people (in the 9-man STT setting) is quite a task. Imagine doing it for > 1000 people. The ultimate issue is that your $EV is a weighted average of your equity to each finishing position, when the majority of the remaining finish positions are small$ or $0 the average will not change in odd fashions compared to cEV. If you start looking for situations relatively early in tournaments to adjust your play for $EV considerations you're more likely to make bad adjustments than your are to make good ones because the different in cEV/$EV is so small as to be negligible.

@Pat - When thinking of MTTs the best players basically ignore $EV until they approach large $ differences. To deviate much from that is to play sub-optimal poker frequently (i.e. passing up a +cEV decision because you fear it isn't proper $EV) and it will more likely hurt your bottom line than improve it. $EV is a concern mainly with short fields and/or flat payout structures...like you find in satellites and 9-27 man SNGs.

 

[bonflizubi]

Absolute proofs for cEV=$EV are just a nightmare to do which is probably why you didn't find any through a quick online search.

http://www.pokerhelper.com/articles/independent-chip-modeling-part-1-derivation-and-sample-analysis/

The above link shows how you arrive at $EV and doing those calculations for only 4 people (in the 9-man STT setting) is quite a task. Imagine doing it for > 1000 people. The ultimate issue is that your $EV is a weighted average of your equity to each finishing position, when the majority of the remaining finish positions are small$ or $0 the average will not change in odd fashions compared to cEV. If you start looking for situations relatively early in tournaments to adjust your play for $EV considerations you're more likely to make bad adjustments than your are to make good ones because the different in cEV/$EV is so small as to be negligible.

@Pat - When thinking of MTTs the best players basically ignore $EV until they approach large $ differences. To deviate much from that is to play sub-optimal poker frequently (i.e. passing up a +cEV decision because you fear it isn't proper $EV) and it will more likely hurt your bottom line than improve it. $EV is a concern mainly with short fields and/or flat payout structures...like you find in satellites and 9-27 man SNGs.

everything this guy said

 

[bonflizubi]

That makes sense. And of course, the ranges you assign your opponents are always subject to uncertainty.

I'm using SnGWiz to fine-tune my internal neural networks for gaining a "feel" for the correct shipping and calling ranges. I find the 54 man SuperTurbos perfect for practicing this.

But, I've begun wondering what adjustments you'd need to make if you gave your opponents a 10% skill edge. I'm not sure it translates linearly to a x% equity edge using std ICM assumptions, though maybe it does. (I don't know if I'm making myself clear here or not).

you are taking a strict quant approach here, which is a fundamental error as ranges are not by any fashion linear, not to mention lining up your ranges with their ranges.

IF yo uar talking push fold poker, generall bad players dont shove tight enough or cal wide enough, while solid regs shove wider.. and call regs lighter and randoms tighter.

SNGwiz will only help you if you know the optimal ranges to begin with and you set the player types to match those. You can articles etc which have nash or near nash optimal shoving ranges by position and stack size (assuming cEV here).

In terms of what adjustments to make when you know they have a skill edge, it's going to be very subjective. Essentially,, there style of play will dictate differing adjustments in hand ranges and hence resulting equities. While Moorman1 is known to 5 bet random players with J6ss you'll likely neversee that from a guy like pearljammer. Or if you are looking at a BvB situation there shoving ranges on you are going to be determined to a degree by their perception of *you*. The more competent they think you ar ethe tighter they will shove you. The less competent they think you are the lighter they will.

What I'm trying to say here is that it is incredibly imprecise most of the time, whether one would like it or not. I think the simple rule would be, when given the chance to get your money in vs a much better player that is going to eat your lunch all day, never turn down the proverbial coinflip (regardless of whichever side of it you are on.)

 

[bonflizubi]

@loopmeister:

thanks for the math, cheers! will check out in detail some time


I'm a semi-perfectionist with big ambitions with poker; it may not be a huge differences in the ranges, but there will be differences for sure. I also like playing very laggy early game but not sure if it's profitable, due to the ICM tax. This discussion though is quite advanced and it's probably safe to assume $EV=cEV until we're a the $60 games/plugged bigger leaks

FWIW, very laggy early game is generally NOT profitable unless you have an incredibly nitty table. The deeper the starting stacks the worse a play it will be for you. Laggy play is FAR more profitable post antes and in the end-game. It's safe to say that this is one of your leaks you need to plug.

