Hi,

I am currently studying Turn value:bluff ratio in betting range (whether we are talking about 2barrel spots, donk spots, delayed cbets, or whatever...).

There's this common thought that on turn, the value:bluff ratio should be 1:1 for a pot sized bet. I wanted to check examples and go into more details.

I set up a few spots 100b with Pio (most of them with 6max ranges BTN steal vs BB defense).

For example this board : 9d8d2c flop check-bet-call, then see the 2barrel frequency depending on turn cards.

I found very different results from one spot to another. But I could not find any general rule that would make sense.

I was expecting I could find some general guidelines like :
- bluff more when the Turn card gives you a range advantage (in terms of Hero's range EV vs Villain's range EV)
- bluff more when the proportion of TPWK+ in your range > the proportion of TPWK+ in Villain's range


Have you got any idea of what the general rule of thumbs is to estimate the value:bluff ratio on Turn?
Any idea of which metrics really matters (EV range vs range? proportion of strong made hands in both ranges?) ?

Thanks

It's because there isn't one. When Matt Janda wrote his first book, in which he postulated (and accidentally popularized) the idea that value:bluff ratios would go from 1:2 to 1:1 to 2:1 (flop to river), the theory seemed to have merit, but he was writing before solvers were available.
Unfortunately, a frequency-based approach isn't massively useful when trying to build post-flop strategies. As you've found with Pio, range advantage can vary greatly from street to street, and that advantage is one of the factors that alters how much bluffing you can/should do.

So basically, you think the stronger our range advantage, the more bluffs we can bet, right?

If so, how can I estimate the range advantage?

I think the definition of "range advantage" would lead us to calculate Hero's range EV vs Villain's range EV ; but this is impossible to estimate with only my human brain while playing.

the proportion of TPWK+ in our range vs the proportion of TPWK+ in Villain's range is easier to estimate. But is it relevant to evaluate the range advantage?
Maybe the proportion of TPTK+ would be better?

While doing simulations, I was looking for a metric that would be correlated to the value:bluff ratio, but so far I couldn't find one.

The more equity the average hand in our betting range has vs opponents calling range, the more often in % we should be bluffing.
Also, when using bigger sizings, we should be bluffing more.

once again, this is pretty hard to estimate.

comparing the proportion of strong made hands in both range is not accurate? I obviously understand that it's a slightly different idea, but I am looking for a method I could put actually use while playing.

Maybe if some of your bluffs have equity and will in reality be value hands on river it changes the frequency. Are the variations from Pio that drastic ?

For example if you only bluff flush draws and value hands, on a flush river you have no bluff anymore.

I never saw what pio says but i would guess you have to be balanced somewhere around 1-1

For example this board : 9d8d2c , 100bb, 6max ranges BTN steal (Hero) vs BB defense
Flop goes check-bet-call.

On such a flop, given the BB and BTN preflop ranges, here is what I found about BB and BTN flop ranges :
BTN part of the range >= TPWK (after flop cards are dealt) : 22%
BTN part of the range >= TPTK (after flop cards are dealt) : 11%

BB part of the range >= TPWK (after flop cards are dealt) : 12%
BB part of the range >= TPTK (after flop cards are dealt) : 2%

After BB check-calls, BB part part of the range >= TPWK (after flop cards are dealt) : 19%
After BB check-calls, BB part part of the range >= TPTK (after flop cards are dealt) : 12%


Depending on the Turn card, the proportion of strong hands change for BB and BTN :

Part of the range >=TPWK :

Turn card
/Hero's strong part of the range (after Turn card is dealt)
/Villain's strong part of the range (after Turn card is dealt)
/Hero's range advantage (after Turn card is dealt)

7c 33% 29% 1,2
Qc 23% 28% 0,8
Ac 23% 30% 0,8
Kc 16% 17% 1,0
2c 25% 20% 1,2
3c 24% 21% 1,2
5c 24% 21% 1,2
5d 34% 31% 1,1

And if we only consider the part of the range >=TPTK :

Turn card
/Hero's strong part of the range (after Turn card is dealt)
/Villain's strong part of the range (after Turn card is dealt)
/Hero's range advantage (after Turn card is dealt)

7c 17% 21% 0,8
Qc 15% 16% 0,9
Ac 10% 15% 0,6
Kc 8% 11% 0,7
2c 8% 13% 0,6
3c 7% 14% 0,5
5c 10% 15% 0,7
5d 17% 24% 0,7


In the above numbers, the last column shows the ratio between the proportion of strong hands in Hero's range vs the proportion of strong hands in Villain's range.

