Sizing wise how small could you go here till AK/AQ is a value bet? If you bet say 30% pot flop what would be the disadvantage here?

If you're betting AK for say 60% pot are you planning to triple? What are you aiming to fold out once opponent calls turn with large sizing and board remains unchanged? What are you doing with weaker parts of range on turn and rivers?

Balance night be very different for both players on some boards where one player always has a significant range advantag .
Not really a fan of pokerbooks.

Every street, you strength the ratio of value bets to bluffs (more value bets on later streets). This is a basis of game theory.
Now, here is why we shouldn't be betting 30% pot...
Our opponents range is mostly merged and our range is mostly polarized; therefore, the bigger bet sizes is clearly more beneficial for our range.
The only times you should consider betting 30% pot is in very specific situations such as when your opponent's range is very polarized and he showed weakness and has longshot draws. Betting small avoids losing much on a check-raise, but gets to fold the weaker part of the range that might draw out.
Clearly though, this is not the case. We should be betting much bigger than half-pot just based on range vs range equity distribution alone.
What are my planning to fold out? Most of our villains range is merged, and we are looking to extract max value with our range. Now, as an aside, even if AK isn't considered a value-bet, it can still be correct to bet or raise in first position.

In very simple terms, our range mostly benefits from
A bigger sizing because the bigger the bet size, the more the ratio of value bets to bluff can be smaller. Furthermore, we bet mostly with a polarized range vs a merged range where a bigger bet sizing extracts more value. Finally, our range distribution is mostly stronger, and we should therefore adopt a more aggressive strategy as oppossed to passive.

The bigger the betsize the more bluffs you can incorporate compared to valuebets.

It's unlikely our range is "polarized" on this board as a lot of A highs and stuff that has plenty of equity and some of those we'll certainly want to bet.

Also when we hold the range advantage it's better to bet smaller so we can get calls from villain's weak range.

Yes! The bigger the bet size, the more bluffs you can incorporate compared to value bets; and hence, the greater equity you obtain!

As a matter of fact, in last position our range should be somewhat polarized. Think about preflop. In the SB (out-of-position) you mostly 3-bet a merged range. In contrast, on the button (last position), you mostly 3-bet a polarized range. This concept should be fairly intuitive and obviously applies postflop.

Our "plenty of stuff that has equity" can and should check behind, to strengthen both our checking-behind range and c-betting range. This should obviously be balanced with strong hands occasionally through mixed strategies.

It is true that in some situations we should bet smaller to induce calls and go for thin value. However, realize that if you polarize your range (rightfully so in my opinion), then when we consider your betting range with Bayes Theorem, the hands that do want to bet benefit tremendously with a bigger sizing. Furthermore, the EV you get with a 30% pot bet is truly small, and I doubt you'll bet for more than one street of value with A high (when the turn does not bring an ace); thus, effectively turning your hand into a bluff-catcher against aggressive villains who will lead on rivers. A smaller bet sizing, also sets a better price for villain to check-raise, and can telegraph your hand if you don't balance this or use multiple bet sizes within your range.

I am not saying that you should never bet hands like AK on the flop. In fact you should some of the time for multiple reasons already discussed. However, I really doubt a small bet size is the optimal sizing here; unless of course, we have reason to employ exploitative strategies.

Not sure what you mean by the greater equity we obtain. Do you mean EV? Any way that concept is sort of moot before the river when hands still have equity. I mean it's not entirely irrelevant, but it's not as clear cut as in river scenarios.

I only brought it up because you seemed to be saying the opposite in your previous post.

Yes I have heard this before. It's not always that cut and dry as our opponent can change our decision to merge or polarize our range.

Yes I think we should be checking some of our stronger non-paired hands but we will likely have quite a few hands that will triple this board especially with our range advantage so carrying enough bets forward in a b/b/b line is important.

Choosing a smaller sizing for all of our hands helps because we can buy the pot more cheaply, we can get lighter calls from worse hands, and we actually might save some of our showdown bound hands money from preventing larger bet sizing bluffs on later streets (say AK for example).

Choosing a polar line is not so great here because choosing bluffs with little or no equity leaves us in a bind on future streets. We'll be betting into stronger ranges (because we don't block anything) and there will be many more cards that make it difficult for us to continue.


Well I'm not sure what you mean here. Any "nut" hand on the flop will likely go for 3 streets so as long as we don't prevent ourselves getting all in by the river or force ourselves into awkward betsizing then this doesn't matter because they will get all the money whether we shovel it in on the flop or the river. The rest of our range benefits from the smaller sizing.

