Fold Equity (2) - Continuation Bet
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Fold Equity (2) - Continuation Bet
by MiiWiin
In the previous part there was a lot about the basics of fold equity to discover and why it can be an advantage in every spot.
Mainly, fold equity will be of interest to you in a bluff. You can find out here how you can estimate it.
PartyPoker $25 NL Hold'em (6-handed)
Stacks & Stats
UTG ($25)
MP ($25)
CO ($25)
Hero ($25)
SB ($25) TAG
BB ($25)
Preflop: Hero is BU with 
3 folds, Hero raises $0.75, SB calls $0.75, 1 fold
Flop: ($1.75) 
(2 players)
SB checks, Hero bets $1.20, SB folds
This example is from the first part. The realisation was that because of the good flop, your position and your opponent the fold equity will be really high so the bet is +EV.
But these are just assumptions which apply roughly but definitely need to be researched more precisely.
Mathematics
In theory, the mathematics is simple. You'll generate fold equity (FE) with a bet, so FE (required) < FE (available).
The value FE (required) is easy to calculate:
You bet $1.20 on the flop in order to win $1.75.
Required fold equity: 1.20 / (1.20 + 1.75) = 40.66%
So you need about 40% fold equity, to make the 'continuation bet' move profitable. The question now is: do you have it?
40.66% < FE (available)
The fold equity needs to be practically over 40.66% to make the bet profitable.
Hints
There are three ways to estimate the fold equity:
This is done from top to bottom. The opponent's alright so far, it's a good board and you're in position. The perfect conditions for a contibet.
You can work with stats to look at your opponent more closely. How often does your opponent fold generally? Does he call more in position? Does he fold a lot on the turn?
What is his went to showdown stat?
You can estimate your fold equity better with these values, but always whilst taking the rough variant into consideration. Even if your opponent likes to fold, you need to stick to the basics.
Generally he'll fold more here out of position on a dry board than in position on a wet one. Moreover, the values pertain to all situations, so multi-way pots could also change the stats.
Now things are very precise. You're looking carefully at your opponent, you give him a range and look at what portion of the flop he'll continue to play.
For this you need the VPIP value of the respective position, ideally a cold call value.
The calculation won't be easy in the end, as you don't work it out in 'hands' but in 'combinations'. So as not to let things get too much out of control, the small blind in example 1 has a cold call value of 12% in the small blind vs. steal.
Now comes the parameters which you need to create yourself:
- What sort of 12% range does this player call in the small blind?
- In light of this, what does he fold and what does he 3-bet?
- Which hands does he keep playing on the flop?
It's important to know how many players 3-bet. It makes a difference if a player with 12% cold call also 3-bets 3% of his hands or 13%. This alters the ranges.
Thus the final stats:
Cold call value in the small blind vs steal: 12%
3-bet value in the small blind: 6%
Now you can work with this.
The range
Now you need to determine the small blind's range.
Starting from the top, what does he 3-bet?
6% isn't an awful lot, the distribution will be around 50% bluffs and 50% value 3-bets.
You can just about bet the following: JJ+, AQs+, AKo (3.32%).
About 3% of bluffs would be possible here: 22-33, A5s-A4s, K5s, QTs, 98s, 87s, 76s (3.02%).
This makes his 3-bet range: JJ+, 22-33, AQs+, A5s-A4s, K5s, QTs, 98s, 87s, 76s, AKo (6.33%).
Thus these hands won't cold call.
Now you need to make some rough assumptions:
- He calls with medium pocket pairs [44-TT ; (3.17%)]
- He calls suited connectors, but just over 50% of JTs-54s [JTs-87s ; (1.21%)]
- He calls broadways and AQo [AJs-A9s, KTs+, QJs, AQo-ATo, KJo+ ; (6.64%)]
- Extra hands, sometimes a suited ace, sometimes a suited gapper [A7s, A2s, T8s, 97s ; (1,21%)]
This gives the following range: 44-TT, AJs-A9s, A7s, A2s, KTs+, QJs, JTs, T8s+, 97s+, 87s, AQo-ATo, KJo+ (12.22%)
You can live with this.
The combinations
The hands your opponent folds are now decisive on the flop.
- A pocket pair has 6 combinations.
- With a potential set only 3 remaining combinations.
- A suited connector has 4 combinations.
- An offsuited hand has 16 combinations.
- With a potential top pair only 12 combinations.
At the same time you always need pay attention to whether the board makes some combinations impossible.
Sounds quite horrid but it's quickly sorted:
44-TT (39 combinations)
Process of elimination on the board: 99 hit set.
Combinations:
6 pocket pairs * 6 combinations = 36 combinations
99: 3 combinations
JTs-87s (14 combinations)
Process of elimination on the board: T9s and 98s have hit.
Combinations:
JTs/87s => 2 * 4 combinations = 8 combinations
98s/T9s => 2 * 3 combinations = 6 combinations
AJs-A9s, KTs+, QJs, AQo-ATo, KJo+ (82 combinations)
Process of elimination on the board: all Ax/Kx hands have hit something.
AJs-A9s: 3 * 3 = 9 combinations
KTs-KQs: 3 * 3 = 9 combinations
AQo-ATo: 3*12 = 36 combinations (-AJs/ATs) => 30 combinations
KJo/KQo: 2*12 = 24 combinations (-KQs/KJs) => 24 combinations QJs: 4 combinations
A7s, A2s, T8s, 97s (13 combinations)
Process of elimination on the board: Ax and 97s hit.
A7s/A2s: 2 * 3 = 6 combinations
T8s: 4 combinations
97s: 3 combinations
Villain's flop play
After all the combinations are present, the question needs to be asked: what will your opponent play out of position.
To avoid bringing too many assumptions into the game there's the following compromise:
Still in the hand:
99, 50% proportion of TT => 6 combinations
50% of his T9s, 98s hands => 3 combinations
AJs-A9s, AQo-ATo => 39 combinations
75% of his Kx hands => 25 combinations
A7s/A2s => 6 combinations
33% proportion of 97s => 1 combinations
Total: 80 combinations
check/fold it:
50% proportion of TT, 44-88 => 33 combinations
50% of his T9s, 98s hands, JTs, 87s => 11 combinations
QJs: 4 combinations
25% of his Kx hands => 8 combinations
T8s: 4 combinations
67% proportion of 97s => 2 combinations
Total: 62 combinations
The result
You need: FE (required) < FE (available)
FE (required) = 40.66%
FE (available) = 62 combinations / (62+80) combinations= 43.66%
FE (required) < FE (available) = 40.66% < 43.66%
So the continuation bet is good.
| » SUMMARY |
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In this example you should recognise how you can derive similar fold equity calculations. Ultimately, it's not easy as you need precise values for a large sample size, you'll need to assume ranges and estimate your opponent's flop play. That your opponent calls a lot of hands once on the flop, but check/folds marginal hits on the turn is not taken into account. |
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