Card removal effect, or the card bunching effect, describes the changes to opponent card ranges considering that other players have folded preflop. Let's take an example from sit n' go wiz:



Here we have hero in the SB, looking at an ATC push. With the BB calling as loose as 37% of his top range, this is a +EV shove with 23o.

However what this simulation doesn't take in to account is that 4 players have folded before you. These players folded ranges of hands that included less higher cards. That means the stub of cards to be dealt to the BB includes more higher cards, and hence card combinations - especially Ax and Kx - are more heavily weighted in BBs potential holecards. So the question is, is this card removal effect great enough to make this move a fold?

This has been discussed a lot before. This zoo thread, once you wade through all the zomgrigged posts, includes posts from microbob who suggested this could be an effect for why large samples of all-in hands became below expectation. The author of pokerEV also posted to confirm this effect could exist for certain styles of play. It's been brought up various times before (see here, also here I brought it up in STTT a few months back). But I haven't seen any actual maths.

So armed with our new favourite friend - Stox EV - it seemed a doddle to calculate this and see what the effect was.

First, here's the same scenario as we had in wiz above:



Note here that the EV of hero's 32o push is 0+.27, same as we get in SNGW.

Stox EV shows more clearly the problem with this simulation - the 4 players before SBs folded all their hands. This is unrealistic. So I add in raising ranges for each player. For simplicity, if one player pushes all in, then everyone else in the hand folds (this won't effect what we're looking for).

Without further ado:



The most important figure here is the EV of SBs push - it is now -0.01, an unprofitable push. You can see the opening shove ranges I've put in - from top 9% for UTG through to 21.5% for button.

This example is obviously cherrypicked to get a negative EV result "punchline", but from a little playing around I've found that in this setup, the EV reduction is between 0.15 and 0.3, depending on blind size, BB calling range, and opening ranges.

I also ran the same setup but at 120/240 blinds, with BB calling top 18%. This is +0.28% without card bunching effect; around +0.1 or 0.05 without.

Interestingly, I am finding that changing the opening ranges of the players before isn somewhat unintuitive. I ran the original sim again, but with tighter ranges - removing some Ax hands and low pocket pairs. IT came out at -0.03:



Anyway I'll leave it at that. I can upload my stox files if anyone wants to play around with it, but now you've seen the screens it should be quite easy to setup yourself (see previous tute on stox ev).

Very interesting, I always assumed that any "bunching" effect would be statistically insignificant. Presumebly we should start adjusting EV thresholds for ICM by position?

nice thread

That drop from +0.27 to -0.03% is correctly interpreted as just a drop of -0.3%, right? That number isn't what we usually think of as the difference between pushing and folding, but rather the difference between pre-post and pushing, which in this case isn't really relevant, right?

As there is no one left to act behind us, folding is an EV neutral move, correct? So with this card removal, it shows pushing as (just barely) a worse option than folding.

Without card removal considerations, it's a clear push.

I thought that in the current version of the program, all of those Ev: numbers were compared to pre-post...

I must be missing something because it looks like you just changed BB calling range from 38.1% to 20.9%. Can you explain how you are taking card removal effects into account?

Sorry, I've got the wrong screenshots posted. It's for a different sim. I'll sort it out when I've finished this set.

Right here's the correct one:



Here'll you'll see that the % calling from BB is about 1.5% higher than in the folding simulation. This highlights the card removal effects nicely - because of the 4 folds behind, there are more combinations of cards in his calling range, thus he calls slight more frequently. This lowers hero's EV.

Now I'm confused Here is the EV calc for all folding:



Hero folding 23o is 0 EV. So it can't be compared to the pre-post, because hero losing his SB and BB increasing his stack reduces his equity.

Perhaps in this example pushing is still better than folding, but surely the interesting point is how much deduction there is from the push EV when taking in to account the card reduction.

No, I'm saying it's a drop from 0.27 to -0.03 (or in the new sim, EV 0). I guess I'm not really comparing fold to push, but just "look at how less profitable a push is now we're taking in to account card removal effects."

Hood : I read this and it's like super interesting but there is something I fail to understand about how StoxEV works.

