Applying Renton's theorem

Something I've been trying to work on is not only putting opponents on ranges, but playing our ranges as well. This is a very simple hand where I'm making a marginal play with 87s, but I used to just give up on this type of flop, figuring someone hit this board with a weak ace.

Instead I think about my range here...I'm raising at CO so my range is presumably stronger than a button raise, even though this is a bluff. My opponents ranges: Caller is pretty tight and he didn't 3-bet, so his range on the button is largely pocket pairs, some KQ type stuff, some suited connectors, and the occasional suited ace. BB is loose and with a raise and caller, is getting odds to call with a wide range...again he didn't three-bet so we don't expect him to have a big ace or huge pair here very often. The board is very dry and hits my range a hell of a lot more than theirs.

$0.25/$0.50 No Limit Holdem
5 Players
Hand Conversion Powered by weaktight.com

Stacks:
UTG ($51.35)
Hero (CO) ($50)
BTN ($59.90)
SB ($49.50)
BB ($49.30)

Pre-Flop: ($0.75, 5 players) Hero is CO 8♣ 7♣
1 fold, Hero raises to $1.50, BTN calls $1.50, SB calls $1.25, 1 fold

Flop: K♦ A♣ 5♥ ($5, 3 players)
SB checks, Hero bets $4, BTN folds, SB folds

Final Pot: $9

Hero wins $8.75 (net +$3.25)

BTN lost $1.50
SB lost $1.50

Since it is a dry board and it doesn't hit their ranges. You can make your flop cbet smaller in this spot. $2.5 or $3 will be just as effective and since you are risking less, more profitable.

Def bet a little less $3 ish.

As said its a dry board, so you wouldn't normally bet bigger here.

Its also polarised, either they have an ace or they don't.

There are 2 players, your bluff instantly works less often than HU.

The bigger you bet with a bluff, the more often it has to be successful to show an auto profit.

In your description of their opening ranges, you missed out all the Ax hands that people will call pre but not raise, especially from the blinds.

87s is a great hand to do this with on the flop because there is the possibility of the BD flush (its worth a couple extra percent of equity)

As played, its great, the A does hit your range, but I dont think it completely misses theirs. I think if you were talking about a turn barrel where the reasoning was that if they had an ace it was a weak one because of the preflop action and if the player is capiable of folding Ax then a turn bet would be lilkely to work as this flop hits your range and mises his.

But on the flop, I think the Ace is certainly in villians range, and even more likely to be in the ranges of 2 villians, but as its difficult to continue without an ace its a good spot to c-bet. The only issue is that as the c-bet is a tad on the larger side it needs to work more often to show a profit and the fact that there are 2 villians automatically reduces the frequency that it will work.

Just trying to be less spewy...

Who calls a $3 cbet with KQ on the BTN here?

If I were BTN, I call $3 with a good K but fold to $4.

Assuming he's an unknown.

Well that is 1 hand combo. I am not going to do the math but I am almost certain it is still way more profitable a bet size even if his calling range increased by that hand.

Agree with betting less on this flop. $3.25 is probably what I'd bet here. Maybe $3.

If called in 1 spot what's your plan for turn/river?

C/F barring 6 or club.

It's not 1 hand combo, it's just near the bottom of a range.

A2-A4, KQ, not sure if I can or can't add KJ after the pre-flop call, but it will show up sometimes just with a lower frequency.

What makes me think the question is relevent is that my range is significantly wider against the smaller raise size, if this is common then the larger bet sizing may make sense. - I still agree with $3 being the optimal bet size because as far as I know most opponents ranges do not change significantly depending on your bet size. However if significant amounts of people do change their range a lot here, based on bet sizing, then there will be common situations where we should adjust our sizing.



FWIW, even just KQ isn't 1 combo, it's 12. It's just 1 hand though.

$3 has to work 37.5% of the time to show a profit
$4 has to work 44.5 of the time too show a profit

In terms of his calling range, the extra amount paid does does little.

If someone calls with Ax /Kx they do not fold when they hit the flop to one bet.

So if Ax and Kx could be called on this flop, what is being folded? QT, QJ, JT are all possibilities

This flop hits villians range 64% of the time. So with the $3 bet its a break even c-bet with the $4 its a losing c-bet. The BD flush possibilities make it a good c-bet to make because of the times it is called, you will pick up some equity on the turn sometimes.

10-03-2010 12-41-48J.jpg (http://www.cardschat.com/attachment.php?attachmentid=26727&d=1268225073)

But be under no illusion, this board does not MISS our opponents (there are 2 of them which means the SB probably entrered with a very weak hand (Ax or Kx)

IF the K were a 9, then THIS board misses our opponents

10-03-2010 12-53-29B.jpg (http://www.cardschat.com/attachment.php?attachmentid=26728&d=1268225715)

Notice that the absence of the K means this board hits him only 44% of the time rather than 65%

However, you should still bet only $3 here because the fact it hits him less means that he will FOLD more, you dont profit when he calls and you dont fold all that much extra out by betting bigger, therefore the smaller your bet the bigger your total profits.

A $4 is 33% bigger than a $3 bet, do you think you fold out 33% more hands with the bigger bet? if not its reducing your winrate!

The BB's range in this case is so wide as to be almost undefinable...people call wide from the blinds to begin with and with a cold caller on the button, they think they have odds to call even wider. At best guess, it's any pair, any broadways, offsuit connectors down to 54o and any 2 suited cards.