I was considering this as an estimate of range advantage.


Here is what I found with Pio about turn spots :

Turn card
/bluff combos
/value combos
/B/V ratio

7c 75 70 1,07
Qc 91 80 1,14
Ac 118 96 1,23
Kc 151 100 1,51
2c 78 64 1,22
3c 81 78 1,04
5c 78 78 1,00
5d 75 61 1,23


So if we compare the criteria of range advantage I estimated and the bluff:value ratio from Pio :

Turn card
/Hero's range advantage TPWK+
/Hero's range advantage TPTP+
/B/V ratio from Pio strategy

7c 1,2 0,8 1,07
Qc 0,8 0,9 1,14
Ac 0,8 0,6 1,23
Kc 1,0 0,7 1,51
2c 1,2 0,6 1,22
3c 1,2 0,5 1,04
5c 1,2 0,7 1,00
5d 1,1 0,7 1,23


Conclusion :

even if these are only 8 examples taken from one same flop, these examples show no correlation between the range advantage criteria I estimated and the bluff : value ratio calculated by Piosolver. Of course the sample is not large enough to calculate a correlation, but I expected to find some convergence.

Looking for ideas...

I don't understand all these numbers.

But I think range advantage or disadvantage, if you bet you have value range & bluff range.

range advantage will change frequency of the bet. Not the frequency or ratio of the bluff inside the frequency of the bet. The number of bluffs is more related to sizing and equity of those bluffs.

It's not forbidden to bet because range is disadvantage. but if bc your range is at a disadvantage you just don't bluff, you become exploitable when you bet.

I understand you don't say you don't bluff. But if you bluff less, you are just closer to that point; so 'not as' exploitable as if you would not bluff at all. Because zero is just a number. So bluffing less is just a number closer to that number. if you bluff more, same thing.

I think it's just sizing and equity.

I haven’t examined value:bluff ratios in years. I think that the flowchart for bluffing looks like this:

Do I have value hands that I would bet here?

If yes: is bluffing more profitable than checking or calling??

If yes: if I bluff this combo at high frequency then am I bluff heavy?

If yes: if I bluff this combo at medium frequency then am I bluff heavy???

If yes: if I bluff this combo at low frequency then am I bluff heavy?

If yes: I don’t bluff.

If no, I bluff.

Then I guess you still think about which combos you would bluffs so you have an idea of your range. Anyways if you think you are too bluff heavy it means you know what you bluff.

I find it difficult in game to practically keep track of the frequencies. I know pio often recommend a low frequency bluff per combos of many combos. But I read it's difficult for humans to evaluate properly frequencies and statistics in real life.

Right, having done extensive research into my own value:bluff combos was quite valuable to my progression.

It is difficult to randomize actions at the table, but it's not all that difficult to realize that some players never have low equity bluffs in certain spots.

thanks guys for your replies.

Do you think the position IP/OOP impacts the bluff:value ratio?
I would say that IP you can bluff more than OOP because it'll be easier to make profit from your bluffs on River IP.

I think it affects the betting frequency. With equal equity IP can bet a bit more bc more ev IP.

My idea for ratio is still same. But dont forget value or bluff on turn is kind of a fiction for us human to put name on things. But bluffs and value are not 0 or 100 equity on turn. Thats why the 1-1 ratio is a rule of thumb. and it s for the 1psb anyways but there are equivalent ratio for different sizings.

Yes, it's hard to estimate, but I think getting your bluffing frequencies correct can come from a mixture of study and experience, and doesn't specifically require numerating combos of arbitrary hand strengths (like "X combos of TPGK+"), mathematical formulas or ratios.
I've done almost no math for this kind of thing, but I've developed a "feel" for how often I should be bluffing. Primarily this "feeling" comes from seeing spots where I just kind of know that villain will be folding a lot. If my spider-senses tell me "This is a spot where villain can't continue very often", then I'll bluff a lot more. Sometimes the turn or river will bring a card that you just "know" is terrible for villain's range, and that should automatically cause you to increase your bluffs.
I don't use Pio (Snowie is my coach), but if you can go back and look at the turn cards you mentioned in Pio, does it tell you villain's folding frequency if you bet each of those cards? If you have lots of fold equity, that's a good indication you can bluff more.

