Okay, so recently we've had a bunch
of (http://www.cardschat.com/f50/10-nlhe-full-ring-kk-oop-193497/) threads (http://www.cardschat.com/f50/10-nlhe-6-max-line-check-193562/) where (http://www.cardschat.com/f50/10-nlhe-6-max-tpgk-scary-193462/) the hero finds himself in a "Clarkmeister" type situation, where you only need 1 card (or one of many cards) to make a near-nuts hand. Lots of people have been saying "Clarkmeister theorem, bet!" without really knowing why (myself included).
So quick background:
Originally posted by Clarkmeister here (http://archives2.twoplustwo.com/showthreaded.php?Cat=0&Board=&Number=1241345&page=&view=&sb=5&o=93&fpart=)
If you are -
1. Out of Position
3. The 4th flush card comes *on the river*
You should bet out 100% of the time.
All 3 qualifications must be met.
Notice, this theorem does not apply to the turn. Now many reasons for this exist, but most of them stem from the fact that we're 2 betting rounds away from showdown rather than one. If we bet the turn, the nuts can flat our bet & slowplay, sets can call in order to fill up, and we may want to check for pot control with our small flushes. There are many reasons not to auto-bet on the turn.
So anyways, why does this theorem work on the river, and why does this work with any two cards?
As a Bluff
First, lets think of the bet as a bluff. In order for a bluff to be profitable, we need our opponent to fold a certain percentage of the time. For example, if we bet $1 into a $5 pot, we're risking 1 to win 5.
EV = 5*F - 1*(1-F), solve for F = 0.17 or 17% folds for a bet of $1 into a $5 pot to break even.
So on a 4 flush board (or a 4-straight board like 2KTJQ), we can usually get enough folds for that bet to be profitable. So obviously, betting our complete air on a Clarkmeister board is profitable.
In conclusion: We have fold equity on a 4-flush or 4-straight board.
As a Value Bet
Now, in order for a value bet to be +EV, we have to be ahead of the range that calls us. Clarkmeister's theorem asserts that if you were going to check and call a river bet, that you are better off bet/folding yourself for the following reasons:
1) If raised, you can safely fold knowing you're beat. This is because it is very easy for us to have a near-nut hand and our opponent is afraid of this fact.
2) More made hands call the river than bet the river themselves. Because your opponent is in position, he will very often take a free showdown with many hands he feel he cannot get value with on this board.
So imagine this scenario, where your opponent has the nut flush, or a set on a 4-flush board (just those two hands). If we have a 2nd nut flush, obviously bet/folding will show a larger profit than check/calling if our opponent bets all his nuts and checks all his sets.
And this is how opponents typically play. When they are one street away from showdown, and they have a decent hand, they typically will check and see a showdown. But since they're only 1 bet from showdown, they'll often call one bet with some of those hands because they get to see a showdown. Being close to the end of the hand and getting to see your cards often affects people's decisions on the river, and you should exploit their desire to see a showdown.
So obviously, if we have a near nut hand like a big flush on a 4-flush board, we should bet.
In conclusion: When you are 1 betting round away from showdown, your opponent will call with more hands than he will bet himself for value.
The In Between Range
A lot of the controversy on what this theorem implies comes from hands that are "in between". And by "in between" hands, I mean hands that can beat many hands that weren't completed by the scary river card. If we have 6♦6♣
on a 6♥
J♠T♠2♠K♠ board, what's the best line?
Well the theorem implies that the margin for error in betting is smaller than that for checking. If we bet, irregardless of cards, we know that it will be +EV as a bluff alone. So we KNOW this line is +EV. Don't get caught up in "what worse calls, what better folds", if we bet $X on the river and get X% folds, we always profit, and that X% is almost always obtainable given the board texture.
Also, our opponent could call with K♥J♥
, or fold A♥Q♥
. Both of these results would add to our expectation over checking (since villain likely checks back both of those hands).
Now yes, check/calling could possibly be more profitable with these in between hands. Our opponent could bluff X% of the time, and given the pot odds
we get, we could pick off those bluffs and profit more than betting ourselves. However, the problem with a Clarkmeister board is that villain very rarely has pure air. Since just about every draw got there on a Clarkmeister board, your opponent does not typically have many hands he can turn into a bluff. For a player to bluff on a Clarkmeister board, he'll typically have to turn hands like top pair or two pair into a bluff.
Therefore, we know bet/folding is profitable, and we know our opponent does not have the typical hands (like broken draws) that he will turn into a bluff. Lastly, even if we did know our opponent had some broken draws, we're not certain that he will bluff them more often than bluff catching with his hands that have showdown value. In order for check/calling to be more profitable than bet/folding, we have to be very accurate on those 2 assumptions. And there's a lot of margin for error there. Thus, bet/folding is typically the line we choose since its reliably profitable.
The Annoying Caveat
Now, if you click the link to that evil forum the mods don't like me linking to, you'll notice the Clarkmeister post was originally created in the limit hold'em
forum. So what does this mean?
Well playing limit hold'em, you see showdown far more often. Calling the river for 1 bet with any hand that has some showdown value is standard, since the pot is usually large compared to the size of the bet. Also, our opponents are generally less likely to bluff playing LHE than NLHE, because you don't have very much fold equity (because of that tiny bet size).
So therefore, Clarkmeister's assertion that many non-flush hands call a bet on the river is probably true for limit hold'em, but may not be true for NLHE where the bet size is a ton larger and our opponents are used to folding a lot more. Additionally, NLHE allows for a lot more bluffing since its easier to get people to fold when you bet out for the pot size rather than 20% of the pot. Therefore, its my opinion that this theorem shouldn't be applied to 100% of rivers playing NLHE. So you should consider the following as reasons to *not* apply the Clarkmeister theorem:
1) Against overly aggressive opponents.
2) In pots where its possible for our opponent to have many "air type" hands in his range.
3) Our hand is on the weaker end of the "in between" range.
- Fish with a high AFq
($0.35) Hero is OOP with J♠
Hero raises to $0.75
, MP calls $0.75, 4 folds
9♥ (2 players)
Hero bets $1.25
, MP calls $1.25
($4.35) 2♥ (2 players)
Hero checks, MP checks
($4.35) 4♥ (2 players)
In this hand, our opponent likely has a lot of air in his range (Tx, Jx, 6x, random overs & ace highs). In this scenario, I would check/call the river. We don't really benefit from non-flush hands calling us because those hands likely still have us beat (9x, 8x with a better kicker, TT). And while betting this board is likely +EV, I would say that picking off a bluff is likely more +EV in this specific situation.
So what have we learned? I'm not sure I've learned anything other than the fact that "it depends" is still the answer to every question. The more I research Clarkmeister's theorem, the more I start to believe it isn't universally applicable to NLHE. The three key points of Clarkmeister's theorem are still universally true though:
1) We have a lot of fold equity on scary boards like 4-flush/4-straight boards.
2) Its hard for most of our opponents to raise many hands other than the nuts on these boards.
3) Typically your average player is more likely to convince themselves that you're bluffing, and call with hands that are usually strong (top pair, two pair, sets, straights) than they are to turn showdown value into a bluff when they're just one check away from a showdown.
If you want to read more on the Clarkmeister's Theorem, I could link a billion threads, but this post really contains everything:
Clarkmeister Theorem: a Review And Discussion (http://forumserver.twoplustwo.com/35/micro-stakes-limit/1700-post-clarkmeister-theorem-review-discussion-looong-but-has-summary-430765/)