I think you are now trying to pick ranges that allow your play to be "good" but even with the range you just gave, and I think the any two suited is a bit far fetched, it still hits him 47.3%.

If we pull out "silly suited" hands we still get a range hitting him almost 60% of the time.

10-03-2010 23-52-59cc.jpg (http://www.cardschat.com/attachment.php?attachmentid=26743&d=1268265311)

just off the page but it hits 59% of the time

It is definatley a board to c-bet, but you are roughly breakeven in doing so, therefore the c-bet needs to be on the smaller side.

The other aditional factor is that you have the BD FD and he cannot have the nut FD. Because AK,AQand AJs are all probably out of his range, should you pick up equity on the turn you can double barrel. This allows you to push him off some of his weaker hands, and if he refuses to fold, you may hit the flush on the river (and your flush should be good most of the time).

But he does have a lot of aces and kings in his range! plus quite a few gunshots.

But a $3 bet here would have to work less than 40% of the time and therefore should show a slight auto profit

Stu, I'm less interested in playing against their ranges (although that's always a consideration, obviously) but playing my "range," instead of my actual hand. I'm raising at around 16% on the CO, this board obviously smacks me a lot more than them...I'm not even sure they are at all aware of this, just recognize the fact that I'm a PFR and this is a scary board to continue on with less than TPGK...they make top pair + less than 30% of the time by your charts and can almost never have a hand they want to raise on this board. I don't think I'm being silly about ranges, if you don't think the BTN can have J8s and the BB 54s here a lot I think you need to see some 50 NL showdowns ;D

The reason I'm showing the opponets ranges is for bet sizing.

I am fully agreed that you should c-bet here and that you are representing a bigger hand than your opponent can ever represent on this board. However your bet size is too big because although you are repping a big hand, your opponent can stil lcall with 50-65% of his range, meaning that your c-bet size results in less profit.

Basically what you are trying to do here is c-bet and have him fold and if he dosent then you may or may not barrel the turn.

With a $3 c-bet you are break even against my original range and quite profitable against the wider range.

With a $4 c-bet you are loosing against my original range and break even against the wider range.

What I thought you were trying to do was to widen his range so that the c-bet shows an auto-profit rather than say OK, maybe the c-bet itself should be a bit smaller.

gotcha, I hear what you are saying, but I think tpk123's point is pretty valid: obviously we rarely have the best hand here but we may have more fold equity if our bet looks more like a "omg i haz monster, stuff in da monies" bet than a standard c-bet (i.e., he folds KQ to $4 and calls $3).

But you pay an extra 33% for that fold equity, but dont get anywhere near an extra 33% folds.

That extra $1 folds out 3 or 4 extra hands maybe and if you happen to be in the exact situation where he has one of those few hands that would call $3 and fold to $4 then it sucks. But as you dont get an extra 33% folds you are reducing the winrate of your c-bets because the alternative is to get a few less folds but to risk 1/3 less money in this spot.

It also reduces the cost of a turn barrel should you decide to do that.

If bet size to fold equity were linear then betting the most would make sense, but its not a linear relationship

A great lesson I learned a while back about representing a hand:

Almost never rep the nuts. You've never got the nuts, no one has the nuts. No one believes anyone has the nuts. Your range gets polarized to nuts/air and you've almost always got way more air (plus, pot odds always favour calling).
Rep TPGK. I raised with AT-AQ maybe even just Ax and I hit my A.

Interesting concept, I like it, but I believe that many villains in this situation understand implicitly that this specific flop (AKx) hits my nut range a lot more than their preflop cold-calling range.

Another lesson I learned recently: Don't raise a PFR cbetting this board with ANY hand.

AA/KK/AK/55 give you the nuts here. For most villains this wont feel like many hands, anyone who actually thinks will know it's not many hands. AA/KK/AK/55 have 18 combinations after card removal, AQ/AJ/AT are 27. - If this isn't making sense, there's a thread on combinatorics around here somewhere if you do a search.

The range of KK+, AT+, 55 is really very narrow and assumes you've never got air or just a K. The reason for the narrow range is because it's for after you bet, your range as PFR has a lot of air and depending on your cbet frequency we can add more air and underpairs.
We're also assuming villain doesn't have an A or K, which would make it less likely you've got the effective nuts.

I'm not saying don't bet, I'm just saying that you should know WHY you should be betting, and that is to represent a range of Ax/Kx + occasional bluffs, so this range is strong enough that no one should play back at you with less and we're avoiding the two main problems with representing the nuts:
1: It's more expensive.
2: You polarize your range.

A. Our nut range comprises hands we bet for value and are happy to get stacks in -- as you said, AA/KK/AK/55. There is a pretty good argument for slowplaying AA and AK and betting KK/55 as there are fewer combinations for villains to continue with when we have AA/AK.

B. Our value range -- That we bet for value and call/reeval if we get raised.

On this board I suppose we can subdivide this:
Ax -- is our basic B value range. I think there's actually a good argument for including AQ in our nut range and we can profitably stack with this hand, as if we get raised on this board villain is representing basically too thin a range to be believable (55, K5 and nothing else).

JJ-QQ/Kx -- We c/c, c/f turn and try to get to showdown, as we have too much showdown value to turn into a bluff.

C. The range we c/f for showdown value, 88-TT

D. Our air and gutters (JT/QT/QJ) that we c/f or turn into a bluff.