Big vs Small Mistakes

[Paul Thomson]

There are lots of poker decisions that are marginally EV, where all decisions will yield nearly the same profit or loss. On the other hand, there are some poker decisions where the opportunity to make a small -EV decision or a large +EV decision. In these latter cases, it's imperative to choose the latter.

MARGINAL EV DECISIONS
We see them all the time.

For example, Hero has 7[img]/images/graemlins/club.gif[/img] J[img]/images/graemlins/club.gif[/img] with $50 behind.

FLOP ($50) Q[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/club.gif[/img] 2[img]/images/graemlins/diamond.gif[/img]
Villain bets $50. Hero?
We know the Villain at least has a Q. We are getting 2-1 on our call and have a flush draw which is 33% to win. The difference between folding and calling for the Hero is marginal in terms of EV in a vacuum. In other words, it really doesn't matter if hero folds or calls.

BIG vs small Mistakes
Here's a post from a couple days back that illustrates my point well.

Pushing off a better hand

1)
villain is 36/19/5 i really think he's squeezeing here so i 4bet light, planned on calling a push but don't really know what to do when he flat calls... should i shove flop? c/f?

Full Tilt Poker
No Limit Holdem Ring game
Blinds: $1/$2
6 players
Converter

Stack sizes:
UTG: $325.90
UTG+1: $0
Hero: $400.35
Button: $105.30
SB: $211.85
BB: $183.85

Pre-flop: (6 players) Hero is CO with 6[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/club.gif[/img]
UTG folds, Hero raises to $7, Button folds, SB calls, BB raises to $25, Hero raises to $89, SB folds, BB calls.

Flop: 4[img]/images/graemlins/club.gif[/img] K[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/spade.gif[/img] ($185, 3 players)
BB checks, Hero ?.

There's 95$ behind. If hero pushes and gets called there will be $280 in the pot. So worse case scenario Hero is getting 280:95 more or less 3-1 and has to be good 25% of the time when called.

If we assume that Villain will call us with JJ+,AK then we have 25% equity and pushing is a marginal decision. However, if Villain will ever fold JJ or QQ on the flop then pushing is significantly +EV.





2.
Here's a post from yesterday where the Hero had the choice between a big and small mistake.

Calling a push


Villain is 20/15/5 and has an flop aggression of 10 (!!), what do we do here?

Everest Poker No-Limit Hold'em, $1.00/$2.00 (HH Converter by Kreatief)

MP2 ($148.35)
MP3 ($119.00)
CO ($375.90)
Button ($342.75)
SB ($272.20)
BB ($200.00) (Hero)

Preflop: Hero is BB with J[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/spade.gif[/img]
1 folds, MP3 calls $2.00, 2 folds, SB raises to $8.00, Hero raises to $26.00, 1 folds, SB calls $18.00,

Flop: 9[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/club.gif[/img], 7[img]/images/graemlins/club.gif[/img] ( $57 )
SB checks, Hero bets $38.00, SB raises to $118.00, Hero ???

So we have to determine if the Hero should stack off here. Hero essentially has to call $144 and there's $277 in the pot. So Hero's getting 277:144 to call and has to be good here about 35% of the time to be +EV.

Should hero call depends on the Villain's range:
If Villain's range includes the nuts: all sets and straights...then hero's equity is 9% and this an auto-fold.

However, given Villain's aggressiveness this seems to stark. A more reasonable range which includes pocket pairs 55-TT, AA, AcXc,KcQc, big combo draws, draws:
equity win tie pots won pots tied
Hand 0: 45.123% 44.63% 00.49% 33138 365.50 { JdJs }
Hand 1: 54.877% 54.39% 00.49% 40381 365.50 { AA, TT-55, AcKc, AcQc, AcJc, AcTc, Ac9c, Ac8c, Ac7c, Ac6c, Ac5c, Ac4c, Ac3c, Ac2c, KcQc, T8s+, 97s+, 86s+, 75s+, 65s, 54s }

We have 45% equity and folding would be a big mistake.

Or let's assume that he only plays pocket pairs and doesn't raise with TT.

equity win tie pots won pots tied
Hand 0: 34.250% 33.63% 00.62% 6325 117.50 { JdJs }
Hand 1: 65.750% 65.12% 00.62% 12250 117.50 { 99-66, AcKc, AcQc, AcJc, KcQc }

We still have 35% equity.

Therefore, even if we are relatively conservative with his pushing range, then calling is a must, since worse case scenario it's marginally EV and best case scenario it can be hugely +EV.

Aggressive Games
Effective stacks $200.

Villain raises on the Button to $7. Hero reraises from the BB with TT to $28. Villain calls.

FLOP ($57) J[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/heart.gif[/img]
Hero bets $40. Villain raises all-in to $172. Hero?

Hero has to call $132 and there's $269 in the pot. Therefore, Hero's getting better than 2-1 on his call and has to be good 33% of the time.

If Villain will push with JJ+, AK+ then hero has 36% equity and should call. The reason that we should call is that there are a reasonable number of ways to make AK (16) vs hands that dominate us (21) that calling is +EV. If Villain will also do this with AQ, then calling is imperative.



FOLDING EQUITY in a big pot.
Effective stacks $200.

Hero raises to $7 with 8[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/club.gif[/img] from UTG+1:. Villain calls from the button.

FLOP ($17) 6[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/club.gif[/img] 2[img]/images/graemlins/spade.gif[/img]
Hero bets $13. Villain calls.

TURN ($43) 6[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/club.gif[/img] 2[img]/images/graemlins/spade.gif[/img] 3[img]/images/graemlins/club.gif[/img]
Hero checks. Villain bets $30. Hero raises to $150.

I'm too tired to do the math, but your FE is huge here and just calling the turn would be a huge mistake even though you're getting good odds since our EV against his calling range is still pretty decent.

I think these last 2 examples just point out how important it is to play correctly in big pots. I know this is kinda rambly but I hope it's helpful to some of you.