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