This is a game of small edges. EV is EV. I wouldn't be opposed to multiple barrels with A high either depending on villain's calling range.

I'm sure there are other hands that we can bet 1 street for value and check to protect our A high or bet our a highs as bluffs.

If villain is skilled enough to c/r us here on a bluff because we bet small should mean he's skilled enough to know that our range has the advantage and that means he can just c/r with impunity.

Like I said the small sizing definitely benefits most of the rest of your range for a lot of different reasons.

In vacuum 3 barreling here seems questionable. He is going to have Ax probably about 60% of his range at least and I don't see how you get someone off that without reads. Basically saying you want to triple this runout means he has had to peel the turn so super light with any pair meaning your turn bet wasn't great.

Checking the turn should also be a viable option.

I think Ax is a pretty big part of his range

just_grindin,
I think we probably disagree on two important aspects, namely: Bet sizing on the flop and (probably) the frequency we bet the flop as these strategies are inherently related.
Personally, I don't c-bet too often (unless I play vs fit-or-fold players), and rarely c-bet over 75% of the time unless my range advantage is tremendously superior than my opponent.
Furthermore, I think it is important to polarize your ranges, in position. However, upon polarizing my range, I employ mixed strategies, meaning that I sometimes bet with middle part of my range, often check-fold the weakest part of my range, and sometimes check-raise/call the top of my range.
Obviously, I strengthen my betting range (and calling range) on every street, by reducing the ratio of value bets: bluffs type hands.
Yes, I agree that if you mostly bet all of your range 100%, then the smaller sizing is mostly beneficial. I also agree on range construction (especially with deeper stacks) that it is important to bet flush draws or AK type hands of the sort to be able to represent these hands later on. In fact, Bill Chen showed how having a "nut depleted" range is typically very bad for one's expectation. This is why I occasionally bet those hands, while making sure to polarize my range.
Finally, the hands I usually bet, namely TT+ with weak semi-bluffs(/air depending on range and board), and occassionally AK type hands benefit more from the bigger sizing, given the range is somewhat polarized.
The only time I think you should be c-betting 100% of the time is when your range is soo strong, that you can bet, and your opponent should always surrender the pot.

Yes I would say our disagreement is more about the former than the latter, but I agree the are related and that our cbetting frequencies may differ.

That's fair. I doubt I cbet 75%+ of the time without the range advantage either. Cbetting alone is certainly not as profitable as it once was.

I personally don't think being in position is the largest factor in determining whether we should polarize our range or not. It seems like other factors would be more important.

Not quite sure what your point is here maybe you could elaborate more? Basically you don't always play the same hand the same way depending on certain circumstances?

You don't have to bet 100% of your range to see an advantage to betting smaller. Many parts of your range benefit even beyond cheaper bluffs while very few parts suffer from the smaller sizing.

I'm not sure what this means. Sometimes your range is nuts and very low equity hands and sometimes it's nuts and some medium equity hands and no bluffs?

Well they don't really suffer from the smaller sizing because they will bet more streets. So in the end you'll probably have a better situation on future streets for all of your range.

From your explanations it really seems like you're thinking as if this was a single street game.

The optimal bet size for a range composed of either nutted hands (the pure nuts) or bluffs is one where we bet an equal percentage of the pot on all streets, while being all inn on the river. This is shown in many books such as: Applications of No-limit Holdem by M. J. - Not sure if its in the mathematics of poker book.
Thus, if we bet 30% of the pot on all streets, we will have a total river pot size of 61.44 BB. With a 60% pot size on all streets, we will have a total river pot size of 159.72 BB. Finally, with a 80% bet size on all streets we will have a total pot size of 207.36 BB, but the effective stack size is 100 BB so we will be all inn for a pot of 200 BB.
Moreover, given our range isn't comprised of either the nuts or bluffs, but hands that will change in equity, this holds to reason that we should bet even more on the earlier streets (Matthew Janda goes into this concept in his book).
Now, if our opponent does decide to fold more to deny our value with the top of our range, our bluffs become more valuable obviously.

Thus, sure we might get cheap bluffs by betting smaller, but our overall range (especially the hands that want to go all inn) benefit a lot more from the exponential growth of the pot. Pocket aces gets a lot more value (more than twice as much!) with a bet size in the vicinity of 60-70% pot on every street.

Now what do I mean by mixed strategies? Consider the following example: The game is 9-max and UTG opens. UTG +1 can employ a strategy of say: 3-betting 80% of the time (or else calling) with AA-KK-AK; 3-betting 20% of the time with QQ-99, AQs (calls the remaining 80%), and 3-bets KQs-76s around 15% of the time (or else folds). Notice that this range is polarized: It Usually 3-bets its stronger hands, but not always; usually calls with its medium strength hands, but not always, and bluffs with the bottom part of the range.
Therefore, polarized ranges are usually seen as either betting the nuts or air, but this isn't necessarily always the case for range purposes.

