I have seen a few different frequencies and value:bluff ratios being thrown around as optimal.

When it comes to frequencies I've seen that you should defend anywhere from 30-40% of your range.

As far as ratios I've seen 3/5 value and 2/5 bluffs, 2/3 value and 1/3 bluffs, and even 1/2 value and 1/2 bluffs.

Am I missing something, or is the needed defense frequency simply based off the opponents raise sizing?

ex:

Hero opens to 3bb, Villain 3bets to 8bb - Hero must defend 35.48% (I think this is the hardest size to play against...)
Hero opens to 3bb, Villain 3bets to 9bb - Hero must defend 32.84%
Hero opens to 3bb, Villain 3bets to 10bb - Hero must defend 30.56%
Hero opens to 3bb, Villain 3bets to 11bb - Hero must defend 28.57%

I think as a general rule of thumb anywhere from 30-33% is fine since villain will sometimes call and you may actualize some equity with your bluffs or may already have the best hand when 4betting for value... I'd probably lean towards the lower side of that (30%) in games where 3-bets are weighted towards value. Thoughts?

The ratios depend on the sizings, but including 4+bet sizings and stack sizes, as they change the risk reward ratio. Furthermore, note that the defend-numbers are only correct in a GTO sense if you always 4b - if you call his 3b, he has still equity > 0, which makes his bluffs more profitable.

I have been modeling things off the following assumptions.

Open Raise: 3bb
3-Bet: 9bb
4-Bet: 19.8bb
5-Bet: 100bb

Villain never calls a 4-Bet.

In reality this happens quite a bit whether opponent has some middling hand like KQs, AQs, JJ, AJs, or is slowplaying a big hand, in this case against a competent opponent, I am not going to put any more money in unless I have a strong hand in relation to the board, flop a ton of equity, or MAYBE on good board textures against some opponents.

I think defending frequencies instead of certain combos is a better plan for game flow reasons. Defending combos does not seem like it would even out as well over the long run. You could end up being dealt a 4-bet bluff hand and get 3-bet 3 times in a row and have to 4-bet every time... I guess it could happen with the frequency method as well, but at least you have the benefit of your opponent not being able to easily narrow your range or rule out any possibilities. There are also uncertainties regarding the effect of your opponent 3-betting light with blockers which could effect the frequency with which you are able to defend by blocking out part of your defense range. On the other hand you will also be blocking out part of his 3-betting light range when you hold certain cards... but I'm not sure how one would calculate the effects of these ideas.

By defending a frequency you can classify your hand pretty easily as a pure bluff, semi-bluff, or value regardless of if your Villain calls, or 5-bets all in. The only part where it could get nasty is if you have something like K9s and flop a K or even a 9, you have no idea where you're at... but probably leaning more towards a pure bluff than value. Basically a bluff catcher...

You don't need to defend a certain percentage if your opponents aren't 3betting you with any two cards.

There will be lots of players you play against that only 3bet you 3% of the time. In that case you should certainly not be trying to defend 30% of the time against them.

I am aware of this... 4-betting that kind of player with anything less than KK is going to lose money if they 5-bet all-in the entire range (or even if they do it with just QQ+,AK) and against them I'm just going to fold unless we are really deep, think I'll get their stack by hitting a set, or have KK+ myself

Unfortunately the micro stakes aren't what they used to be. Wish I had a chance to play them in the good old days... but I only started playing poker at the beginning of 2012. People are getting in to 3/4/5 bet wars at 25NL at least on the sites available to us here in the US...

there's no easy way to answer this question without a bunch of assumptions.

I'm starting to question the idea of 'you must defend x% in the blinds' or 'you must 4-bet x% of the time vs a 3-bet' to avoid being exploited etc...

It seems that people are just using math to make an educated guess what GTO MIGHT be.

Who is to say that in certain spots, assuming everyone is playing a perfect GTO strategy, that Player A can not exploit Player B (i.e. Player A can put Player B in a -EV spot and Player B can not ever be break even or +EV in this spot)?

All Player B can do is play perfectly to keep Player A's profit in that spot (and his own losses) to a minimum. This would likely be when out of position with hands other than KK+.

Assuming everyone is playing perfectly Player B can later put Player C in the same spot which Player A put Player B in, and will make up the difference he lost to Player A.