I was under the impression the opposite is true - out of position players should be more inclined to bet than in position players with similar hand strength to protect their equity from proper bluffing.

In position players have the advantage they can end the betting and just realize their equity.

To summarize what others are saying you should move away from considering hands as value or bluff and move towards the idea of how do I make the highest EV play with my hand.

The frequency with which you bet will be determined by how favorable the board is for your range relative to villain's range. Typically that means where the very high equity combinations are distributed and how many their are.

It's also important to consider where future nut combinations are more likely to be distributed, as it should effect how much money you may want to put in now and how effective your betting will be on future streets for both value and bluff.

In terms of the ratio that should solely be affected by the size of your bet. The larger the bet the more polarized (i.e. very strong hands and good bluffing candidates with little or no showdown value) your range should be.

Also don't forget how blockers affect the types of hands you want to bluff with. The more you block villain's calling range or do not block villain's folding range the more likely your bluff is to succeed.

I think what you say is true too but I think it applies more to river situations.

For example flop favour a lot of checking from OOP, and more betting from IP. Because IP has more EV in the hand, OOP wants the pot small on flop, so check most or all of his range.

I would guess this effect is less important on turn but still present, while on the river maybe you are right. I would have to think about it. I was more thinking about flop & turn when I said this.

I don't know if with equal equity, OOP has to bet more than IP on river. Because he also does not end the round of betting and still has a check-raise possible. But I think it makes sense.

yes I just revised the Matt Janda book and I interpret what he says as betting river more OOP than IP with equal equity. Checks have more value IP than OOP on river.

Ah yes I see what you meant now on he previous streets. That definitely makes more sense especially with money behind.

I think comparing in position spots and out of position spots isn't useful. This is because no two spots are the same as far as ranges and tendencies go.

I agree. Consider when you're in the BB and are considering a donkbet. You can't fire with much total air, because the player in position will often float. Although you can obviously balance your value-donks with bluffs (although there is no specific ratio for this balance), your bluffs usually need some actual equity. You don't want to bloat the pot with weak hands OOP, when you're unlikely to actually win.
When you're in position (and you usually have the range advantage, because you were the PFR and/or villain has checked to you, indicating his range is somewhat weaker), there is more scope for making low equity bets ("bluffs"), because it's so much harder for the OOP player to continue (e.g. by floating OOP), and the player IP can realize his EV much easier.

Take for example a CO open and BTN call, with the flop coming T86r. This is a pretty good flop for the BTN, because CO has many more combos of Ace high, king high, queen high etc.
This would likely mean that CO can't c-bet at a high frequency (he's going to get floated or raised a lot), but when he checks, the BTN can bluff with many hands that the CO couldn't turn a profit with. e.g. It's probably a mistake for the CO to c-bet with KJs (with no BDFD) or any combo of AQ, but when he checks, it's probably +EV for BTN to bet both those hands as bluffs.

The range advantage accounts for modifications/adjustments in the way Minimum Defense frequency is applied by the solvers. I havent looked much in NLHE bluffing spots with solvers but it should be following the same trend as MDF. How exactly its working is not apparent to me. There might be a hidden weighting factor into it as well to account for not perfectly polarised ranges (i.e. that has to do with the nuttiness/equity of each card combo in our range or something similar).
But is should be looking something like this:
I.e on a river spot if IP range is WAY stronger than OOP then IP will defend close to a value of MDF' (MDF for the most part will be > MDF' but there can be also cases where MDF'>MDF).
It is based on this MDF' that IPs ratio of Value/Bluffs will be approximately created or at least in principle they should.
Position (shouldnt have much weight)/opponents range and the number and type of possible total actions for both players in the current betting round can also affect the results.

So if you want to make an extensive testing on it i ld start with a very simplistic polarised river spot see if there can be any astute/definitive correlation of the above observations. And then see how this can translate into earlier streets.