Equity vs Strategic Advantages [Beta]

Introduction

In this Article

To what extent is it worth exchanging pot equity?
How to gain advantage on tle flop?

This article deals with the question of to what extent it is worth exchanging pot equity pre-flop to gain a strategic advantage on the flop.

The classic example for such a situation can be found in HPFAP, p. 40.

Quote:

Let's suppose you have AKo in the BB and one or two aggressive players have called from an early position. Your best play is usually (but not always) to just call and (perhaps) try for a check-raise later

The play advised by Sklansky is a big mistake. A PokerStove equity analysis delivers the following:

Quote:

Source: PokerStove
equity (%) win (%) / tie (%)

Hand 1: 38.7700 % [ 00.38 00.01 ] { AKo }
Hand 2: 30.6090 % [ 00.30 00.01 ] { TT-55, ATs-A6s, KJs-K9s, QJs-QTs, JTs }
Hand 3: 30.6210 % [ 00.30 00.01 ] { TT-55, ATs-A6s, KJs-K9s, QJs-QTs, JTs }

Against our 2 opponents we have an equity edge of 8%. If we raise, 3 extra bets come into the pot, of which 38% belong to us. Hence, a raise here will raise our EV by .14 SB's, from an equity point of view. This raise alone is already worth as much as a good hand like 99, on average!

The standard argument against this calculation is that you can make back the EV you lose pre-flop in the post-flop game, since you can protect better with a smaller pot size and bring your opposition into positions where they either fold or make bad calls. A pre-flop raise- it is argued - allows our opposition to automatically make correct calls post-flop since the pot is simply too big.

This implies, however, that a good call by the opponent must be bad for us. While this is believed by 70% of all "good" players, it is not quite true.

SB vs BB

Imagine that we are heads-up on the flop and the opponent will hit his draw on the turn with a probability of 25%. Furthermore, let us assume that we know our opponent's cards and he knows ours. We are interested in the mathematically perfect play.

Let us separate into 2 cases:

a) We checked pre-flop. Pot = 2 SB
b) We raised pre-flop. Pot = 4 SB

Case a) He checks, we bet, he folds. Frequency: 100%, Extra Value= +2 SB

Case b)
Flop: check, bet, call. Pot 6 SB

Turn, he hits his draw: bet, fold
Frequency: 25%, Extra Value - 1 SB

Turn, he misses his draw: check, bet, call Pot 10 SB
River, he hits his draw: bet fold
Frequency: 18,75 %, Extra Value -3 SB

Turn, he misses his draw: check,bet, call
River, he misses his draw: check, bet, fold
Frequency: 56,25 %, EV +7 SB

Total:

Post-Flop value unraised Pot: 2 SB
Post-Flop value raised Pot: +3.9375 - 0.5625 - 0.25 = 3.125 SB

Now of course we have invested an extra SB into the pot in the second case. Even if we include this, we still have an extra value of .125 SB in the raised pot as compared to the unraised pot.

This effect occurs because our opponent is forced to make correct calls with hands that have a weak pot equity simply because of the pot size. The size of the pot binds him to the pot. Since we raise pre-flop and already have an equity edge, we will more often bind our opponent to the pot than ourselves. Hence, the pre-flop equity clearly beats the post-flop equity. The size of this effect is not to be dismissed. Sklansky's assertion that one should not raise hands like AQo in the BB in loose games is absolutely wrong and would be a fatal mistake.

Limit pro Izmet Fekali discusses this topic in the following contribution. The gist here, too, is that pre-flop decisions are made almost entirely on pot equity. If your equity is higher than average, it is almost always correct to invest as much money pre-flop as possible. That doing so might lead your opponents to make correct calls is usually just a further gain in value for you!

Summary

In brief: Pre-Flop Strategy is based almost entirely on pot equity. If your pot equity is higher than the opposition's, you can increase the pot to force them to stay in the hand longer and give you extra value.

Here is the promised article:

Quote:

Source: Izment Fekali's website

>Dear Izmet, 6-12 hold'em
>
>I'm in the big blind last night at the Normandie, where they have
>no small blind. About 5 callers and a regular 10-20 thru 20-40
>player(whose regular game broke)raises on the button. I have A-Q
>both diamonds, I called. Would 3 betting have been best, in regards
>to what you refer to as the EV(estimated value?).
>
>Everybody but the raiser could have been holding almost any two
>touching cards(unsuited). And all the limpers would have called my
>re-raise, and then certainly a cap at that point from the button.
>
>I think the main reason I didn't re-raise was due to my horrible
>position, and then to a lessor extent, that I was somewhat intimidated
>by the higher limit player.
>
>Thanks for any help, Connie
>
>PS: I like the super-simplified explination for implied odds you
>provide at your site.