So who is to say that just because Player A can profitably steal the blinds or 3-bet you light, means that you need to defend your blinds against a min-raise at least 42.85%, or that you need to defend against a 9bb 3bet 33% of the time.

Maybe GTO strategy says that you only need to defend 15% of your blinds and defend against a 9bb 3bet 25% of the time because defending any more than this amount will actually lose more money in the long run. Then you must make up for this loss by putting other players to the same decisions.

Now I'm not saying people aren't on the right track, I do think they are on to something.

What I am saying is just because math says you need to do something x% of the time or villain can make money doesn't mean we can stop him from making money in that particular spot even if we play perfectly.

Are you saying that you pick certain combos to always bluff with no matter who the villain is in the hand? When do you decide it is the right time to pull the trigger with bluffs? It seems to make sense just would be easier to understand with more examples. Thx

I think you're a bit confused. Let's say that you open in the SB to 5x, now if you make the simple ASSUMPTION that the BB is supposed to have a folding range (ie, he shoudn't be able to defend 72o in this example and that he should fold it), then you MUST defend enough that your opponent cannot profitably 3-bet any two cards otherwise there would never be an incentive for him to fold 72o.

I understand the logic behind the idea that you must defend X% or villain can profitably 3-bet ATC.

What I'm getting at is since nobody actually knows what GTO is, maybe you are only supposed to defend 20% (I'm just making this number up) of the time, so while villain may seem to have what appears to be a 'profitable' 3-bet with ATC against you, it actually may not be profitable since a GTO strategy might say when someone 3-bets you another person is supposed to cold 4-bet with X range which means you do not need to defend as much as we think, and that maybe it's not optimal in the first place for villain to be 3-betting ATC.

Or in the case of defending the blinds who is to say in a GTO strategy villain isn't supposed to be able to min-raise the button with ATC profitably?

I think the strategies we are creating now are good but just because you are going to lose money in a certain spot if you don't defend x% of the time does not necessarily mean you will lose less money by defending that % if everyone else on the table is playing GTO. Jandas theory says you should defend at least 42.85% combined vs a min raise in the blinds - but who is to say that if you defend this % that villain can't now redefend 60% and still profit anyway since he is in position?

Janda, afaik, is saying that blinds need to defend often enough that BTN cannot open profitable ATC. While we are not totally sure, I think most ppl will agree that BTN shouldn't able to do that (against two blinds). Assuming this is correct, it means imo that blinds need to defend even more if BTN has an effective way to 'redefend', which has to be due calling more.

First I just want to make it clear that I am not disagreeing with anything Janda or others have said. I believe there is a lot of merit to his strategy and have purchased his book & asked him questions and also recommend his book.

I'm just trying to keep an open mind and approach the problem from another angle.

What I've seen is that Janda is recommending to defend 42.85% vs a min-raise from the button.

I am suggesting that in this spot the disadvantage of being out of position may mean, assuming the player on the button is playing perfectly, that there is nothing we can do to stop him from being profitable with ATC. He may be able to redefend 60% of the time and use the power of position to make it a profitable play even if you are also playing perfectly with a stronger range out of position.

Assuming that is true the actual optimal percentage of defense in the blinds would be whatever percentage that causes you to lose the least amount of money - which may be more or less defense than the 42.85% suggested by Janda.

Since you are also playing optimally it means you must mimic that players strategy when you are on the button, otherwise you will be deviating from GTO strategy and begin to lose.

Note: I am not saying opening ATC on the BTN is GTO just using it as an example

In reply to EmptyPromises here is a better example to illustrate my point about being 3-bet.

You open 66 UTG for 3bb and MP (who is an aggressive 3-bettor IP) 3-bets you to 9bb.

The math we use today says we should defend against this 3-bet 33.33% of the time - some part value and some part bluffs.

What is missing from this math is that a non-zero percentage of the time CO,BTN,SB,BB are going to wake up with a strong enough hand to cold 4-bet, probably something like AA,KK,QQ,AKs,AKo.

So automatically some part of the non-value part of your defense percentage might actually consist of the other players waking up with a hand or even just running a squeeze play, where as if it had folded around to you 66 may or may not have been a 4-bet bluff.

