i constructed a situation that i thought would be significantly affected by card removal effect, and the result was like 0.3. We can say this is a worst case scenario. Take a situation with only 4 or 5 players and i think we can extrapolate that card removal effects aren't significant enough to respresent a significant edge of folding. In the situation that was constructed here, yes, i think with a 6-9 player table, sngwiz overestimates 0.2+

So let's say every "+ev" bvb push is now reduced by .15 to .30 every time due to the card removal effect. Since all of us have obv. been succeeding without applying this change, does this suggest that if a normal sb shove in a given situation is X then we can basically always shove x - .15 or x - .30? ie - slightly -ev shoves are good in these spots.

I always wondered about this and how it could be calculated.. thanks for the bump

good location

I mean, i can't think of a response other than, "yes (?)". Iirc you're a big proponent of the take-every+shove-thats+ev, and not one of the pass-up-on-the-thinner-shoves guys. this shows that, in the right situations (lots of folders), the thinnest shoves are probably -ev in a vacuum.

fact is i play 6-max and card removal is really negligible. in 9-man, esp at higher stakes where you are push/folding with large tables, yes i think it has a significant impact and you should shove tighter than wiz dictates. something like -0.2 when lots have people have folded prior sounds right.

Nice bump, strange enough I thought about this lately. But I always thought about it the other way around, i.e. shoving Ax cause opponents are less likely to have one.

ronny this is already taken in to account in standard equity/ICM calculations in stove/wiz/etc. Card removal isn't.

jeeez, I can be so stupid some times. Well but card removal, makes it even less likely

Jeez this is pretty advanced, cool thread. Sort of explains why when we make those ATC pushes sb vs bb it seems the bb wakes up with a hand more than expected...

Good thread hood.

An interesting related bit of data is that an analysis of tens of millions of actual boards in NLHE, regardless of whether the hand ended on the flop, turn, or showdown, shows that the frequency of deuces on the board is almost exactly 0.3% higher than the frequency of Aces, and the other ranks are on a smooth slope in between. This removal effect is pretty well established, in that players tend to see flops holding higher cards, causing lower cards to flop more. However, the effect isn't big enough to affect playing decisions, particularly since trying to exploit it by seeing flops when holding low cards yourself completely negates it.

hate to bump an old thread but doesn't seem like anyone has solved this so my question is what hand the bb has in a walk, if anyone actually knows

OK the way i look at the bunching effect is like this when all the cards are face down, everyone has a superposition of all possible hands or you can look at it as distinct quantum states the math is the same and the value of the summation of all quantum states is Q7o

as soon as UTG looks at his hand the quantum state of all cards to act after changes since if he folds he did not hold a top hand so each hand increases in value if he plays each hand decreases

well this becomes important because now if everyone folds then the value of the bb hand has increased signifigantly to the point where shoving Q7s is not profitable because it is behind the average value of the BB but what hand is profitable to shove?

is there any way to calculate without using brute force?

i personally use QTs coz it seems to be good enough just curious if anyone has figured this out yet

^
I am pretty sure I understand what you are getting at, but you have to take the value of the blinds into account. You're right in saying that BB will now hold a hand that is better than Q7o on average, but the value of the blinds is not insignificant either. While I don't have actual numbers for you, I can say that it is within the realm of possibilities that Q7o is still the hand you should be shoving with.

This is an interesting observation. At first I thought, 32o does not gain value just because 7 other people folded. So I went to ProPokerTools and ran a sim with 32o vs. 20% and 32o vs. 20% with some dead cards. 32o can in fact gain showdown % when dead cards were added into the sim.

No Dead Cards

ProPokerTools Hold'em Simulation[/url]

5,383,483,776 trials (Exhaustive)

Hand	Pot equity	Wins	Ties
32o	28.38%	1,505,210,892	45,673,548
20%	71.62%	3,832,599,336	45,673,548

No Dead 2 or 3

ProPokerTools Hold'em Simulation[/url]

600,000 trials (Randomized)

dead cards: 456789TJ

Hand	Pot equity	Wins	Ties
32o	32.27%	191,527	4,159
20%	67.73%	404,314	4,159

Dead 3

ProPokerTools Hold'em Simulation[/url]

600,000 trials (Randomized)

dead cards: 3 5 6 8 Q J 6 T

Hand	Pot equity	Wins	Ties
32o	28.46%	168,435	4,649
20%	71.54%	426,916	4,649

Obviously my choice of dead cards is not scientific and we need someone good at the maths to answer this - does 32o gain value or lose value because of folders? If its value changes then the OP's calculations (specifically the +.27) need to take into account the higher +EV 32o has when called.