There are good arguments for calling only (as Jim suggests in his
reply). You have bad position for all betting rounds, but a good
chance to check-raise the button if the flop hits you, thus, narrowing
the field easily. This is the standard play "by the book," which
increases chances to win the pot and enables you to get out cheaply
if the flop doesn't hit.

It's a good, bulletproof, profitable strategy.

See, if you make the pot too big, postflop play turns into a
crap shoot and anything can happen. Most poker players hate that,
they hate getting sucked out by freak draws that would have folded
on the flop, hadn't the pot been so big. And that's exactly what
happens often when a multiway pot gets blown up out of proportions.
There are no guaranties, you can flop good and still lose big. You
have little control of the play on the flop and beyond, and whatever
your edge in postflop play was, it's gone through the window.
Swelled pots are a source of frustration. For a drunken, Rolex-wearing
German tourist with a miniskirt chick hanging on his shoulder, this
is fun. For a pro with a modest bankroll, big pots are toying with
death. You can see traces of sweat on his forehead and upper lip.
It's a nightmare.

But so what. If you have a bankroll, you should ram 'n jam on the
flop. Yes, the skill factor goes way down postflop, but you are
having way best of it now. Jamming is profitable.

I assume Connie is talking about a typical California-stye game
where players are loose and trigger-happy. The limpers would surely
raise with AQ/QQ or better, so we are safe to assume our only
concern is the raiser on the button.

This guy can have a wide range of cards, if he is a good player
(and even a wider one if he is a maniac). There are many hands that
show profit with a raise against multiple limpers. The only hands
you that can give you trouble are AA, KK, QQ and AK. Against these
hands, reraise with AQs is not such a good idea, as you are either
dominated (against KK, QQ and AK) or destroyed (against AA). But
even here, the five dupes in are covering for you with
their contributions (as a good chunk of their money is dead, since
they have a relatively small chance of winning the pot). You are
not in bad shape even when dominated.

But against other possible hands the button could have
(Axs/K9s/98s/77/KJo or better), you are a happy camper. You will
make a load of money even when against a better hand like JJ. But
remember, you are increasing EV (drastically, I might add) here at
the expense of higher variance. Reraise is a most profitable play,
yet you still might not want to do it. Profitability is not the
only factor when judging a certain poker play. For some pros living
in the van by the river, variance is baaaaaaad. They prefer calling.

How profitable is the reraise (and a subsequent cap if rereraised,
Nevada style) with AQs?

I ran a $10-20 Turbo sim for Connie with a player on the button
holding JJ and a player in the big blind with AQ (I did not bother
to set up the sim with a single blind like Connie's game, because
if the game is loose, the blind structure is not that important).
The lineup was loose, with players that tend to go a bit too far
postflop. To put it simply, it was a fishy table, except for the
two test players. I used the same profile (optimized for playing
in loose games) for both the button (JJ) and the big blind (AQs).
The results after 500000 runs with 5 or more opponents (at least
4 limpers + the button raiser):

AQs calling a raise in the big blind, min. 5 opponents:
---------------------------------------------
JJ, win rate: 28.0%, $ net per hand: $39.27
AQs, win rate: 26.1%, $ net per hand: $20.78

AQs jamming preflop in the big blind, min. 5 opponents:
---------------------------------------------
JJ, win rate: 30.0%, $ net per hand: $61.61
AQs, win rate: 27.2%, $ net per hand: $36.81

Against JJ and four other opponents, AQs just flat called, tried
to keep the pot small and went for a check raise with top pair on
the flop. With no hit, AQ called for one bet on the flop with two
overcards (which is a pretty much correct play, given the size of
the pot). It did quite ok, earning a big bet per hand.

But, when AQs capped it preflop, it earned almost twice as much!
The difference between calling and jamming was more than one and
a half small bet. And that's a lot, baby! Note also the difference
your jamming made to JJ's profits. The button should buy you a
drink for making him $20 with your aggressive preflop play. You
both profited, but the fish should think twice before entering a
pot with trash again...

Here's the same sim, but with QQ on the button. The situation seems
hopeless, but the fish covered the losses. Jamming with AQs against
QQ boosted profit per hand from $3.74 to $09.91. It's not that
much, considering the increased variance, but hey, I can use every
dollar...

AQs calling a raise in the big blind, min. 5 opponents:
---------------------------------------------
QQ, win rate: 31.5%, $ net per hand: $40.76
AQs, win rate: 19.6%, $ net per hand: $03.74

AQs jamming preflop in the big blind min. 5 opponents:
---------------------------------------------
QQ, win rate: 33.7%, $ net per hand: $69.93
AQs, win rate: 20.7%, $ net per hand: $09.91