Here is another crazy idea I've been thinking of. Maybe a truely GTO strategy actually is an adaptive strategy based on your opponents ranges.

Here is an example to illustrate what I mean.

GTO Bot opens UTG with QQ, a hand that is part of his 'value range'. MP Bot 3-bets GTO Bot. MP Bot only 3-bets AA and plays perfectly post-flop.

Since both bots play perfectly post-flop, in the end MP Bot will always gain in this scenario.

The only way for GTO Bot to minimize his losses and maximize his profit in this spot is to fold since MP Bot won't make any mistakes post-flop.

Obviously MP Bots style of play is probably not profitable in the long run due to the blinds, but I don't think it's debatable that if both bots play post-flop perfectly that GTO Bot can't do anything to reduce his losses here and must fold.

If he calls or 4-bets it's going to be massively -EV in the long run.

A little math I thought up to back above post up.

If GTO bot calls the only time he would be +EV post flop is if a Q flops. Even if he flops a combo open ended straight flush draw he will be a slight dog vs a range of exactly AA since AA has a better flush draw 50% of the time.

So that means if you run 100,000,000 trials and GTO Bot flops his set 11.8% of the time he will flop a set 11,800,000 times. If MP bot bet-folds (to a raise or a call) 11.8% of the time and felts his hand the other 88.2% of the time GTO Bot should be more -EV than if he just folds pre, because he needs to get MP bots stack almost every time to be +EV.

This is correct and has been taken into account in most models today and doesn't change the logic of the argument.

This is the ASSUMPTION of the argument. But it probably wouldn't be too hard to prove it, but it's fair to call this into question.


I can't follow this part of your post. Do you mind rewording your argument.

The biggest limitations with Janda's preflop model in my opinion is that his value to bluffing ratios are built around raise or fold action. Whereas, the ratio of value to bluffs should really take into consideration postflop action when your opponent calls your raise... however, this is very difficult to do.

I'm not so sure that it has been taken in to account - but I haven't read the entirety of Janda's book yet - only bits and pieces and may have missed it. (or missed someone else's theory)

Here is the idea I am trying to illustrate in more detail.

Assume the optimal UTG opening range is 22+,ATs+,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,AJo+,KQ o, or 14% (186 combos)

186 * 0.3333333333333333 = 62 combos of defense needed

My point is maybe in a GTO model we actually only need to *personally* defend our value range (QQ+,AKo,AKs 34 combos) and bluff 20 (this number is arbitrary) of the remaining 28 combos because the other 8 times someone else will defend for us.

So in my example we would only personally defend our range UTG:

.333333~ * ((34+20) / 62)) = 29.0% of the time

and the remaining 4.333~% would be taken care of by the other players at the table.

Assuming that idea is true it would mean defending more than 29.0% (again this number is arbitrary) would fall in to the realm of exploitative play.

I'm saying if we try to resteal with the top 42.85% of the deck villain may be able to profitably redefend against our resteal with the top 60% of the deck since he has the value of position. Thus we can't stop him from making money, only minimize our loss.

The optimal resteal percentage for us would be the percentage that causes us to lose as close to zero as possible. That percentage may be lower than 42.85%

Likewise the optimal steal percentage for the player on the button is whatever percentage will make the most money in the long run.

I'm positive that Janda has at least talked about it in his videos.


Sorry, I still don't get what you're saying. I'm a little confused when you say things like "minimize our loss" because from a GTO standpoint, we don't play a hand if it loses money overall and we don't take any action which would be -EV.

And I'm not sure why you're talking in %s of the top of deck.

I see - I have most of them except the newest ones that came out in the past week or two... but have only had a chance to watch a few.

I guess what I'm getting at is that if everyone is playing GTO you should always be losing money in the blinds because you are out of position which puts you at a disadvantage, and you already have money in the pot (.5bb or 1bb).

You can lessen the amount you lose by defending your blinds.

Logically the optimal percentage of defense should be the percentage that makes you lose as close to 0 as possible.

If you defend 42.85% it may be -EV so you could actually be losing some EV by defending too wide (42.85%). Since villain has the value of position he might be able to defend profitably with a slightly wider range than you are trying to re-steal with (i.e. 60%) and retain some of the profits built in to his steal.

