I've read, that if you have a range advantage on a board, you should have a 2 to 1 bluff to value ratio. Meaning, that for every value hand in your range, it can be supported by 2 bluffs.

If you have 70 value hands on a King high dry board, than you should have 140 bluffing hands < OTF.

That should go to a 1 to 1 ratio on turns. Then to a 1 to 2 on rivers.

My question is, if that is for betting HALF pot - What should your bluff to value ratio be when you decide to bet FULL pot?

When should we be potting also?

I think I've come to the conlusion that villains make MORE mistakes vs FULL pot bets because they aren't used to seeing them. More mistakes = way more money with more money in the pot.

Someone please help...thank you.

Replying to subscribe. I'm working on developing a better understanding of range construction and value/bluff ratios, but I'm not really qualified to answer.

In general I try to think more in terms of equity and showdown value than straight value/bluff ratios. And in general I bet smaller when I'm going for value with a merged range that includes a lot of thinner value hands/ is more heavily weighted toward value. I bet bigger in spots where I'm more polarized between strong value hands and bluffs.

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To actually do the math for this you have to make assumptions like "its a nut/air situation" and "neither player can improve their hand". The bet size is also usually fixed. Off the top of my head the above ratios are NOT correct for a half-pot betting size.

The solution also gives you what sizes you should be using, and for a simplified game it should all be the same size. If we're changing the bet size as part of the game rules, then your bluffing ratio increases as bet size goes up.

This idea doesn't really have anything to do with solving games and I disagree anyway. Lots of time potting will scare a villain into thinking a bit about their hand, while small and medium sized bets just get routine non-thinking calls. Your "proper bluff ratio" in the exploitative sense will just be very small since you're simply taking advantage of the fact that your opponents (typically loose-passives) call too often.

Bet	Bluff %
1/4 P	17
1/3 P	20
1/2 P	25
2/3 P	29
3/4 P	30
1 P	33
1.5 P	38
2 P	40

If you're betting this than you are playing balanced right? In most situations it's better to have a different bluff % to exploit your opponent.

Repost from something I wrote in a different forum:

You should read "Applications of No Limit Holdem" by Matthew Janda for a very an in-depth answer to your question along with basically everything else you need to know about Game Theory Optimal poker.

The bluff-to-value ratio will be dependent on your bet sizing. Here is a "simple" case. Let's assume you will be making pot sized bets on the flop, turn, and river. Therefore, you are offering your opponent 2:1 odds on every street. If you can get to the river and bet with 66% value hands and 33% bluffs, then you don't care if your opponent calls or folds because you have effectively "won" the hand or broke even against an optimal player.

Let's assume you see a flop and 20% of your range is composed of "value hands" which have 100% equity (meaning they can never lose) and 80% of your range is composed of bluffs which we'll assume has 0% equity.

The easiest way to do the math is to work backwards. To maintain the 2:1 value:bluff ratio, on the river you will bet those 20% "value" hands and will need 10% "bluffs" to keep your opponent indifferent to calling. You are effectively betting 30% of your hands on the river.

On the turn: As we just stated, if you can bet a balanced range on the river with 30% of your range, you have effectively won the hand. On the turn you will be betting the 30% of the hands that you will barrel the river with plus you will also add 15% of "turn bluffs" which will have to give up on the river. 30% + 15% = 45% turn bets. notice that 30:15 = 2:1

On the flop: You know that by the turn will bet 45% of your range (which include 15% turn bluffs, and 10% river bluffs, and 20% river value hands). You need to balance this range by adding 22.5% flop bluffs, 22.5 + 45 = 67.5%. Note that 45:22.5 = 2:1.

Recap: Assuming you only make pot sized bets and you see a flop where 20% of your range is "value hands," you will bet 67.5% of the time on the flop, 45% of the time on the turn, and 30% of the time on the river. Your range will be comprised of 22.5% flop bluffs, 15% turn bluffs, 10% river bluffs, and 20% value hands.

We can confirm the findings above with the following calculations --> (2/3)^3 = 8/27 = ~30% of our flop bets need to be for value and (19/27) = ~70% of our flop bets will be as a bluff. In the example above, we will bet the flop 67.5% of the time and 20% of the time we will have value hands --> 20/67.5% = ~30%.

Nah - Agree to disagree here.


You wind up making more money by inflating pots with opponents who fold to much in a lot of spots - and call down too lightly in others.

Hero HJ = AdQs Opens to 3x BB
Villain Sb = 8h8d Flats

Flop = Qh 5c 7d Pot = 7$

Villain checks, Hero bets 6.5$
Villain folds.

I'd routinely run into spots to where my TPTK would not get much value. I used to think, that In order to get value a lot of the times, I would have to xb Flop - to then induce a guy trying to actualize equity/or stabbing turns with air. But that way has so many flaws. I've found that the fundamental problem is that my bluffing frequency is too low on the flop to give villain incentive to call with hands like these.

I've noticed, that after they notice that you will stab flop with missed ace Highs at a certain frequency, along with a certain frequency of low pps with no sdv - they will call big bets on the flop / allowing you to get value the times you DO have TPTK. You would also be able to bet hands like JJ on a Q57dry board for thin value. I've come to the realization, that bluffing at the right frequency increases my ability to get 3 streets of value with tptk....as well as 2 streets of value with thin value hands at times.

Long story short, in the long run, wouldn't you make way more money, betting more with bluffs and value hands, to give villain the incentive to call light and make more mistakes? I just don't see how you wouldn't/

Man, this is good stuff to study on. My main question is.....how would structuring my range in this way be beneficial to me?