Thanks for taking the time to respond. Just so you know this will probably be my last post on the subject. I feel like we're going in circles and not getting anywhere.

Not many board/hand combinations have 0 or 100% equity before the river. There's no reason nutted hands prefer to bet an equal percentage of the pot. I can believe that there are toy games that illustrate nut hands may prefer to bet pot,pot,pot but that doesn't equate to always preferring the same relative bet size on every street. As long as we get all in it shouldn't really matter.

I would be interested to hear the logic on this. The fact that hands change equity would lead me to believe we should be putting in less money on earlier streets.


Well the hands that benefit from going all in are a very small fraction or your range so saying your overall range benefits from the larger betsizing just because those hands benefit seems odd to me. I agree that more money that goes in earlier the easier it is to get all in, but that doesn't mean you can't get all in with smaller betsizing on the flop.

just_grindin, I would like to point out that I enjoy your posts regarding the subject, and it got me thinking.
Now, onto the post...
Poker bet sizing is very subtle. I recommend you read the mathematics of poker, because it shows a formal proof that a player with a polarized range of the pure nuts or air should be betting equal fractions of the pot on all streets and be all in by the river to maximize his earnings.

Regarding making bigger bet sizing on early streets when our hands can be easily outdrawn, here is a passage from M.J.'s theoretical book: "When our hands are susceptible to being outdrawn on later streets, we choose a descending bet sizing structure." Once again, I recommend you read the book for better understanding of the rationale and ideas implemented into practice.

I also quote from the book that: " Small bets are often effective against polarized ranges. They prevent our opponent from getting to see free cards with his weak hands while minimizing the effectiveness of his raises."
In the example, we (not villain) have the polarized range with more nutted hands, and should be betting bigger.

I also believe that upon somewhat polarizing our betting range, most hands we do want to bet benefit tremendously by playing a pot more in the 200 BB range than the 60 BB range since hands such as AA or KK (without a turn A) really want to go all in.

I own MoP but it's been ages since I read it. I'll go through it and look for the information you're describing. I assume it's in the AKQ game section, but I suppose [0,1] and other toy games illustrate the same point.

I assume by theory book you mean Applications of No limit? I don't own that one so Google might have to be my friend there.

As I said there's nothing preventing you from playing for stacks at 100bb. FWIW I would pretty much never bet a flop for 30% pot, but 40% is not out of the realm of possibility.

Yes, I am referring to applications of No limit Holdem. However, I find that the Mathematics of Poker was much more helpful in understanding poker theory; however, you do need a strong mathematical background and did Calculus which, sadly, most people do not know.
I do not object to betting 40% or even sometimes 25% of the pot in some situations especially on later streets; especially versus polarized ranges.

I didn't look at MoP yet but Janda wrote an article for donkr and I think I remember why he choose equal pot sized bets for 3 streets. It's because he wanted to be able to put as many bluffs as possible in his polarized range. That also means he's betting the flop with very high frequency, because some of his "value hands" on the current street are bluffs on later streets.

Applications of No-Limit Hold'em discusses this case in detail (with many examples). However, I would like to point out a few things:
1) By employing this strategy, M.J. does not necessarily bet the flop frequently (in fact, sometimes he rarely bets at all); he just has the appropriate ratio of bluffs to value bets for every street.
2) The value hands he does bet are usually bet all three streets. If not they mostly strengthen his checking range.
3)He does not advocate value betting a hand on earlier streets, and betting as a bluff with that hand on later streets. Think about it, if this is the case, the flop "value bet" is just a bluff then!

In regards to 3 I meant he considers bluffs on the river as part of his value bets on the turn when calculating the number of turn bluff combos, same for the flop with turn bluffs.

And yes that would tend to increase your betting frequency given the large ratio of 1 street, 2 street, and 3 street bluffs to value bets in your range on the flop.

Yes of course. This is some of the most fundamental basic theory of the book. It is obvious that we are attempting to making are opponent indifferent to calling or folding, and therefore, our river bluffs are in fact winners. Therefore, they are sort of like value bets on the turn, etc.
By the way, strengthening your range on every street is one of the most fundamental basis of game theory with hold'em poker.
Anyhow, here's a little video of David Sklansky who briefly touches upon the subject (M.J. gets a lot more technical):
https://www.youtube.com/watch?v=ADm93eLppNQ
Start watching a few seconds before 40 minutes.