 

[pat3392]

"If you start looking for situations relatively early in tournaments to adjust your play for $EV considerations you're more likely to make bad adjustments than your are to make good ones because the different in cEV/$EV is so small as to be negligible."

" To deviate much from that is to play sub-optimal poker frequently (i.e. passing up a +cEV decision because you fear it isn't proper $EV) and it will more likely hurt your bottom line than improve it."

These are so absurd I can't even begin to explain how this line of thought is incorrect.......

FWIW, very laggy early game is generally NOT profitable unless you have an incredibly nitty table. The deeper the starting stacks the worse a play it will be for you. Laggy play is FAR more profitable post antes and in the end-game. It's safe to say that this is one of your leaks you need to plug.

huh? Any proof? How can you say this?

First of, if cEV=$EV early game then doesn't early game follow the same principles of a cash game? So you're saying there's no successful lag cash game players?? and wtf on deeper stacks makes lag worse; have you ever heard of small ball??????????????????

 

[bonflizubi]

huh? Any proof? How can you say this?

First of, if cEV=$EV early game then doesn't early game follow the same principles of a cash game? So you're saying there's no successful lag cash game players?? and wtf on deeper stacks makes lag worse; have you ever heard of small ball??????????????????

1) it's not a cash game, with the fundamental difference that you can't rebuy at all. (ignoring rebuy tourneys here obv). Chips lost are not easily regained

2) I've heard of small ball too, but you can't play laggy and play small ball. small ball is the antithesis of lag poker. Maybe you play loop poke- loose passive. If yo uare saying you like to limp /call a lot of hands with a wide range in the early levels then OK, not the worst leak - if the stacks are deep enough. FYI tho, they are almost never deep enough for this in a 1500 chipper - it netter be 3k or more...)

If you are really playing lag, opening for araise with all sorts oif crap, 3 betting constantly, IMO you are going to be very -EV in these early levels, unless you are extremely talented and/or playing super-nits.

There are successful lag cash game players, but you've got to be even better to a succesful lag than TAG- it takes a lot more skill to pull off. And to translate it to tourney play, you may never reach the point of the big payoff of being lag- which is showing everyone you are a maniac and then showing up with the monster that you'll stack someone with. (Likely that you either get moved or never get that monster in a tourney.) That's where the real profit in playing lag is - unless there are antes involved of course and simply taking pots pre is enough to accumulate alot.

No, I don't have an article to prove this to you. But by rebuttal, I'd say name me one successful lag player in tournaments - who isn't an absolute beast. All the players that I am friends with personally who had been playing laggy early (and I mean truly lagggy, not loose-passive...but loose aggressive- 3betting pre, 2 and 3 barreling air etc) discovered that they were ridiculously more profitable once they got it reined in a bit, or a lot.

I'll give you an example of a hugely successful LAG - Yvgeny Timoshemko (sp?) who goes by Jovial Gent. He won the WPT title a couple years ago for 2Mill+ and has IIRC at least one if not two 1 Million + online cashes. The man is a monster. I was shocked to see him play something like 33/25 vpip/PFR in the first levels of a deepstack (5k chips) sunday tournament (I was at the same table ,so i have the actual stats if you need to have me dig them out.)

On that given day, while I was still at his table stacks were in the 80-100+BB range, and he happened to sorta sine wave up and down around the starting stack. THe table also adjusted around him once people noticed his laginess. Now obviously this works for him and he has the results to prove it. My expectation is tho that he has the ability to switch gears at will and probably owned some fools by the time he got table moved.

That is the example of an expert.

THe likelihood is though, that you aren't remotely at that level (and neither is anyone else on this board). So it's equally likely that you would have much better results if you weren't as laggy (or whatever it is you are really doing) early in tournaments. I'm sure for every time it lets you chip up massively there are one or more times it really dents your stack.

