Intro:
We usually 5-bet shove pretty strong hands as
a SB vs. BU 4-bet (like TT+, AQs+, AQo+),
but sometimes it can be profitable to shove small pocket pairs, too.
Have fun reading this.
Examples will be shown in BB not in $, so all the players would get it easier.
I don’t know the rake stuff, so there won’t be included one.
Let’s get started.
Situation:
- Game: NL Hold’Em 6-max;
- Effective stacks: 100 BB’s;
- Players playing: BU & BB;
- BU is TAG, 10k hands, 4-bet range: 9%;
- BB (Hero) with 55.
Action:
Everyone folds to BU:
- BU opens to 3 BB’s,
- SB folds,
- BB 3-bets to 10 BB’s,
- BU 4-bets to 24 BB’s;
- BB shoves other 90 BB’s with 55.
Task:
Calculate the EV of Hero’s shove in this situation, if BU value range is:
a) QQ+, AKo, AKs (2.6 %);
b) JJ+, AKo, AKs (3 %);
c) TT+, AQo+, AQs (4.7%).
Just try to think yourself about EV calcs before you click “spoiler”.
Answers:
Fold Equity:
Spoiler
First of all, let’s calculate how much Fold Equity (FE) we got vs. each range:
A) BU value range is QQ+, AKo, AKs (2.6 %), but his whole 4-bet range is 9%.
FE = (What we win) / (All 4-bet range) = (9-2.6)/9 = 6.4/9 = 0.71 = 71%
B) BU value range is JJ+, AKo, AKs (3 %), but his whole 4-bet range is 9%.
FE = (What we win) / (All 4-bet range) = (9-3)/9 = 6 /9 = 0.66 = 66%
C) BU value range is TT+, AKo, AKs (4.7 %), but his whole 4-bet range is 9%.
FE = (What we win) / (All 4-bet range) = (9-4.7)/9 = 4.3 /9 = 0.48 = 48%
Structure of EV calculation
Spoiler
Now we have to do EV calcs. To understand the equations better I made some picture: 
As you can see, there are 2 possible actions that can occur after our 5-bet:
1. BU folds and we win the pot.
2. BU calls, now again we have another 2 possible scenarios:
2.1. We have some pot equity (EQ) and we win sometimes;
2.2. However Villain has some more EQ too and we lose.
EV calc - theoretical
Spoiler
EV(5-bet) = Pot * (FE) + (1-FE) * [EQ*(What we win) – (1-EQ)*(What we lose)]
Here are the explanations of each calculation’s part:
- Pot = sum of BB’s each player has put into the pot before Hero 5-bet shoves.
Pot = (SB) + (BB) + (BU) = 0.5 + 10 + 24 = 34.5 BB’s
- FE = 0.71 as we calculated, therefore (1-FE) = (1-0.71) = 0.29
- EQ = 33% = 0.33 (From PokerStove), therefore (1-EQ) = (1-0.33) = 0.67
- What we win = his stack + dead money =
= 100 (BU) + 0.5 (SB) + 10 (BB) = 110.5 BB’s
- What we lose = other part of money = 200 – 110.5 = 89.5 BB’s
EV calc - practical
Spoiler
Our EQ vs. QQ+, AKo, AKs (2.6 %) is 35% = 0.35
EV (A) = 34.5 * (0.71) + (0.29) *[0.35*(110.5) – (0.65)*(89.5)]
EV (A) = 24.5 + (0.29) * [38.5 – 58]
EV (A) = 24.5 + (0.29) * [- 19.5]
EV (A) = 24.5 – 5.6
EV (A) = 18.9 BB’s
Our EQ vs. JJ+, AKo, AKs (3 %) is 36% = 0.36
EV (B) = 34.5 * (0.66) + (0.34) * [0.36*(110.5) – (0.64)*(89.5)]
EV (B) = 18.5 BB’s
Our EQ vs. TT+, AKo, AKs (4.7 %) is 37% = 0.37
EV (C) = 34.5 * (0.48) + (0.52) * [0.37*(110.5) – (0.63)*(89.5)]
EV (C) = 16.5 BB’s
Conclusions so far:
Spoiler
When we look at PokerStove for other hands to shove vs. 4-bet,
we can clearly see, that pocket pairs are the best hands for this trick.
If Villain is 4-betting wide, then even 95s or 67o could be profitable to shove,
although we shouldn’t forget, that we want to use hands with better equity more often.
Small, medium pocket pairs are also pretty hard to play on the flop,
simply because our equity often sucks.
So, our semi-bluffs would be just bad, because we only want to see set.
However, suited connectors or gappers are better for FE+EQ on the flop and turn.
We analyzed our EV of 5-bet shove vs. opponent, who has a huge 4-bet percentage,
but most often it won’t be so huge (I guess).
In this case we have to find our FE using the same calculation.
Finding FE:
Spoiler
This is the previous calculation:
EV(5-bet) = Pot * (FE) + (1-FE) * [EQ*(What we win) – (1-EQ)*(What we lose)]
Now, we have to change it:
Pot * (FE) + (1-FE) * [EQ*(What we win) – (1-EQ)*(What we lose)] = 0
The only things we want to change are:
- We set the whole calc equal to zero;
- We know these: pot, both equities, what we win, what we lose;
- Only thing, we don’t know is: Fold Equity.
So we put “x” and “1-x” in spots of “FE” and “1-FE” and find out our “x”.
It would look like this:
KNOW * (x) + (1-x) * [KNOW*(KNOW) – (KNOW)*(KNOW)] = 0
KNOW * (x) + (1-x) * [KNOW] = 0
How can we use our FE from this calculation?
Well, we can simply find our breakeven point and then go up from there.
I’ll do some math and explanations later about it, too.
Please give me your comments.
Maybe you have something to add?
