Ed Miller on Preflop

Great preflop analysis from the great Ed Miller:

Hi,

Well, there are two basic types of preflop errors: giving too much action (calling or raising too loosely), and not giving enough action (playing too tightly or too passively).

It's relatively easy to quantify the mistake of giving too much action... or at least to narrow its cost down to a reasonable range. That's because the mistake CANNOT POSSIBLY cost more than the extra action you gave.

That is, if you are playing $2-$4 and you call with seven-deuce under the gun, that is BY DEFINITION, no worse than a $2 mistake. That is, after your initial call, you could simply resolve to fold to any subsequent bet or raise at any time, no matter what. That would be pretty dumb, but it shows that the mistake can be no worse than $2.

(Now, making that mistake might get you into a situation where you make more mistakes and lose more... but the ORIGINAL mistake costs at most $2. Remember, you can always fold.)

Furthermore, giving too much action almost never costs you the full $2. That's because you will win some percentage of the time. With seven-deuce, you will sometimes flop trips or two pair, or a straight draw that comes in, or a pair of sevens that holds up, etc. You don't win your share, but you win sometimes, and that defrays the cost of your error. So calling UTG with seven-deuce might cost somewhere between $0.75 and $1.50 instead of the full $2.

In my quiz, I had three examples of giving too much action:
1. Calling with J2s on the button after three loose limpers
2. Raising UTG with 22
3. Calling from the small blind with 72 after two loose limpers

None of these errors is particularly bad. Calling with J2s after three loose limpers is barely an error. Q5s would be break-even or slightly profitable in that spot. J5s is similarly very close to the line. J2s is not much worse than J5s. So that error is maybe a $0.10 error in a $2-$4 game.

Raising UTG with 22 is a little tougher to quantify. But remember that calling with 22 UTG is correct in many games, and when it is wrong, it isn't a big error (on the $0.05-$0.25 scale). So let's assume that calling is break-even... what is raising on top of that? Well, it is at most $2, but it's not nearly that bad because if the first bet is nearly break-even, the second bet cannot possibly drop off so quickly. So again this error is probably in the $0.10-$0.30 range.

Calling from the small blind with seven-deuce costs at most $1. It is actually probably more like $0.50. So that's probably the worst "giving too much action" error of the bunch, but it's still only a quarter of a bet.

Now examine the "not enough action" errors. Using the "it must be less than X" logic doesn't help you as much here. So the estimates will be less precise... for the purpose of this post, I'll resort to pitting against random hands for the ATs hand.

So there are five loose limpers and you have ATs on the button. Against six random hands (assume the big blind comes along), ATs wins 23.5% of the time (from gocee.com). Your "share" is 1/7 or 14.3%. Thus, ATs wins approximately 23.5 - 14.3 = 9.2% "more than its share." Raising nets you 9.2% of all the post-raise action (in this case, one bet for each player, or seven bets), so failing to raise costs you about 0.092*7 = 0.644 bets or about $1.30 in our $2-$4 game. Now that's obviously just an estimate... real poker isn't played hot and cold. But that $1.30 number is WAY bigger than the numbers we got for the other errors, so we can conclude that failing to raise ATs in that spot is almost certainly a bigger error than the others.

Folding the AQ from UTG is the hardest one to quantify. You can do it logically, but I'm going to resort to using the Pokerroom.com data. Pokerroom says that AQ UTG in a 9-handed $1-$2 game is worth $0.34. So in a $2-$4 game, it's worth $0.68. Now that's how an AVERAGE player might play it, so a good player could possibly make it worth somewhat more. And the data comes from a small enough sample that it will have some error associated with it. But from that $0.68 number, we could fairly place an upper bound at $0.90 or $1 at most.

So based on this analysis, I'd rank the errors as follows (ordered from worst to least bad):

1. Just calling with ATs
2. Folding AQ
3. Calling 72
4. Raising 22
5. Calling J2s

The last two are very close.. perhaps too close to call using this very rough estimation technique. Hopefully that helps...

