Should we consider that not all cards are folded in the same frequency so the probability of Big Blind has a good hand when everybody fold is higher than when the hand starts and UTG did not act yet?

He has a higher probability of having an Ace for sure, but how much?

The effect has been called bunching.

Think of a three player game where A (UTG) will only play if he has at least one ace, B is you in small blind and C is the big blind. Without any stipulation, the probability C was dealt at least one ace is 1- 48/52*47/51 = 14.9%.

Now given that player A has folded, we know he did not have an ace, so the probability C has at least one ace is 1-46/50*45/49 = 15.5%.

Clearly for this case there is a dependency. While more realistic conditions will likely show a smaller difference, logic would dictate that if all early position players fold, it is more likely that later players have a better chance for aces and kings than if no statement on early folding was imposed. Barry Greenstein analyzed this type of situation and concluded that a bunching effect does exist

See the following site that analyzed hundreds of millions hands to look at card removal effects:

http://www.spadebidder.com/category/flop-analysis/

And to the specific question there are these posts:

http://www.spadebidder.com/statistic...nsteins-claim/


http://www.spadebidder.com/statistic...-claim-part-2/

So why no one talks about this?

When discussing +EV Shove Hands in blind wars no one considers this effect

Why?

People do. You aren't the first to realize the effect of card removal. That said, the effects are small so it doesn't really make much practical difference.

Actually, what Barry G hypothesized was that more aces would appear on the flop if lots of players folded making AK more of a favorite over pairs than its equity with no assumptions on folders. Spadebidder’s analysis of millions of hands showed this to be true but the effect was small and not statistically significant. Only in the case of seven pre-flop folders in a full-ring game was there a shift of any significance . Here is the concluding paragraph:

“So now we’ve looked at about 152 million hands of full ring NLHE. The theory required an equity shift of at least 2.17% for AKs to become a favorite over 99-44 (actually closer to 2.3% after seeing that the pair distribution is weighted towards the top). We didn’t find a shift that large, so my earlier conclusions didn’t change. The only positive case is when 7 players fold around to the blinds and then we have a blind vs. blind all-in. And even though the sample size in that case is so small that our offset from the mean is barely over 1 standard deviation (even combining both sites for n=361), I’m convinced that the AKs actually does become a favorite over medium pairs in that one special case. But only that one, which is not the same as the more general theory of becoming a favorite “after several folds”.”

The OP actually was in reference to the big blind having an ace when lots of players folded which is not quite what Barry G looked at but is basically the same idea. I think it is not discussed that much because the effect is not that significant especially when compared to so many other uncertainties in doing a math equity/EV analysis.

yeah, what the guys above said, the effect is well known but the practical implications should be slim.

you can actually use CREV to get a better feel for it; for instance setting up a 3-player shove/fold game where every player puts all the money in with 22+, all broadways, Ax, and all suited connectors and folds otherwise, leads to:



check out the different frequencies. (don't get misled by the magnitude in differences though, this game doesn't make any sense as is )