Introduction to Equity and Expected Value (EV)September 23rd, 2015 by LD1977
Understanding of equity and expected value is a crucial step towards profitable poker career.
I will avoid heavy math at this point and just define the concepts verbally and with a few examples. In practical play, complicated formulas are not all that useful, simple estimates are normally good enough.
It is best to start with definitions:
Pot Equity (usually shortened to just “Equity”)
The Fraction of the pot a hand will win on average against opponent’s hand or range of hands if (critical distinction!) the hand ends in a showdown. It is important to note that this is not the same thing as the chance the hand will win the pot. The Reason for this is that there are situations where there are split pot possibilities.
Additional equity that is the consequence of aggressive action (betting or raising).
The math can be complex. It is enough to understand that, unless we have a hand with huge pot equity (so the opponent doesn’t have implied odds to call), we gain some profit when he folds to our aggression because usually at least a few hands he folded had positive equity against our hand.
This concept is very important in tournaments in later stages when there is a lot of shoving to steal/re-steal situations. The idea is that we hope everybody folds to our shove, but if we get called there is usually still decent equity to fall back on if we know what we are doing. Suited Aces are famous for guaranteeing 30%+ heads up against anything except AA, while many other decent hands usually do well against unpaired hands or wide ranges.
It is, however, even more common in cash games in many pre-flop (blind stealing and re-stealing, 3betting, 4betting etc.) and postflop (mostly continuation betting and raising continuations bets) situations.
When estimating fold equity, it’s important to note that it is highly dependent on player types. Against a calling station, we have little fold equity and must rely almost exclusively on pot equity. “Never bluff a station,” is a well-known saying.
This is a screenshot from tracking and analysis software (explains why we see the opponent’s hand).
We are out of position against two players on the flop with a good combo draw (open ended straight draw + medium flush draw). JTs has decent pot equity here, but we still don’t mind if opponents fold their own equity. Luckily, one of our 6 nut* outs hit and we stack the stubborn opponent. The third player also adds money into the pot on the flop.
In situations like this one there is a balance between fold equity (when both players fold) and situations when our bet gets raised. I would be inclined to call if the raise is not too large and expect to be against a set most of the time. My UTG range contains both KK and QQ so I expect to be raised fairly rarely on this board (nut flush draw would rather draw in position than get shoved on).
* Flush outs are not completely “clean” since we will be against the nut flush draw some of the time. On the other hand, we will be against small flush draws sometimes so it balances out.
Not a good man to bluff if we don’t hit our draw!
Expected Value (EV)
Unlike equity, which is a percentage, expected value is a real number and represents the payoff (in tournament chips or real money) of an action. It is calculated differently depending on the nature of our action:
For calling all-in bets, expected value calculation is based on:
- Size of the call compared to size of the pot
- Pot equity (which needs to be estimated)
In tournaments, ICM needs to be taken into consideration. I won’t go into details here since it is easy to find details on ICM and tournament strategy elsewhere. General rule is “shove wide, call tight”.
In cash games, assuming correct bankroll management, the decision is almost purely mathematical (there are some image considerations against regular players).
For shoving, it is based on:
- Fold equity
- Pot equity when called (which needs to be estimated)
For betting, it is based on:
- Fold equity
- Equity and implied odds when called (which needs to be estimated)
- Percentage of time we will face a big raise and have to fold
- Percentage of time we will have (implied) odds to call a raise or shove over it (and expected result of that action)
This is fairly complex and goes beyond the scope of this article.
In the example from the previous Fold Equity paragraph, it is enough to note that size of flop bet ($3.75 bet, pot after bet is $9) means that we would need to have 41.66% pure fold equity to be break even on our bet. However, since we have a fair amount of pot equity and implied odds, the actual break-even % is much smaller.
For calling non-all in bets, it is based on:
- Equity and implied odds (which need to be estimated)
I will probably go deeper into this topic in later articles (especially when I start talking about ranges) but this should be enough for now.