You would think that there would be more dead 2s and 3s than higher cards like As and Ks since there should be more 2s and 3s being folded making its showdown value less than it seems not more? I think in the simulation the results are like that because theres only 600k trials with the dead 3 compared to 5 billion trials with no dead cards.

but i don't think that's the right way to look at it i think it's more of a summation of all quantum states so if everyone folds to the BB then the BB is less likely to have a 2 or a 3 but that's an unnecessary complication because you only have to look at the avg hand on the BB so instead of Q7o the BB has a hand more equal to Q9

was thinking about taking all my hh's and filtering only walks to the BB...and then average the hands but not sure i even know how to avg the hands

23o loses value because the BB has a stronger hand than normal...also there should be an unexploitable hand to shove on the SB, i believe it's QTs just from experience in poker and intuition

just think it's interesting that no one has solved the bunching thingamajiggy, seems kinda important

8k posts and you still reason as such: "If folded to me in the sb, and I have a hand that's ahead of bb's random hand, I can profitably shove"?

This is absurdly wrong.

The only way to do this properly, and in saying this I do not in any way think this work would be worth the effort, would be something like this:

Deal bb cards from a deck that is somewhat weighted so that higher up cards are somewhat more frequent. Let's say an 8 is just as likely, and a 7 would appear 99.9% as often, a 9 100.1% as often etc. A sliding scale. And then sim things. The actual weighting can obviously be refined, but it's beyond me how this could ever provide us with much insight.

hmmm....never thought of trying it that way...lemme play with it

I'm actually kinda surprised that SNG wizard hasn't included the bunching effect into their program. I am fairly certain that you dont need large brute force simulations for every hand situation.

Simply compare each folder's calling range against the weighted probability of them getting such hands.

Then balance that against the villains that act after the hero. Additionally you could take it one step forward and compare it against the hero's hand as well and simulate how that effects cards that help their hand

Although fairly complicated, I don't think it would be computationally challenging.
Would be great to add that sort of accuracy to SNG Wiz =)

nice

As a super turbo player, I feel that the card removal effect is much more pronounced than in formats where push/fold mode generally occurs when the table is short handed. I believe there is a lot to be gained by analyzing common situations where several people have folded in front of me (especially because it feels like the only times I'm even given the opportunity to steal is when BB has a monster).

Before I go and purchase Stox/CR EV, is there any freeware available that would allow for me to calculate the impact of card removal?

do you play A2 or K3 under in early position?...I do not believe in the card bunching effect..last thing I need is another reason to call in tough spots...

not quite sure what you mean by your question, but this pertains more to blind steals with the bottom of my range in 8-10BB spots. if 7 folds in front of me increase the likelihood of BB having a good hand, it is in my best interest to know which hands i should actually be folding that wiz says I should push with.

Deep down I always knew about this thing but could not describe it mathematically .
Thanks Hood, nice thread.

If BB calling 30% and all players folded to SB, that means that BB will have top 30% of his range more often then 30% of the time (calling range is the same but probability of having this range and calling probability are increasing).
And what about SB range, if all players folded, SB will have same increased probability of better hand. Should it affect BB calling range?

Awesome post hood. I generally enjoy your posts tho.

So my first thought is, for 6max, we could extrapolate that if 4 folds ahead denotes a .28 min edge in SB, then perhaps each position after UTG needs .07 (HJ) .14 (CO) .22 (BTN) A .07 edge for each fold in front.

However, the value of the blinds relative to stacks is going to be important. I feel like these figures may be correct say, beginning of a hyperturbo, but as the blinds increase and stacks diminish (in terms of # of BBs) these min edge figures should also surely erode. Is my logic right in that?

My second question, and one I've been giving a lot of thought to in wiz recently, is how does this factor into my calling ranges, if at all. Suppose we're in BB and facing a SB shove. Well at a 6 handed table, there were 4 folds in front of that SB shove. So I have Villain shoving say 15BBs with 33% of hands, but how much more likely is villain to have that top 33% of hands given the 4 folds in front. How can I extrapolate the answer to that question into a minimum edge I now need to call? Does that even make sense?

Discuss.

I think this is even more important nowadays because more precise and thin calls are needed to maintain an edge over the competition.