This type of analysis has been beneficial to me and the 25NL cash games I play by looking into my hand database, finding hands where I triple-barreled and then categorizing my hands into Value (which triple barrel), Flop Bluffs, Turn Bluffs, and River Bluffs. Then I do the same analysis for different runouts.

Doing this analysis would probably help you solve your previous question, "I've found that the fundamental problem is that my bluffing frequency is too low on the flop to give villain incentive to call with hands like these." Categorizing your range should give you confidance that you are bluffing/value betting in correct proportions against a "standard/unknown reg."

It's an excellent book, but the ratio-based approach has precious little to do with GTO poker. 100bb deep cashgame poker is not a toy game. Hand values (and relative range strengths) can change completely on the turn or river, so dividing hands into 'value hands' and 'bluffs' on the flop, and then sticking with arbitrary frequencies for the next two streets is absurd.

I agree. Here are my thoughts on bluffing frequency in a nutshell:

Generally speaking, the wider my opponent's range is, the more I'll bluff. The tighter my opponent's range is, the less I'll bluff. Of course there are exceptions to these rules, but those exceptions involve having good confirmed reads.

Can someone help me out and explain why we need our opponent to be indifferent, rather than looking from out own point of view?

From Hero's perspective, if the pot is 100$ on the river and he has 66% bluffs and 33% value (guaranteed to win), wouldn't he break even on this bet if he gets called 100% of the time?

Is the flaw in my thought process that I see the 100$ as dead money, while it is in fact money we have "invested" in previous streets?

I always thought that on flops, if I bet small like 1/3rd, I only need to win 20% of the time for the bet to be +EV. Now I'm getting incredibly confused since it seems like the smaller I bet, the more value I need?

Sorry for being a dumbass, I feel like I'm missing something super obvious.

When you say "30% of your range" do you mean 30% of your flop range? Would your "river c-bet percentage" be higher if we were to look at it in a HUD?

This.

One plays ranges, so the hands changing value on later streets generally makes no difference, when the range is right.

The ratio of value vs bluff is also about gto but the ranges can be looser or tighter.

Plus the board can favor the others range, and some boards favor bluffing or value betting more or less, and one might do better with different sizes.

Additionally, one plays the opponent.

If hero is betting pot, he should have 66.7% value and 33.3% bluffs (you've got it the wrong way around above) to make villain indifferent. When villain is indifferent, hero's EV is "pot", because - when villain calls - hero wins 2x pot two thirds of the time (when hero has value), and loses 1x pot a third of the time (when his bluffs get caught).
(2/3 * 2pot) - (1/3 * 1pot) = pot. If hero's EV is pot, villain's EV is zero, hence him being indifferent.

As posted above, this indifference principle shows up in many game theory analyses. It is essentially a mathematical result which is quite powerful. (You can think of it as a mathematical "trick" if you want.)

If you have two options and you want to find the right mix of them to use to maximize your EV, in a wide variety of game situations it is optimal to employ the mix that makes your opponent indifferent between his options.

If not, you could make more EV by changing the mix (e.g., value betting more or less). This is presented early on in many game theory books.

In the scenario you quoted the poster arbitrarily chose 20% of all hands on the flop as 3 street value hands. That means to have the correct value to bluff ratio on the river, hero would choose 10% of hands as 3 street bluffs.

So it would be 30% of your hands on the flop. Some are 3 street value bets and others are bluffs.

I intuitively disagree with this. I don't have solid facts to back me up but I'll try to explain my intuition.

To start, it would seem like it doesn't matter what hands you intend to bluff if they could be in your range, but card removal actually eliminates the possibility of them being in your range. So even with perfect range construction (whatever that means) there will be times where your range falls apart due to card removal.


My second problem would be that some boards intersect both players ranges so well that hand values become so close it's much more difficult to properly construct the right range for optimal betsizing.

There is a non zero percentage of the time that villain folds, right? This doesn't account for that... and, I think, that drives our overall EV up and really means we should be bluffing even more often.

See the AKQ game. Villain should be folding some of the time vs your strategy and can still force indifference.

The point is that it doesn't matter what villain does. If he always calls our EV is POT in that indifference example. If he always folds our EV is clearly POT. If he plays any mixed strategy our EV is POT. That's what it means to make him indifferent. Our EV is the same no matter what strategy villain uses.

Thanks, I'm over-thinking this.

Why doesn't this theory ever talk about blockers? Pretty often villain's river bluff catchers are selecting based on beneficial blocking effects. For example let's say all of our value hands in a spot contain a card, 'A' and all of our bluffs are independent of the opponent's bluffcatcher range. Villain will prefer to select bluffcatchers which also contain A.

The problem for us if we are betting POT and bet 2 value combos for every 1 bluff combo is that villain doesn't see us betting 2:1 value:bluff when he is holding cards containing A. If we use this ratio villain is not indifferent and we are overbluffing. So it seems in this type of case we need to bluff less to account for blocking effects?

Conversely, if villain's bluffcatchers are independent of our value hands (rare, but it could happen), but many of them block our bluffs, we can bluff more often to achieve indifference?

but do blockers not increase our chance of bluffing successful even more, because we will also use blockers for bluffing, and we are choosing the "time" (a good hand in our range on that board) when to bluff and when not.

for example I would imagine we bluff less frequently on a board with more than 2 spades, without having the Ace of spade in our hand. we actually don't have to because we should have the Ace of spade quite often in every range. thus we don't need to bluff a black broadway board with 87 of diamonds..

also I think in general villain does not really know how our value/bluff ratio looks like.. he can make assumptions but he still has to work it out.

but by putting villain in a situation, making him indifferent from calling or folding he still has to make a decision. and if his call/fold strategy is not balanced we can sooner or later start improving our value/bluff ratio and exploit his river play by making more or less bluffs...