I have seen a few streamers say something along the lines of:

"I don't have any/many bluffs here, so I should only bet small" when they have a nutted hand.

Isn't this sort of backwards logic? Doesn't your value range determine your bet sizing, which determines how many bluffs you should have in a spot? If we are struggling to find bluffs in a certain spot, how does it even matter if the spot doesn't come up that often and we have the nuts when our opponent can't?

When the opponent calls, we are going to show down a nutted hand, so they won't gain any information about our entire strategy.

i agree that choosing size by number of available bluffs is like putting the cart before the horse, so to speak.

also if you don't have many available bluffs on a particular river, that would imply that you exploited somewhere previous in the hand, and thus you should finish the hand under that exploitive plan. to do otherwise would be strategically inconsistent.

also, you could have all the available bluffs possible in your range, but this most definitely would not determine your betsize. i think this extreme shows exactly that the strength of the value range determines betsize and bluffs are added as available up to the saturation point where bet/(pot+bet) = bluffs/total combos.

The idea comes from the equity needed to call by an oponent on the river.

The old theories using toy games showed the bigger the bet the more you're 'allowed' to bluff in situations, because your opponent needs more equity to call bigger bets so you can expand your bluffing region. Conversely then if you don't have enough bluffs it's better to bet smaller to provide your opponent more incentive to call.

I agree people over generalized it to more situations than they should especially within real poker games where some conditions don't hold true from the toy games.

If we flip the problem over, if we had a strong value hand an a board with a lot of missed draws, we want to make a big bet because Villain might think he still has the pot odds to call with a pair. This makes sense to me

the bold is the crux of the matter. without value hands there is no bet. with no bet there is no bet size. thus betsize is dependent on having value hands that maximize profit at that particular betsize.

if my opponent has chosen a turn strategy that leaves his range full breakeven river bluffcatchers, while my river range has all different kinds of hands, then I'm actually in a position to bet a specific, yet different amount with each individual hand combination in my value range. this would maximize my ev with every combo, and i could presumably have bluffs from the bottom of my range to make my opponent have to call with bluffcatchers. Unfortunately for the bettor, the opponent gets to have slowplays in range, as well as draws that improve. slowplays and draws both have the effect of giving our opponent the option to raise, which can turn your river value hand into a bluffcatcher, which comes with liability, in an instant.

The liability of a bluffcatcher comes in two forms:

a) sunk cost of hand strength regression

b) future cost of playing vs players that don't bluff frequently enough to make calling an 0ev bluffcatcher profitable.

even if your opponent bluffs the river too much, you're not actually making profit on the hand as a whole after calling a river raise with a bluffcatcher that would be 0ev in equilibrium. you only slightly profit vs over bluffers unless they absolutely play backwards. but these days almost everyone knows you need value hands to bet.

this is why i consider these factors when choosing betsize on the river:

my hand strength relative to my opponents range and how i should play given these ranges.

how my opponent should play his range

how my opponent will actually play his range.

if the same, how to best extract value from that range

if different, how to exploit that range.

That's the issue though. Smaller bet sizes, from a theory perspective, should have less bluffs overall, since villain is getting such a good price on the call.

Another factor is that if a villain calls a bigger bet at a much lower frequency than he calls a smaller bet, we still make more money with our nutted hands by betting larger. Let's say the river we have an SPR of 2 on the river. These 2 scenarios yield the same amount of EV.

Bet 200% pot: Villain calls 15% of the time

Bet 30% pot: Villain calls 100% of the time

In this scenario, if we think villain calls more than 15% of the time when we jam for 2x pot on the river, we instantly make money over betting 30% pot.

Right but I am not sure what point you're trying to make with your comment.



I agree with this but would add it's slightly more complex as you're trying to maximize EV across all decision points/hands in your range and that ranges can still intersect complicating the whole 'value' and 'bluff' notions.

I hope in my previous post it didn't come across as advocating for that particular strategy. I was just trying to explain the thought process behind it.

I think you might be misunderstanding the statement. They are betting smaller bc given the hands they are going to bet for value on the river they do not have the right amount of bluffs to balance a larger bet size. Taking several different bet sizes from a theoretical standpoint, the larger the bet size the more bluffs they need to balance the range and the smaller the best size the less bluffs they need. This can’t be viewed in a vacuum though as since the larger the bet size the lmire often your opponent has to win and the smaller the bet size the less often he has to win when he continues. Since opponents are continuing less often they will have stronger hands to call large bets with. That means your largest bet sizes should be reserved for your strongest hands but you can have more bluffs. The opposite is true for the smaller size and enables you to value bet thinner since they will be calling lighter.

