Rolled on the River

Recently StoxPoker coach Stosh McConnell and I started discussing the concept of four betting light versus four bet shoving. What do we mean by this? Well, basically Hold’em betting patterns are commonly referred to using numbers. (Although a common misconception, this use of numbers doesn’t have any correlation to the bet size.) For example, the first bet into a pot is usually referred to as “opening”. If this bet is then raised, the person who raised them is said to have “three bet”, while the next person to raise would be “four betting”. What Stosh and I were discussing is whether it would be profitable to four bet shove our Ax (An ace with any second card) hands, as opposed to four betting these hands lightly (by lightly we mean raising the three better by a small amount - the strength of the play often having enough merit that the raise itself doesn’t need to be large). We were mostly focusing on the $0.50/$1.00 stake online, and thought the play may have some merit due to how lightly people currently three bet at these limits.

Example NL100:

SB: $.5
BB: $1

Hero opens for: $4
Villain three bets to: $13
Hero four bet shoves for: $96

There is now $114.50 in the pot, and Villain needs to call $87. To make this call profitably, Villain needs to have at least a 43% equity (87/(87+114.5)=0.43176).

Assuming Villain calls, and we only have one overcard (our ace), then we are still 30% likely to win. Villain is less likely to call with an ace, since there are fewer aces available due to card removal effects. The merit of this play, however, doesn’t come from Villain making a call here, but rather from the fold equity that the strength of our play has (generally we will also fold out most hands that completely dominate us, except for AK and AA combination’s).

I then spoke to Felipe Mesquita (another StoxPoker coach) to take this further. We made the following assumptions:

Assuming these are the ranges for our Villain, then, taking fold equity in consideration, we lose 17bb’s each time we make this place. Fold equity is a much lower consideration in this example, since Villain is three betting us with QQ+,AK and calling with any AA-KK, AKs combination, essentially he’s only folding a small portion of his hands (QQ, AKo).

We adjusted the second example’s ranges to take into account a more typical NL100-NL200 opponent. In this example, Villain three bets with 22+,AJ+,KQ (10% of hands), however, his calling range stayed the same. In this instance the play actually became profitable for us, making 7bb’s. If we then adjusted his calling range to include AKo and QQ, it becomes 2bb’s.

Basically, the end result of our experiment is that it can be profitable to four bet shove against the right opponent (one who three bets 10% of his hands).