Ed

And followup:

Now, I want to make something clear.

It is a bigger error to play way too many hands than to play way too passively.

But how can that be, since I just showed that playing too passively was significantly worse than all three of the "loose calls/raises"?

Frequency. The net effect an error has on your winrate depends on two things:

1. The magnitude of each individual error
2. The frequency with which you are presented with situations to make the error

The total cost of being prone to make a certain error is the product of the two... the individual cost times how many times you make it. When you play a hand you should fold, that individual error is relatively small. But you get presented with the opportunity to make that error 30 or more times per hour.

On the other hand, opportunities to raise come up much less frequently, and even the most passive players find the most profitable raises (AA-QQ).

So you are better off if your error of choice is to play too passively with big suited aces like ATs than you are if your error of choice is to play loosely and call with hands like J2s and 72. But you'd be even better off if you didn't make either error. Smile

Finally, your question about "how low do you go" with the suited aces? Well, this is, to some extent, a guess... but I generally raise limpers on the button with A8s... sometimes with A7s... and usually not with A6s or lower. A7s-A4s are relatively close in value... the wheel power of the weaker hands makes up somewhat for the lack of strength... so A7s and A5s are about equal and A6s and A4s are about equal. A3s and A2s are weaker, and A8s is definitely stronger. So that's about where I stick the line, A8s/A7s.

finally:

Wenona wrote:

I was wondering how universally you can apply this type of analysis.

For example you say the break even in your example might be around the A8s mark. A8s has a win rate of 20.3% against 6 opponents (gocee), so obviously those win rates must be discounted because the six limpers surely would average better than six random hands.

However, I see KJo has a win rate against six opponents of 20.2%.

Would you consider this a reasonable (say 0ev) hand to raise on the button with 5 limpers and the expected big blind? Or are there other factors that need to be considered that would make KJo a call or fold as compared to the A8s hand, even though their win rates against 6 opponents are nearly identical.

Well, if the hands win approximately the same amount against random hands, then you have to evaluate two more variables:

1. How does the fact that hands are non-random affect your results?
2. How will raising affect the way your hand plays post-flop?

Item 2 is the more important, generally. In this example (A8s vs. KJ), you are clearly better off raising A8s due to post-flop effects.

Effect 1 is that, even though A8s and KJ win equally often hot-and-cold, A8s will win more often IN PRACTICE because you will see the river more often with A8s. A suited hand like A8s will FLOP DRAWS more often, allowing you to continue with the hand when you would have folded an offsuit hand. A king or jack on the turn or river does you no good if the betting forced you to fold on the flop.

Effect 2 is similar, but relates to how your play DIFFERS from your opponents'. Say you were playing $1-$2 hold 'em, but you made a strange rule that everyone had to ante $100 before each hand. How much could you beat that game for?

Not very much, if anything at all. The huge pot makes it correct to go to the river with almost any two cards. And that's exactly what everyone will do. So you cannot be "skilled" at that game... you'll chase to the river, and so will everyone else. You have no edge.

The smaller the pot post-flop, the more your skilled play earns you. If the pot is $1000 already, you cannot outplay your opponents. But when it is only $10, you can.

One of the main ways you outplay your opponents is by folding when you are supposed to (and they don't). The smaller the pot, the more opportunities you get to outplay your opponents in specifically this way.

That's relatively obvious, and most people seem to understand that. What people don't know is that, therefore, you should be more willing to raise suited hands than offsuit hands. Offsuit hands miss the flop more often (because they only rarely flop flush draws), so it is correct to fold them more often. Thus, you get more chances to outplay your opponents by folding with offsuit hands than you do with suited hands. Therefore, there is a stronger incentive to keep the pot smaller with offsuits than with suiteds.

Now don't take that too far... if you have a huge preflop edge (you win far more than your share) like with AK or AQ, you raise... that incentive to keep the pot small isn't large enough to overpower the huge immediate gain you get from raising.

But if you are comparing two hands that win exactly as often (as A8s and KJ), then be more inclined to raise the suited one.