If you take a board like K55r89 with no flush draw possible it is going to be very hard to reach the river with natural bluffs since no flush or straight on flop and only one backdoor straight possible. If we are OTB in a SRP We can have a few strong hands like KK, 99 K5s that would want to maximize our earnings over betting but how do we balance. We can bet smaller which also enables us to put a few more hands in for thinner value and we don’t have to have as many bluffs.

if you gave me a river range that was less than 33% bluffs and i had a pot sized bet left? i'm shoving 100%.

however I think that finding oneself in this situation is evidence of deviation from equilibrium. if intentional deviation, then stick with the plan.

And this imbalance (you're not bluffing enough) means villain shouldn't call with his bluffcatchers, so your value-hands won't get paid.

To maximize EV, you should generally go small when your range is overly weighted towards value, but you go bigger if a larger proportion of your range is bluffs.

e.g. 2:1 v:b for a pot-sized bet, 60:40 for a 2x pot bet, 75:25 for half pot.

You don't need to have draws to bluff. The only requirement is that they have low showdown value. On k5589 the solver will have plenty of bluffs like JT type hands. Yes it will triple barrel with no chance to imorove if the situation is correct. The drawing chance is only a bonus

Ok this is what happens if you set up some toy games:

-Our range is 90% strong hands and 10% bluffs, pot bet behind on the river and villain only has bluffcatchers. We are IP and he checks.
Here we can shove or bet small and it's the same, our ev is always the entire pot unless we bet some tiny size. We can also check some value because why not.

-same situation, but now villain has some few nutted slowplays.
Here we only shove or check. We shove a balanced range and we check the rest. This maximizes our winnings by forcing villain to 0ev bluffcatch while minimizing the amount of successful traps he can raise/callshove.

-same first situation, but now we are on the turn and villain has plenty of draws.
Here we bet enough to fully deny his pot odds, and we never check. Not sure what happens when his draws all have different equity. I'm guessing we just shove range against most setups

Note that we always want to bet big or are indifferent between small/big. We have no incentive to bet a balanced small size. We can just shove and win the pot that way. Our objective is always to win the pot, we can't force villain to give us more ev than the pot if he's an optimal player and for that reason it doesn't make sense to bet smaller so he can call. Well, except that's wrong.

If we are on the turn, and villain has some draws and some few slowplays, then we are incetivized to bet small. We actually bet enough to fully deny equity from draws with our entire range and that's the only sizing we use.

So yes, before the river, you can definitely find situations where you bet smaller to let villain have a 0ev call. But those situations are rare. You should never be unable to find bluffs on the flop if you bet a balanced range preflop. I guess it might happen in some 1000bb deep 6bet ranges. And just one card, the turn, can't change this fact much. And we showed that we never go smaller on the river.

this is why i was so confident in my last statement.

it's actually quite intuitive if you think about it from the caller's perspective:

a) my opponent makes my bluffcatchers indifferent, so it doesn't really matter what I do. I'm breaking even either way. my opponent's ev is (pot)

b) my opponent is value heavy, so i fold all my bluffcatchers, fold = 0ev = breakeven. my opponent's ev is (pot).

notice that the second situation puts our opponent in the position to make big errors. and that if you find an opponent like this that consistently plays extremely capped river call/fold ranges due to over aggression early in the hand or good old fashioned calling station habits or both, you will do best to bet the highest amount that they will call, but not a penny more. this is not some mathematical trick used to determine this amount. it's a mind game vs such opponents.

Surely it depends on how polarized your range is? "Thin value" hands maximize their EV by betting small and getting called by a wider range of worse hands, not by checking back, because checking back literally misses out on value.

I'm sure you can run Pio/GTO+ to find spots where the solver clearly does bet small on the river at some frequency. And those spots would be where it's not airballing (for the small size) very often, because it expects the small size to get called. Fewer bluffs => smaller betsize. QED.

If you were to set up a situation where you have 80% strong hands, 10% mid strength and 10% bluffs, the solver will just turn those mid strength hands into bluffs. Yes villain will overfold anyways but we showed that's fine. In other words, whenever you don't have enough bluffs, the next weaker hands should become bluffs too. It's possible that you can set up situations where you play to maximize your thin value ev however like 90% thin value and 10% bluffs but there are no hard rules there, it depends on the specific equity and blockers configurations

I’m sure we can contrive situations that would reveal evidence of many different permutations of the value hand/betsize/bluff frequency relationship, as we have already started.