Cliffs:
-Yes early tournament play is like a cash game, IF STACKS ARE DEEP ENOUGH (ie 80+ BB deep).

-Yes there are succesful LAG cash game players, but they profit on teh small moves by getting paid on the big ones, which come only after many many hours of play to establish image, or working off of historical image vs same opponents. (which isn't likely happening in your typical online tourney for you)

-Successful tourney lags are much more skilled players then average- since they need to make sure they get OUT of trouble... and in fact have to be able to read when they are getting INTO trouble

-Doubt there are many people on here good enough to adopt this style and be super-profitable


p.s. I'm no nit myself- I am usually one of the looser players at the table. But I definitely don't go all laggy early, that is the formula for usually chopping DOWN your stack.

 

[pat3392]

1) it's not a cash game, with the fundamental difference that you can't rebuy at all. (ignoring rebuy tourneys here obv). Chips lost are not easily regained

I'm sure for every time it lets you chip up massively there are one or more times it really dents your stack.

huh? but you were just saying that cEV=$EV

I don't know why you think small ball is a passive version of a lag.

Practice makes perfect. Most regs play tight and don't know how to deal with a lag and as for the fish, I want to get involved with them as much as possible.

And to translate it to tourney play, you may never reach the point of the big payoff of being lag- which is showing everyone you are a maniac and then showing up with the monster that you'll stack someone with.

That statement is incorrect. If a lag only made money when people adapted, then people would adapt to the lag by not adapting....................

1)

THe likelihood is though, that you aren't remotely at that level (and neither is anyone else on this board). So it's equally likely that you would have much better results if you weren't as laggy (or whatever it is you are really doing) early in tournaments.

I'm not remotely there. But you forget a massive fundamental; I only have to be better than my opponents. Sure, they may have better cards, but I pick situations where the other factors make up for my crappy holdings, cards are so over rated. The reality is, most tourny guys suck post flop and don't know how to deal with 3-bets properly. Not sure how much I'm going to lag it up though, just going to keep looking for more spots to exploit

 

[bonflizubi]

huh? but you were just saying that cEV=$EV

I don't know why you think small ball is a passive version of a lag.

Practice makes perfect. Most regs play tight and don't know how to deal with a lag and as for the fish, I want to get involved with them as much as possible.


That statement is incorrect. If a lag only made money when people adapted, then people would adapt to the lag by not adapting....................



I'm not remotely there. But you forget a massive fundamental; I only have to be better than my opponents. Sure, they may have better cards, but I pick situations where the other factors make up for my crappy holdings, cards are so over rated. The reality is, most tourny guys suck post flop and don't know how to deal with 3-bets properly. Not sure how much I'm going to lag it up though, just going to keep looking for more spots to exploit

You are wrong on so many levels here.

It's not a cash game like I siad. ANd yes cev= $EV. THe problem is effective stacks in a cash game are always possible to get to the cap (lets say 100bb+) while in a freezeout if you lose chips you have a reduced effective stack, which can't be topped up. With a reduced stack you lose lots of your spots. So while you might make a cEV move (one that is in fact $ev as well since it is so far from teh money) you do risk reducing your future options by doing so.

And as to lags getting paid off, sure lags can chip up somewhat just by being laggy. But i said the BIG payoff for lagginess is showing you are lag and then playing for stacks when you have the goods and they don't believe you. That is the primary benefit of playing LAG. (In fact negreanu says the same thing essentially in a spam-mail I got today from cardshark media... if you really need me to I'll cut and paste it later...)

You are right that you only have to be better than your opponents, but you cant bluff an idiot or a calling station as they say. And fish get real stationy and flat behind 3bets all the time on deeper stacks. WHich makes it a losing proposition if you are just trying to play position and 3bet with crap - unless you know what flops you need to give up on etc. and excel at reading the mind of a fish.

Lag vs fish works best on shallower stacks when they start to get afraid / in the money. Then they start to fold more easily to pressure or give up on pots.

I'm not saying don't pick your spots, but if you are winning then either you aren't as lag as you think you are, or we are working on different definitions of what LAG is.