You will recoup these losses the times you are on the button eventually resulting in an equilibrium where you break even over time.

well you're talking about EV in terms of absolute EV, while most people talk about it in terms of relative EV. When you use relative EV, than folding is always 0 EV. You get the same answers either way, but it makes comparing folding to other choices easier if you use relative EV. If you're going to use absolute EV, than it's just important to remember that in GTO that you always take the action which is the highest EV.

But to be honest I'm still not sure what you're trying to say. But good luck, I think you've got a pretty good grasp.

Thanks for the good luck... lol. Hopefully it doesn't seem like I am trying to argue with you. I'm not.

It's definitely a fact that folding is 0 EV. I think it's also factual that we can defend certain hands from the blinds in a +EV way (some very +EV)

I am questioning the idea that just because villain can open for example, 100% of hands profitably if we don't defend 42.85%, means that the most +EV thing for us to do is to defend 42.85%.

The weakest hands we use in that range may still be -EV to play against the majority of his 100% range (i.e. 60%) simply because he has position on us. He has the final say on when large amounts of money goes in to the pot and better maneuverability post flop.

Say over 600 hands of 6-max we always fold. That means we will be in the BB 100 times and SB 100 times - so we will lose 150bb by always folding since we must pay the SB & BB.

The point at which that 150bb loss is as close to 0bb as possible should be the optimal percentage of defense.

That point of defense could be 15%, 20%, 30%, 42.85% or even higher (though I doubt it could be much higher than 42.85% given you are OOP)

Here is a chart kind of showing what I mean. Obviously if the defense %'s in the chart were correct then option 3 would be the optimal defense %. While every defense has lessened our absolute loss compared to folding we might be able to do better by defending less - but we don't want to defend too little either.

If you think you can profitably open 100% of hands on the button against GTO opponents in the blinds than more power to you. But you're effectively posting blinds -- albeit ones you can change the size of.

After thinking for a while, I'm pretty sure I see why I confused you. I was thinking of the SB/BB as one position using a 42.85% range OOP against a 60% range IP. In actuality since the ranges are separate, the blinds range would crush the buttons weaker range even OOP - making opening 100% very unprofitable. So by all means if an opponent is min-opening 100% then defend the combined 42.85%.

On to what I believe I was actually trying to illustrate (but was doing so in a very flawed way)

Just because villain min-opens the button it doesn't logically follow that optimal blind play is to defend a combined 42.85% since villain could be min opening the button with a range of 10%, 20%, 30%, 40% etc.

If you defend that wide against a 10% range OOP you will get crushed. If you defend that wide against a 20% range, you will get crushed. If you defend that wide against a 30% range you won't get crushed quite as badly. I think the real debate probably starts around 40%.

Suppose the button is opening 40% and re-defends against your steal using the exact range you're using to re-steal. He only has to fold 40% of his steals - and when he defends he now has position on you with an equally strong range.

I really think the above and especially the example I made in post 13 & 14 really illustrates why true GTO play may actually involve making correct adaptations based on your opponents strategy - in a way that does not open you to being exploited by the other players left to act after you

Just a side note that heads-up strongest players and LHE GTO approx bots open typically (imo) 70 - 100 % of their BTN but often minbetting. So even HU it seems that BTN doesn't necessarily be able to open ATC.

But as you said here the main thing is that the blinds have a combined defending range. That's why it is imo very likely that BTN cannot open ATC. And if blinds are defending by calling they need to defend wider than pot odds are dictating.

GTO play doesn't change it's strategy to different players ... It's fixed based on maximizing the EV against other GTO players.

The max EV against another GTO player is 0, correct?

A question I'm trying to find the answer to now...

What would happen if you had a 6 max table of 5 GTO Bots and 1 Bot which will only play AA - trying to get it in pre-flop regardless of action in front. If it goes postflop it plays the same perfect GTO game as the other Bots.

Regardless of what action the other 5 Bots take against this 1 Bot when he tries to play his hand - it will always be -EV if in this particular spot since postflop is played perfectly by all parties.

Will stealing his blinds the times he doesn't have AA make enough profit for the GTO Bots to overcome the times the GTO Bots play back at him using their default preflop strategy?

What about if he played a 4.1% range of QQ+,AQs+,KQs,AQo+ using an otherwise perfect GTO pre and post flop strategy?