Hidden EV

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PhilGalfond on 31 Dec, 2008

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The expected value of a play is the amount of money you should expect to earn, on average, by making a play.  For instance, let’s say you have no showdown value on the river, and you make a $1000 bluff into a $1400 pot.  You expect this bluff to work half the time. Your expected value is (-1000 x .5) + (1400 x .5) = $200.

You should expect to earn $200 on average with the above river bluff, assuming you are right about it working half of the time.  Cool?  Cool.

The problem with expected value is that it’s often misapplied.  People look at a play, analyze it just like I did above, and decide that it’s a good play just because the expected value is above 0.  The problem is that when you compare the expected value of a play to 0, you assume that the alternative is to give up on the pot 100%.  So, let’s say for instance that I’m considering a flop continuation bet rather than a river bluff.  The numbers are the same as above.

We’ll say I have J-10 on a K-8-7 rainbow flop; your opponent checked to you, and you’re deciding whether you should bet.  Now there are a lot more factors to consider than just the percentage of the time he folds.  Rather than three outcomes (you check and lose the pot, you bet and he folds, you bet and he calls) there are tons of results: You bet and he folds, you bet and he raises, you bet and he calls and you stack him on a nine turn, you three-barrel bluff and get called down, you check and hit a nine turn and stack his 8-8-8 which would’ve raised you off your hand on the flop, you check and hit a jack, you bet and bluff him off his hand on an As turn, etc.

Just to look at the EV of the situation as we did in the river situation would be far too simplistic. So, what do we do?  To be honest, I’ve never taken the time to look at one hand and analyze every possible scenario starting with the flop action; I suspect it would take weeks to do thoroughly enough.  The best we can reasonably do is to mentally weigh the factors and then make a decision based on that analysis.

So, when looking at a continuation bet, you should think about 1) how often he’ll fold on that particular flop; 2) how likely he’ll raise your continuation bet, and the consequences of that; 3) how likely we are to win at showdown if we check; 4) how likely we are to stack him if we hit certain cards; 5) how many better hands fold to our bet; and 6) how many worse hands call.

A lot of people justify their bets with bad logic. An example:

You’re playing a loose, very aggressive player heads up, 25/50 with $5k stacks.  You raise A♠5♠ to $150 and he calls.  Flop is J♥ 6♠ 4♥. He checks.

Most people bet here, using the justification: “I probably still have the best hand here, so I’ll bet.”  They’ve learned from experience that a bet here takes down the pot around 60% of the time, so they win money on average with a $250 bet into the $300 pot.

The problem is that they don’t look at the “hidden” EV of checking.  If you check, not only could you check down and win the pot, but you could pick up one of your two backdoor draws on the turn, or improve to the best hand with an ace.

Also, he folds to your bet on the flop a lot of the time.  But think a little bit about what hands he’s folding. Is he ever folding a pair?  No.  He probably isn’t even folding many better ace-high hands. He’s folding hands like Q-9 and 10-9 and K-2 suited hands that you likely will win the pot against anyways.  So, he calls with hands like 6♠5♠, 5-5, etc.  But he raises with hands like K-J, 8♠7♠, K♥5♥, and some random air hands.  He then forces you to fold the best hand or a hand that had outs to improve.

Now, I don’t want to be one-sided.  He occasionally will hit a 9 on the turn with his 10-9 that would have folded.  Or decide to bluff you off your hand with a picked-up turn draw that would’ve folded the flop.

All in all, this is actually a close decision on whether or not to continuation.  I actually don’t care about which decision is right or wrong.  It really depends on your image, your opponent, the flow of the match, and other things like that.  The point is that you need to be thinking about things differently than you are.

If you continuation bet too often, a good player will pick up on it and beat you up.  Start to think about which hands you might want to check behind.  Ace-high hands are good candidates because of their ability to improve, and the fact that you don’t push out many better hands or get calls from many worse hands (making it not really a bluff or value bet, but what I like to call an “easier play” bet).

The EV of checking behind the flop with a king-high gutshot is not $0.  The EV of checking a flush draw on the turn is not $0.  The EV of calling a three-bet pre-flop rather than four-betting with A-K off-suit is not $0. Think about the value of plays that you often don’t consider.  Think about different ways a hand can play out, and what you have to gain or lose by taking an alternate line.

Just make sure you’re thinking.  Good luck.

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