However I still don’t think that there will ever be a shortage of river bluffs, provided that equilibrium has not been corrupted by cooperation.

I found situations where the solver hits a miracle card and improves so much it lacks bluffs. It's veey very rare however. Most players who think are in that situation are just facing fancy play syndrome.

Seems like it’s dependent on low equity turn bets. I’m curious to know at which point you input the ranges and what did the bottom of the range look like?

Ok I found an easier way to explain this. We have 90% strong and 10% bluffs. Villain 100% catchers, pot bet behind on the river. We are indifferent between 3 extreme options, and any combination in between of them, and our ev is always the pot:

1. shove range, villain overfolds, we win the pot
2. bet small enough with our range so that villain can 0ev bluffcatch, our ev is the pot
3. shove a balanced range and check leftover value. Our ev is the pot for both ranges

Now, if we add 1% nuts to villain range, we still play to win the pot against his catchers, but now we want to pick the option that sacrifices the least amount of ev vs his nutted slowplays:

1. We shove range, we always lose our stack vs his traps.
2. bet small enough with our range so that villain can 0ev bluffcatch, we always lose a small bet plus a portion of our stacks vs his raise
3. shove a balanced range and check leftover value. We lose the pot a small fraction of the time

And it turns out that for most(all of them?) stackdepth/equity/blockers configurations that I've tried we lose less ev vs his nutted slowplays with option 3

I think that in equilibrium, the intersection of (bluff hand/check hand) is maintained as ev neutral, and this ev will always be a value greater than or equal to zero, if we have been provided with ranges as a result of equilibrium strategy. the bluffs will be 0ev out of position and slightly above 0ev in position(depending on the way the bottom of the ranges line up exactly). the in position checking range will have a minimum profit that is a value greater than zero, but with the bottom of the checking range I'm not expecting to win very often.

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in other news, it seems as though the option for variable betsizes on the river has been abandoned in favor of a more clear cut conversation. i use many different betsizes on the river depending on the expected calling/raising tendencies vs different sizes:

my range breaks down like this, but this is obviously not to scale. just trying to illustrate the general progression and location of hand selection for different sizes. from top to bottom increasing from 1/2 pot, to 2/3 pot, to 3/4 pot, to pot. i could have done the same illustration for up to 2x pot, but it seemed unnecessary.

^The bluffs shouldn't be seperated into groups like on the picture. All should be spread across all the bet sizes, unless there are blocker reasons.
Also, those value ranges are very capped and exploitable, so it doesn't represent GTO.

I understand what you're saying, though, and agree that it can be a decent strategy in practice vs passive opponents.

the margins are not exactly defined in practice. the variation occurs due to my limited ability to visualize several different ranges, each with its own betsize. so the ranges and betsizes bleed into each other(for lack of better language).

also, i do bet smaller with some stronger hands exactly because the ranges are capped without these strong hands. the plan is to have a range that can showdown vs a raise of any size at the desired frequency that causes the opponent's bluffs to be 0ev. of course this is easier said than done. I left this part of my strategy out of the picture to lay the general idea of where I'm pulling the hands from the different parts of my range.

I believe that in a raise preflop + triple barrel situation, this condition will be met in equilibrium:

the bluff that uses the biggest betsize will also have the most influential blocking properties(expressed as profit increase due to lowered calling frequency for the opponent relative to his intended calling frequency).

while i think the triple barrel situation provides the strength of value range necessary to make overbets a good option with very strong hands, this condition is likely not met in hands that feature checks on the flop and or turn.

flop + turn check = creates river situations where overbetting for value isn't an option imo due to the lack of strong value hands(implied by the flop and turn checks) the exceptions being slowplays and draws that improve, but these don't represent a significant portion of good checking ranges, thus my bets are smaller on the average river when taking this line(usually 3/4 pot, 2/3 pot, 1/2 pot, 1/3 pot). the intersection of (biggest bluff size) and (bluff with most absolute showdown value) doesn't really scratch the point of showdown value where blockers become necessary for bluffing. I don't have many strong hands here, so I won't pretend to have strong hands by bluffing with big bets.

flop check + turn bet + river bet

flop bet + turn check + river bet

I feel these lines need to be discussed simultaneously, although the river situations created are different. however i need more coffee. the general point i want to make is that the former situation should lend itself to larger betsizes than the latter, because of the strength of the range that takes those actions. on an average board, my betsize probably tops out around 1.5 pots with the former line, but when I bet the flop and check the turn, i generally keep it between 1/2 pot and pot.