* is he, by default, taking the card removal effect into account (i.e. UTG has NOTa top 9% hand so that afffects other people distribution) or did you have to make so manipulation manually for that ?

I'm confused.
Very good post anyway.

Very good post

No body for make a thread with all good LC and k post together ?

When it deals a hand to player 2, it can't give them either card that player 1 received so by default it's taking this into account.

Where do all these awesome threads come from lately?

(not from me thats pretty certain)

The thing to keep in mind is it runs monte-carlo simulations. So really it's quite "dumb" - it deals out a hand for all players, then just follows through the tree mechanically. In my tree, if anyone before SB catches a decent hand, they shove and everyone folds. So when it does get to SB (here you can see that part of the tree occurs about 80% of the time), "card removal" is in effect just as it would be if you were playing the poker hand.

The simulation runs a few million times (or you can force it to deal every possible potential deal for exact results iirc) and spits out the EV results and percentages at all parts of the tree.

So no manipulation is required - you just create every players "line" as some simplified tree you can model and set it off. The power of stox really comes down to:

a) The way you can set up conditions (v. powerful ways to run conditioning on hand holding and type flop)
b) Way to analyse the results with hand breakdowns, tournament EV, and graphing.

cosign

Hood : thx for the explanation. You have the finger on something here.

Can we link that to the All In luck and conclude something like : ok "normal" EV luck is not 0, it's something like -0.x% when we are the pusher. This is a bit of a stretch, right ?

But already concluding card removal effect has a non micro effect is very good, right ? (I mean -0.3% in a 9 handed 100$ SnG is 2.70$)

Is there a place to nominate best thread? This is really cool stuff, man.

hood - Will look over your stuff and try to figure it out when I get a chance.
I'm glad that my theory is going somewhere and perhaps inspired you to look into this stuff again.

A lot of it is MOSTLY negligible on any given hand as far as push/fold decisions go especially when one considers that we never know what our opponents' range is anyway...we are just guessing. And then combine that with our guesses on what everyone else's folding range includes as well.

Somebody else in that thread rather simplistically pointed out that the deck has ONLY 52 cards. Yeah yeah, we all know that. But sometimes we get lost in the confusion of the 8 zillion different possibilities out there.
But when you break it down...52 just isn't that many and I think it's worth remembering.
Every time somebody folds they DEFINITELY don't have AA or KK...and are somewhat less likely to have any A even.

I think that looking into this further could make for some potentially interesting changes in 'standard' SNG strategy but I'm not positive on that.

Regardless, it's pretty darned interesting and I'm glad you are analyzing this as deeply as you are.

Yeah, as far as SNG tolerances go, +0.30% isn't exactly negligible, but also won't make or break a player's game. It's definitely within the margin of error for most situations, and especially one with blinds that high. Never the less, it's more important than I thought it would be. Our original guess for a generalized "minimum edge" back in the day was 0.50%, so this isn't far off.

So I wrote a quick program to go through and grab all the PF all-ins through all my HH's where it was folded to SB vs. BB and only one of them had an A. So going through all those hands, it would make sense that the player holding the "A" is going to win more often than they should, right?

Well, I was able to find a few thousand hands and the player holding the "A" actually lost a bit more than they were supposed to. Granted, a few thousand is a small sample, but if you use pokerstove and assume 7 folds in front of you and none of them were A's, then hands holding an "A" are worth about 4-5% more than normal.

-BK

A wider range folding (e.g. 25% 22+, Ax, K9+, QJ+) has a much bigger card removal effect than a small range (e.g. 9%) folding because more Ax and Kx get removed and the folks who are calling are frequently doing so with Ax and Kx.

Interesting. For cash games players are not shoving PF much so this is not as relevant as it is for tournaments.

Thats one excellent post Hood.

As a question on this, let's say you could somehow find a certain average for the impact on EV in situation, would it then make sense to set that average as your edge in sngwiz, which most people have on 0 as a standard?

It was so good it took funkyj 9 months to fully absorb the post and come up with a response

i linked to this thread in the software forum because someone was asking the stox ev thread about simulating card removal effects